diff --git a/README.md b/README.md new file mode 100644 index 0000000000000000000000000000000000000000..0cb30b9109155d73ee4eff7302825fdbbc40da7a --- /dev/null +++ b/README.md @@ -0,0 +1,54 @@ +--- +license: cc-by-4.0 +pretty_name: ORBench Decision Problems +task_categories: + - other + - text-generation + - structured-data-extraction +tags: + - operations-research + - model-benchmarking + - structured-generation + - synthetic + - evaluation +language: + - en + - fa +size_categories: + - n<1K +--- + +# ORBench problems and recorded results + +100 synthetic inventory, assignment, and scheduling instances for the ORBench demo. + +Organization dataset and collection are public. Live Gradio and the organization card are created by `scripts/publish.py`. Runnable Space source is stored in `demo/`. Collection: [Aria AI — OR + LLM Evaluation](https://huggingface.co/collections/AriaAICompany/aria-ai-or-llm-evaluation). + +Generated data, seed 25. All identifiers are synthetic. Gold objectives come from OR-Tools CP-SAT on the same schema that ships in each row. LLM rows in `results.jsonl` are explicitly `not_evaluated`. + +## Files + +- data/problems.jsonl +- data/results.jsonl +- data/leaderboard.csv +- data/splits.json +- data/sample_preview.json +- data/protocol.md +- demo/ — runnable Gradio Space source +- showcase/ — organization static card + +## Splits + +- development: 60 instances, templates `D-A` / `D-B` / `D-C` with a `SCHEMA_BEGIN` block +- test: 40 instances, templates `T-A` / `T-B` in prose +- interactive: 20 ids listed in `splits.json` + +Development and test do not share `(family, template_id)` pairs. Near-duplicate prompt templates are therefore not reused across the split. + +## Metrics + +Independent validators recompute inventory balance, pack multiples, budget, capacity, assignment uniqueness/eligibility/capacity, and schedule overlap/precedence/release. Optimality gap is reported only when gold status is `optimal`. An unevaluated method is never written as 0. + +## License + +CC-BY-4.0. Keep the synthetic-data label. diff --git a/data/leaderboard.csv b/data/leaderboard.csv new file mode 100644 index 0000000000000000000000000000000000000000..da5c871df63efc150667ce9f2b5fe5b424d1816c --- /dev/null +++ b/data/leaderboard.csv @@ -0,0 +1,11 @@ +method_id,evaluated,n,parse_rate,feasible_rate,infeasible_agreement,mean_gap,mean_fidelity,mean_seconds,mean_cost_usd,n_optimal +heuristic,True,100,1.0,0.91,0.0,0.031919404673584915,1.0,7.628599880263209e-05,0.0,0 +json-extractor+solver,True,100,1.0,0.92,1.0,2.613101900343095e-18,1.0,0.004290478996699676,0.0,92 +naive-direct,True,100,1.0,0.22,0.0,0.0,1.0,4.173900291789323e-05,0.0,0 +structured-solver,True,100,1.0,0.92,1.0,2.613101900343095e-18,1.0,0.004329786997986957,0.0,92 +template-extractor+solver,True,100,0.6,0.6,0.0,2.033026425636911e-18,0.6,0.0030710569996153935,0.0,60 +Qwen/Qwen3-4B-Instruct-2507,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated +Qwen/Qwen3.8-27B,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated +deepseek-ai/DeepSeek-V4.1-Flash,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated +moonshotai/Kimi-K3,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated +zai-org/GLM-5.3,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated diff --git a/data/problems.jsonl b/data/problems.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..e65cd18f38cfd6d5607922547f2ef5ef7ace10c6 --- /dev/null +++ b/data/problems.jsonl @@ -0,0 +1,100 @@ +{"problem_id":"INV-001","family":"inventory","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":25001,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 192 currency units. Storage holds at most 19 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 192\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=6,4,6 pack=1 cost=9 hold=1 short=8 stock=2\nSKU S2 demand=2,7,2 pack=2 cost=5 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 192, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 4, 6], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 7, 2], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 192 واحد پول و ظرفیت انبار 19 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 192\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=6,4,6 pack=1 cost=9 hold=1 short=8 stock=2\nSKU S2 demand=2,7,2 pack=2 cost=5 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 192, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 4, 6], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 7, 2], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 192,\n \"warehouse_capacity\": 19,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 4,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 8,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 7,\n 2\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":192,"warehouse_capacity":19,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,4,6],"initial_stock":2,"unit_cost":9,"holding_cost":1,"shortage_cost":8,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,7,2],"initial_stock":2,"unit_cost":5,"holding_cost":1,"shortage_cost":7,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":159.0,"gold_bound":159.0,"gold_solution":{"family":"inventory","status":"optimal","objective":159.0,"bound":159.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"c064f38a5aa2b27c","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-002","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":25002,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 111 currency units. Storage holds at most 19 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 111\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,3 pack=3 cost=4 hold=3 short=9 stock=2\nSKU S2 demand=7,4,3 pack=2 cost=4 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 111, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 3], \"initial_stock\": 2, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 111 واحد پول و ظرفیت انبار 19 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 111\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,3 pack=3 cost=4 hold=3 short=9 stock=2\nSKU S2 demand=7,4,3 pack=2 cost=4 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 111, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 3], \"initial_stock\": 2, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 111,\n \"warehouse_capacity\": 19,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 4,\n 3\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 4,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 7,\n 4,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 4,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":111,"warehouse_capacity":19,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,4,3],"initial_stock":2,"unit_cost":4,"holding_cost":3,"shortage_cost":9,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[7,4,3],"initial_stock":3,"unit_cost":4,"holding_cost":3,"shortage_cost":8,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":93.0,"gold_bound":93.0,"gold_solution":{"family":"inventory","status":"optimal","objective":93.0,"bound":93.0,"orders":[{"sku_id":"S1","period":1,"qty":3},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":4},{"sku_id":"S2","period":2,"qty":4},{"sku_id":"S2","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"5c4c80b9b28d8fdd","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-003","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"en","template_id":"D-C","seed":25003,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 311 currency units. Storage holds at most 31 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 311\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=2,6,6 pack=1 cost=8 hold=3 short=14 stock=2\nSKU S2 demand=8,3,3 pack=1 cost=9 hold=3 short=12 stock=3\nSKU S3 demand=7,8,6 pack=2 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 311, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 6, 6], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 3, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 6], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 311 واحد پول و ظرفیت انبار 31 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 311\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=2,6,6 pack=1 cost=8 hold=3 short=14 stock=2\nSKU S2 demand=8,3,3 pack=1 cost=9 hold=3 short=12 stock=3\nSKU S3 demand=7,8,6 pack=2 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 311, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 6, 6], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 3, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 6], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 311,\n \"warehouse_capacity\": 31,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 6,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 3,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 8,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":311,"warehouse_capacity":31,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,6,6],"initial_stock":2,"unit_cost":8,"holding_cost":3,"shortage_cost":14,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,3,3],"initial_stock":3,"unit_cost":9,"holding_cost":3,"shortage_cost":12,"pack_size":1,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,8,6],"initial_stock":2,"unit_cost":5,"holding_cost":3,"shortage_cost":11,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":296.0,"gold_bound":296.0,"gold_solution":{"family":"inventory","status":"optimal","objective":296.0,"bound":296.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":5},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3},{"sku_id":"S3","period":1,"qty":4},{"sku_id":"S3","period":2,"qty":8},{"sku_id":"S3","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"b8ded0d56a7c873c","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-004","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":25004,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 208 currency units. Storage holds at most 21 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 208\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=3,3,6 pack=3 cost=5 hold=2 short=13 stock=0\nSKU S2 demand=2,5,7 pack=1 cost=9 hold=3 short=14 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 208, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 3, 6], \"initial_stock\": 0, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 5, 7], \"initial_stock\": 0, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 208 واحد پول و ظرفیت انبار 21 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 208\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=3,3,6 pack=3 cost=5 hold=2 short=13 stock=0\nSKU S2 demand=2,5,7 pack=1 cost=9 hold=3 short=14 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 208, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 3, 6], \"initial_stock\": 0, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 5, 7], \"initial_stock\": 0, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 208,\n \"warehouse_capacity\": 21,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 3,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 5,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 5,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":208,"warehouse_capacity":21,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,3,6],"initial_stock":0,"unit_cost":5,"holding_cost":2,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,5,7],"initial_stock":0,"unit_cost":9,"holding_cost":3,"shortage_cost":14,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":186.0,"gold_bound":186.0,"gold_solution":{"family":"inventory","status":"optimal","objective":186.0,"bound":186.0,"orders":[{"sku_id":"S1","period":1,"qty":3},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":2},{"sku_id":"S2","period":2,"qty":5},{"sku_id":"S2","period":3,"qty":7}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"224e408bade9beae","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-005","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":25005,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 224 currency units. Storage holds at most 28 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 224\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=6,5,8 pack=3 cost=6 hold=3 short=13 stock=2\nSKU S2 demand=6,7,6 pack=3 cost=6 hold=2 short=6 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 224, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 5, 8], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 7, 6], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 224 واحد پول و ظرفیت انبار 28 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 224\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=6,5,8 pack=3 cost=6 hold=3 short=13 stock=2\nSKU S2 demand=6,7,6 pack=3 cost=6 hold=2 short=6 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 224, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 5, 8], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 7, 6], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 224,\n \"warehouse_capacity\": 28,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 5,\n 8\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 7,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":224,"warehouse_capacity":28,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,5,8],"initial_stock":2,"unit_cost":6,"holding_cost":3,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,7,6],"initial_stock":3,"unit_cost":6,"holding_cost":2,"shortage_cost":6,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":232.99999999999997,"gold_bound":232.99999999999997,"gold_solution":{"family":"inventory","status":"optimal","objective":232.99999999999997,"bound":232.99999999999997,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":9},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":9},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"df2f98c85b303667","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-006","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":25006,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 336 currency units. Storage holds at most 37 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 336\nCAPACITY: 37\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,2 pack=2 cost=9 hold=3 short=7 stock=1\nSKU S2 demand=6,4,8 pack=3 cost=6 hold=2 short=9 stock=1\nSKU S3 demand=5,3,4 pack=3 cost=6 hold=2 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 336, \"warehouse_capacity\": 37, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 4, 8], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [5, 3, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 336 واحد پول و ظرفیت انبار 37 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 336\nCAPACITY: 37\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,2 pack=2 cost=9 hold=3 short=7 stock=1\nSKU S2 demand=6,4,8 pack=3 cost=6 hold=2 short=9 stock=1\nSKU S3 demand=5,3,4 pack=3 cost=6 hold=2 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 336, \"warehouse_capacity\": 37, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 4, 8], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [5, 3, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 336,\n \"warehouse_capacity\": 37,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 8,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 4,\n 8\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 9,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 5,\n 3,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 11,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":336,"warehouse_capacity":37,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,8,2],"initial_stock":1,"unit_cost":9,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,4,8],"initial_stock":1,"unit_cost":6,"holding_cost":2,"shortage_cost":9,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[5,3,4],"initial_stock":2,"unit_cost":6,"holding_cost":2,"shortage_cost":11,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":280.0,"gold_bound":280.0,"gold_solution":{"family":"inventory","status":"optimal","objective":280.0,"bound":280.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":3},{"sku_id":"S3","period":2,"qty":3},{"sku_id":"S3","period":3,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"37b860c2e403d2c5","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-007","family":"inventory","split":"development","interactive":false,"difficulty":"hard","language":"en","template_id":"D-A","seed":25007,"prompt_en":"A B2B warehouse plans 4 weeks for 4 SKUs: S1 (bearing), S2 (seal), S3 (gasket), S4 (filter). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 596 currency units. Storage holds at most 56 units in total. Minimize purchase + holding + shortage.\nPERIODS: 4\nBUDGET: 596\nCAPACITY: 56\nCOVER_REQUIRED: 1\nSKU S1 demand=5,4,8,4 pack=1 cost=8 hold=2 short=6 stock=0\nSKU S2 demand=4,7,6,5 pack=1 cost=8 hold=3 short=7 stock=3\nSKU S3 demand=8,4,2,5 pack=3 cost=9 hold=1 short=11 stock=3\nSKU S4 demand=2,5,5,4 pack=1 cost=6 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 596, \"warehouse_capacity\": 56, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8, 4], \"initial_stock\": 0, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 7, 6, 5], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [8, 4, 2, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [2, 5, 5, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 4 هفته و 4 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 596 واحد پول و ظرفیت انبار 56 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 4\nBUDGET: 596\nCAPACITY: 56\nCOVER_REQUIRED: 1\nSKU S1 demand=5,4,8,4 pack=1 cost=8 hold=2 short=6 stock=0\nSKU S2 demand=4,7,6,5 pack=1 cost=8 hold=3 short=7 stock=3\nSKU S3 demand=8,4,2,5 pack=3 cost=9 hold=1 short=11 stock=3\nSKU S4 demand=2,5,5,4 pack=1 cost=6 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 596, \"warehouse_capacity\": 56, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8, 4], \"initial_stock\": 0, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 7, 6, 5], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [8, 4, 2, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [2, 5, 5, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 4,\n \"budget\": 596,\n \"warehouse_capacity\": 56,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 4,\n 8,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 7,\n 6,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 8,\n 4,\n 2,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 11,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 2,\n 5,\n 5,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":596,"warehouse_capacity":56,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,4,8,4],"initial_stock":0,"unit_cost":8,"holding_cost":2,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,7,6,5],"initial_stock":3,"unit_cost":8,"holding_cost":3,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[8,4,2,5],"initial_stock":3,"unit_cost":9,"holding_cost":1,"shortage_cost":11,"pack_size":3,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[2,5,5,4],"initial_stock":2,"unit_cost":6,"holding_cost":2,"shortage_cost":12,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":570.0,"gold_bound":570.0,"gold_solution":{"family":"inventory","status":"optimal","objective":570.0,"bound":570.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":8},{"sku_id":"S1","period":4,"qty":4},{"sku_id":"S2","period":1,"qty":1},{"sku_id":"S2","period":2,"qty":7},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S2","period":4,"qty":5},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":3},{"sku_id":"S3","period":3,"qty":3},{"sku_id":"S3","period":4,"qty":6},{"sku_id":"S4","period":1,"qty":0},{"sku_id":"S4","period":2,"qty":5},{"sku_id":"S4","period":3,"qty":5},{"sku_id":"S4","period":4,"qty":4}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"3e101f0e29677e33","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-008","family":"inventory","split":"development","interactive":true,"difficulty":"easy","language":"fa","template_id":"D-B","seed":25008,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 175 currency units. Storage holds at most 24 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 175\nCAPACITY: 24\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,4 pack=1 cost=8 hold=3 short=12 stock=1\nSKU S2 demand=2,4,3 pack=2 cost=4 hold=3 short=7 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 175, \"warehouse_capacity\": 24, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 4], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 175 واحد پول و ظرفیت انبار 24 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 175\nCAPACITY: 24\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,4 pack=1 cost=8 hold=3 short=12 stock=1\nSKU S2 demand=2,4,3 pack=2 cost=4 hold=3 short=7 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 175, \"warehouse_capacity\": 24, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 4], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 175,\n \"warehouse_capacity\": 24,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 8,\n 4\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 4,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 4,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":175,"warehouse_capacity":24,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,8,4],"initial_stock":1,"unit_cost":8,"holding_cost":3,"shortage_cost":12,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,4,3],"initial_stock":3,"unit_cost":4,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":166.0,"gold_bound":166.0,"gold_solution":{"family":"inventory","status":"optimal","objective":166.0,"bound":166.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":8},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":4},{"sku_id":"S2","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f2dfa9f008318786","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-009","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"en","template_id":"D-C","seed":25009,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 287 currency units. Storage holds at most 42 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 287\nCAPACITY: 42\nCOVER_REQUIRED: 0\nSKU S1 demand=8,4,4 pack=2 cost=3 hold=2 short=10 stock=0\nSKU S2 demand=5,8,6 pack=3 cost=6 hold=1 short=12 stock=0\nSKU S3 demand=7,8,7 pack=3 cost=4 hold=1 short=13 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 287, \"warehouse_capacity\": 42, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 4], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 8, 6], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 12, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 7], \"initial_stock\": 0, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 287 واحد پول و ظرفیت انبار 42 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 287\nCAPACITY: 42\nCOVER_REQUIRED: 0\nSKU S1 demand=8,4,4 pack=2 cost=3 hold=2 short=10 stock=0\nSKU S2 demand=5,8,6 pack=3 cost=6 hold=1 short=12 stock=0\nSKU S3 demand=7,8,7 pack=3 cost=4 hold=1 short=13 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 287, \"warehouse_capacity\": 42, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 4], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 8, 6], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 12, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 7], \"initial_stock\": 0, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 287,\n \"warehouse_capacity\": 42,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 8,\n 4,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 8,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 12,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 8,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":287,"warehouse_capacity":42,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[8,4,4],"initial_stock":0,"unit_cost":3,"holding_cost":2,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,8,6],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":12,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,8,7],"initial_stock":0,"unit_cost":4,"holding_cost":1,"shortage_cost":13,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":267.0,"gold_bound":267.0,"gold_solution":{"family":"inventory","status":"optimal","objective":267.0,"bound":267.0,"orders":[{"sku_id":"S1","period":1,"qty":8},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":9},{"sku_id":"S3","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"caebc391dc3f21a3","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-010","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":25010,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 240 currency units. Storage holds at most 28 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 240\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=8,4,6 pack=1 cost=8 hold=1 short=6 stock=1\nSKU S2 demand=2,6,8 pack=1 cost=7 hold=3 short=12 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 240, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 6], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 6, 8], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 240 واحد پول و ظرفیت انبار 28 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 240\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=8,4,6 pack=1 cost=8 hold=1 short=6 stock=1\nSKU S2 demand=2,6,8 pack=1 cost=7 hold=3 short=12 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 240, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 6], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 6, 8], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 240,\n \"warehouse_capacity\": 28,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 8,\n 4,\n 6\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 6,\n 8\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 3,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":240,"warehouse_capacity":28,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[8,4,6],"initial_stock":1,"unit_cost":8,"holding_cost":1,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,6,8],"initial_stock":3,"unit_cost":7,"holding_cost":3,"shortage_cost":12,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":230.0,"gold_bound":230.0,"gold_solution":{"family":"inventory","status":"optimal","objective":230.0,"bound":230.0,"orders":[{"sku_id":"S1","period":1,"qty":7},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":5},{"sku_id":"S2","period":3,"qty":8}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f482821b43520a57","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-011","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":25011,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 167 currency units. Storage holds at most 16 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 167\nCAPACITY: 16\nCOVER_REQUIRED: 0\nSKU S1 demand=2,5,4 pack=2 cost=8 hold=2 short=11 stock=3\nSKU S2 demand=8,4,2 pack=3 cost=7 hold=1 short=14 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 167, \"warehouse_capacity\": 16, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 5, 4], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 4, 2], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 14, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 167 واحد پول و ظرفیت انبار 16 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 167\nCAPACITY: 16\nCOVER_REQUIRED: 0\nSKU S1 demand=2,5,4 pack=2 cost=8 hold=2 short=11 stock=3\nSKU S2 demand=8,4,2 pack=3 cost=7 hold=1 short=14 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 167, \"warehouse_capacity\": 16, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 5, 4], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 4, 2], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 14, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 167,\n \"warehouse_capacity\": 16,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 5,\n 4\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 4,\n 2\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":167,"warehouse_capacity":16,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,5,4],"initial_stock":3,"unit_cost":8,"holding_cost":2,"shortage_cost":11,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,4,2],"initial_stock":3,"unit_cost":7,"holding_cost":1,"shortage_cost":14,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":152.0,"gold_bound":152.0,"gold_solution":{"family":"inventory","status":"optimal","objective":152.0,"bound":152.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"8ad0f8164e7ede31","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-012","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":25012,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 277 currency units. Storage holds at most 31 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,2 pack=3 cost=6 hold=3 short=11 stock=1\nSKU S2 demand=7,8,2 pack=3 cost=6 hold=2 short=10 stock=3\nSKU S3 demand=6,3,5 pack=1 cost=5 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 2], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 8, 2], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 3, 5], \"initial_stock\": 3, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 277 واحد پول و ظرفیت انبار 31 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,2 pack=3 cost=6 hold=3 short=11 stock=1\nSKU S2 demand=7,8,2 pack=3 cost=6 hold=2 short=10 stock=3\nSKU S3 demand=6,3,5 pack=1 cost=5 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 2], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 8, 2], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 3, 5], \"initial_stock\": 3, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 277,\n \"warehouse_capacity\": 31,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 8,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 7,\n 8,\n 2\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 6,\n 3,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":277,"warehouse_capacity":31,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,8,2],"initial_stock":1,"unit_cost":6,"holding_cost":3,"shortage_cost":11,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[7,8,2],"initial_stock":3,"unit_cost":6,"holding_cost":2,"shortage_cost":10,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[6,3,5],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":8,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":253.0,"gold_bound":253.0,"gold_solution":{"family":"inventory","status":"optimal","objective":253.0,"bound":253.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":9},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":9},{"sku_id":"S2","period":3,"qty":0},{"sku_id":"S3","period":1,"qty":3},{"sku_id":"S3","period":2,"qty":3},{"sku_id":"S3","period":3,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"3827beb73596c516","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-013","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":25013,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 256 currency units. Storage holds at most 21 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 256\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,3 pack=3 cost=9 hold=2 short=7 stock=3\nSKU S2 demand=3,6,4 pack=2 cost=9 hold=2 short=6 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 256, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 6, 4], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 256 واحد پول و ظرفیت انبار 21 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 256\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,3 pack=3 cost=9 hold=2 short=7 stock=3\nSKU S2 demand=3,6,4 pack=2 cost=9 hold=2 short=6 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 256, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 6, 4], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 256,\n \"warehouse_capacity\": 21,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 8,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 7,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 3,\n 6,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":256,"warehouse_capacity":21,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,8,3],"initial_stock":3,"unit_cost":9,"holding_cost":2,"shortage_cost":7,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[3,6,4],"initial_stock":2,"unit_cost":9,"holding_cost":2,"shortage_cost":6,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":171.0,"gold_bound":171.0,"gold_solution":{"family":"inventory","status":"optimal","objective":171.0,"bound":171.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":0},{"sku_id":"S2","period":3,"qty":0}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"1a72f172d379cd66","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-014","family":"inventory","split":"development","interactive":true,"difficulty":"hard","language":"fa","template_id":"D-B","seed":25014,"prompt_en":"A B2B warehouse plans 4 weeks for 4 SKUs: S1 (bearing), S2 (seal), S3 (gasket), S4 (filter). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 451 currency units. Storage holds at most 57 units in total. Minimize purchase + holding + shortage.\nPERIODS: 4\nBUDGET: 451\nCAPACITY: 57\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,2,4 pack=2 cost=7 hold=3 short=7 stock=2\nSKU S2 demand=6,6,8,2 pack=2 cost=5 hold=2 short=9 stock=1\nSKU S3 demand=7,2,5,8 pack=2 cost=5 hold=2 short=13 stock=2\nSKU S4 demand=3,8,4,3 pack=1 cost=8 hold=3 short=10 stock=3\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 451, \"warehouse_capacity\": 57, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 2, 4], \"initial_stock\": 2, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 2, 5, 8], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [3, 8, 4, 3], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 4 هفته و 4 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 451 واحد پول و ظرفیت انبار 57 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 4\nBUDGET: 451\nCAPACITY: 57\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,2,4 pack=2 cost=7 hold=3 short=7 stock=2\nSKU S2 demand=6,6,8,2 pack=2 cost=5 hold=2 short=9 stock=1\nSKU S3 demand=7,2,5,8 pack=2 cost=5 hold=2 short=13 stock=2\nSKU S4 demand=3,8,4,3 pack=1 cost=8 hold=3 short=10 stock=3\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 451, \"warehouse_capacity\": 57, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 2, 4], \"initial_stock\": 2, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 2, 5, 8], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [3, 8, 4, 3], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 4,\n \"budget\": 451,\n \"warehouse_capacity\": 57,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 2,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 7,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 6,\n 8,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 5,\n \"holding_cost\": 2,\n \"shortage_cost\": 9,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 2,\n 5,\n 8\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 3,\n 8,\n 4,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 10,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":451,"warehouse_capacity":57,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,2,4],"initial_stock":2,"unit_cost":7,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,6,8,2],"initial_stock":1,"unit_cost":5,"holding_cost":2,"shortage_cost":9,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,2,5,8],"initial_stock":2,"unit_cost":5,"holding_cost":2,"shortage_cost":13,"pack_size":2,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[3,8,4,3],"initial_stock":3,"unit_cost":8,"holding_cost":3,"shortage_cost":10,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":443.0,"gold_bound":443.0,"gold_solution":{"family":"inventory","status":"optimal","objective":443.0,"bound":443.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S1","period":4,"qty":4},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":8},{"sku_id":"S2","period":4,"qty":2},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":2},{"sku_id":"S3","period":3,"qty":4},{"sku_id":"S3","period":4,"qty":8},{"sku_id":"S4","period":1,"qty":0},{"sku_id":"S4","period":2,"qty":8},{"sku_id":"S4","period":3,"qty":4},{"sku_id":"S4","period":4,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"220c39206c2443c2","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-015","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"en","template_id":"D-C","seed":25015,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 277 currency units. Storage holds at most 27 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 27\nCOVER_REQUIRED: 1\nSKU S1 demand=3,4,2 pack=1 cost=9 hold=2 short=10 stock=2\nSKU S2 demand=4,2,5 pack=2 cost=6 hold=1 short=10 stock=2\nSKU S3 demand=7,6,7 pack=1 cost=8 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 27, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 4, 2], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 2, 5], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 6, 7], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 277 واحد پول و ظرفیت انبار 27 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 27\nCOVER_REQUIRED: 1\nSKU S1 demand=3,4,2 pack=1 cost=9 hold=2 short=10 stock=2\nSKU S2 demand=4,2,5 pack=2 cost=6 hold=1 short=10 stock=2\nSKU S3 demand=7,6,7 pack=1 cost=8 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 27, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 4, 2], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 2, 5], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 6, 7], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 277,\n \"warehouse_capacity\": 27,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 4,\n 2\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 2,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 6,\n 7\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":277,"warehouse_capacity":27,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,4,2],"initial_stock":2,"unit_cost":9,"holding_cost":2,"shortage_cost":10,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,2,5],"initial_stock":2,"unit_cost":6,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,6,7],"initial_stock":2,"unit_cost":8,"holding_cost":2,"shortage_cost":12,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":268.0,"gold_bound":268.0,"gold_solution":{"family":"inventory","status":"optimal","objective":268.0,"bound":268.0,"orders":[{"sku_id":"S1","period":1,"qty":1},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S2","period":1,"qty":2},{"sku_id":"S2","period":2,"qty":2},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":5},{"sku_id":"S3","period":2,"qty":6},{"sku_id":"S3","period":3,"qty":7}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"06a75306f2f713c8","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-016","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":25016,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 148 currency units. Storage holds at most 27 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 148\nCAPACITY: 27\nCOVER_REQUIRED: 0\nSKU S1 demand=2,8,8 pack=1 cost=3 hold=3 short=14 stock=0\nSKU S2 demand=4,5,5 pack=3 cost=7 hold=1 short=13 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 148, \"warehouse_capacity\": 27, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 8, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 5, 5], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 148 واحد پول و ظرفیت انبار 27 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 148\nCAPACITY: 27\nCOVER_REQUIRED: 0\nSKU S1 demand=2,8,8 pack=1 cost=3 hold=3 short=14 stock=0\nSKU S2 demand=4,5,5 pack=3 cost=7 hold=1 short=13 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 148, \"warehouse_capacity\": 27, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 8, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 5, 5], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 148,\n \"warehouse_capacity\": 27,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 8,\n 8\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 3,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 5,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":148,"warehouse_capacity":27,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,8,8],"initial_stock":0,"unit_cost":3,"holding_cost":3,"shortage_cost":14,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,5,5],"initial_stock":3,"unit_cost":7,"holding_cost":1,"shortage_cost":13,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":141.0,"gold_bound":141.0,"gold_solution":{"family":"inventory","status":"optimal","objective":141.0,"bound":141.0,"orders":[{"sku_id":"S1","period":1,"qty":2},{"sku_id":"S1","period":2,"qty":8},{"sku_id":"S1","period":3,"qty":8},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7c84e87cc10f3c05","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-017","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":25017,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 182 currency units. Storage holds at most 23 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 182\nCAPACITY: 23\nCOVER_REQUIRED: 0\nSKU S1 demand=7,2,5 pack=3 cost=4 hold=1 short=10 stock=1\nSKU S2 demand=8,2,6 pack=2 cost=7 hold=1 short=9 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 182, \"warehouse_capacity\": 23, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 2, 5], \"initial_stock\": 1, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 2, 6], \"initial_stock\": 0, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 182 واحد پول و ظرفیت انبار 23 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 182\nCAPACITY: 23\nCOVER_REQUIRED: 0\nSKU S1 demand=7,2,5 pack=3 cost=4 hold=1 short=10 stock=1\nSKU S2 demand=8,2,6 pack=2 cost=7 hold=1 short=9 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 182, \"warehouse_capacity\": 23, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 2, 5], \"initial_stock\": 1, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 2, 6], \"initial_stock\": 0, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 182,\n \"warehouse_capacity\": 23,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 2,\n 5\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 2,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":182,"warehouse_capacity":23,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,2,5],"initial_stock":1,"unit_cost":4,"holding_cost":1,"shortage_cost":10,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,2,6],"initial_stock":0,"unit_cost":7,"holding_cost":1,"shortage_cost":9,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":171.0,"gold_bound":171.0,"gold_solution":{"family":"inventory","status":"optimal","objective":171.0,"bound":171.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":8},{"sku_id":"S2","period":2,"qty":2},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7315654a4c498e83","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-018","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":25018,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 209 currency units. Storage holds at most 28 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 209\nCAPACITY: 28\nCOVER_REQUIRED: 0\nSKU S1 demand=4,4,4 pack=1 cost=6 hold=1 short=7 stock=0\nSKU S2 demand=3,3,3 pack=3 cost=6 hold=1 short=7 stock=0\nSKU S3 demand=6,4,7 pack=1 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 209, \"warehouse_capacity\": 28, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [4, 4, 4], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 3, 3], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 4, 7], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 209 واحد پول و ظرفیت انبار 28 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 209\nCAPACITY: 28\nCOVER_REQUIRED: 0\nSKU S1 demand=4,4,4 pack=1 cost=6 hold=1 short=7 stock=0\nSKU S2 demand=3,3,3 pack=3 cost=6 hold=1 short=7 stock=0\nSKU S3 demand=6,4,7 pack=1 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 209, \"warehouse_capacity\": 28, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [4, 4, 4], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 3, 3], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 4, 7], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 209,\n \"warehouse_capacity\": 28,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 4,\n 4,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 3,\n 3,\n 3\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 6,\n 4,\n 7\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":209,"warehouse_capacity":28,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[4,4,4],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[3,3,3],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":7,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[6,4,7],"initial_stock":2,"unit_cost":5,"holding_cost":3,"shortage_cost":11,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":201.0,"gold_bound":201.0,"gold_solution":{"family":"inventory","status":"optimal","objective":201.0,"bound":201.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3},{"sku_id":"S3","period":1,"qty":4},{"sku_id":"S3","period":2,"qty":4},{"sku_id":"S3","period":3,"qty":7}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2db06bd39b73849d","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-019","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":25019,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 169 currency units. Storage holds at most 25 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 169\nCAPACITY: 25\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,8 pack=1 cost=3 hold=1 short=6 stock=0\nSKU S2 demand=4,4,5 pack=2 cost=9 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 169, \"warehouse_capacity\": 25, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 4, 5], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 169 واحد پول و ظرفیت انبار 25 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 169\nCAPACITY: 25\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,8 pack=1 cost=3 hold=1 short=6 stock=0\nSKU S2 demand=4,4,5 pack=2 cost=9 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 169, \"warehouse_capacity\": 25, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 4, 5], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 169,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 4,\n 8\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 1,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 4,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":169,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,4,8],"initial_stock":0,"unit_cost":3,"holding_cost":1,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,4,5],"initial_stock":2,"unit_cost":9,"holding_cost":1,"shortage_cost":7,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":128.0,"gold_bound":128.0,"gold_solution":{"family":"inventory","status":"optimal","objective":128.0,"bound":128.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":8},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":0},{"sku_id":"S2","period":3,"qty":0}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"5a0bc130cf4da2cb","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-020","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":25020,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 191 currency units. Storage holds at most 20 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 191\nCAPACITY: 20\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,5 pack=1 cost=9 hold=2 short=13 stock=3\nSKU S2 demand=5,3,4 pack=3 cost=6 hold=3 short=8 stock=1\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 191, \"warehouse_capacity\": 20, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 3, 4], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 191 واحد پول و ظرفیت انبار 20 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 191\nCAPACITY: 20\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,5 pack=1 cost=9 hold=2 short=13 stock=3\nSKU S2 demand=5,3,4 pack=3 cost=6 hold=3 short=8 stock=1\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 191, \"warehouse_capacity\": 20, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 3, 4], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 191,\n \"warehouse_capacity\": 20,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 3,\n 4\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":191,"warehouse_capacity":20,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,5],"initial_stock":3,"unit_cost":9,"holding_cost":2,"shortage_cost":13,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,3,4],"initial_stock":1,"unit_cost":6,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":195.0,"gold_bound":195.0,"gold_solution":{"family":"inventory","status":"optimal","objective":195.0,"bound":195.0,"orders":[{"sku_id":"S1","period":1,"qty":2},{"sku_id":"S1","period":2,"qty":5},{"sku_id":"S1","period":3,"qty":5},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7504669a6087b21d","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-021","family":"inventory","split":"test","interactive":true,"difficulty":"hard","language":"en","template_id":"T-A","seed":25021,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket), S4 (filter) over a 4-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 667. On-hand stock across SKUs cannot exceed 56. S1 wants [6, 5, 5, 6] at pack 1; S2 wants [5, 3, 7, 4] at pack 3; S3 wants [8, 5, 4, 8] at pack 2; S4 wants [2, 8, 5, 5] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر) در افق 4 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 667 و سقف موجودی کل 56 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 4,\n \"budget\": 667,\n \"warehouse_capacity\": 56,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 5,\n 5,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 7,\n \"holding_cost\": 2,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 3,\n 7,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 8,\n 5,\n 4,\n 8\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 2,\n 8,\n 5,\n 5\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":667,"warehouse_capacity":56,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,5,5,6],"initial_stock":2,"unit_cost":7,"holding_cost":2,"shortage_cost":14,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,3,7,4],"initial_stock":2,"unit_cost":8,"holding_cost":2,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[8,5,4,8],"initial_stock":3,"unit_cost":9,"holding_cost":3,"shortage_cost":9,"pack_size":2,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[2,8,5,5],"initial_stock":1,"unit_cost":8,"holding_cost":1,"shortage_cost":9,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":643.0,"gold_bound":643.0,"gold_solution":{"family":"inventory","status":"optimal","objective":643.0,"bound":643.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":5},{"sku_id":"S1","period":3,"qty":5},{"sku_id":"S1","period":4,"qty":6},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":9},{"sku_id":"S2","period":4,"qty":3},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":4},{"sku_id":"S3","period":3,"qty":4},{"sku_id":"S3","period":4,"qty":8},{"sku_id":"S4","period":1,"qty":1},{"sku_id":"S4","period":2,"qty":8},{"sku_id":"S4","period":3,"qty":5},{"sku_id":"S4","period":4,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"43f6be8e459b5009","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-022","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-B","seed":25022,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 117. On-hand stock across SKUs cannot exceed 19. S1 wants [2, 2, 3] at pack 1; S2 wants [6, 7, 7] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 117 و سقف موجودی کل 19 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 117,\n \"warehouse_capacity\": 19,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 2,\n 3\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 7,\n 7\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":117,"warehouse_capacity":19,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,2,3],"initial_stock":2,"unit_cost":3,"holding_cost":2,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,7,7],"initial_stock":1,"unit_cost":4,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":97.0,"gold_bound":97.0,"gold_solution":{"family":"inventory","status":"optimal","objective":97.0,"bound":97.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":2},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":8}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"e0b2178c1118eb1f","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-023","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":25023,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 241. On-hand stock across SKUs cannot exceed 28. S1 wants [5, 5, 7] at pack 2; S2 wants [6, 3, 5] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 241 و سقف موجودی کل 28 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 241,\n \"warehouse_capacity\": 28,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 7\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 13,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 3,\n 5\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":241,"warehouse_capacity":28,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,7],"initial_stock":1,"unit_cost":8,"holding_cost":3,"shortage_cost":13,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,3,5],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":10,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":222.0,"gold_bound":222.0,"gold_solution":{"family":"inventory","status":"optimal","objective":222.0,"bound":222.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"85786f3b3f0dfbf9","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-024","family":"inventory","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":25024,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 268. On-hand stock across SKUs cannot exceed 26. S1 wants [7, 2, 3] at pack 2; S2 wants [2, 3, 7] at pack 3; S3 wants [3, 8, 8] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 268 و سقف موجودی کل 26 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 268,\n \"warehouse_capacity\": 26,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 2,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 2,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 3,\n 7\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 3,\n 8,\n 8\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":268,"warehouse_capacity":26,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,2,3],"initial_stock":3,"unit_cost":7,"holding_cost":2,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,3,7],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[3,8,8],"initial_stock":3,"unit_cost":9,"holding_cost":1,"shortage_cost":11,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":258.0,"gold_bound":258.0,"gold_solution":{"family":"inventory","status":"optimal","objective":258.0,"bound":258.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":0},{"sku_id":"S3","period":2,"qty":8},{"sku_id":"S3","period":3,"qty":8}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"5c318f4fb63ecf81","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-025","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":25025,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 284. On-hand stock across SKUs cannot exceed 27. S1 wants [7, 5, 6] at pack 3; S2 wants [3, 4, 6] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 284 و سقف موجودی کل 27 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 284,\n \"warehouse_capacity\": 27,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 5,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 3,\n 4,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":284,"warehouse_capacity":27,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,5,6],"initial_stock":3,"unit_cost":9,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[3,4,6],"initial_stock":0,"unit_cost":9,"holding_cost":2,"shortage_cost":6,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":284.0,"gold_bound":284.0,"gold_solution":{"family":"inventory","status":"optimal","objective":284.0,"bound":284.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"34a94761719df506","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-026","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-B","seed":25026,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 222. On-hand stock across SKUs cannot exceed 25. S1 wants [5, 5, 7] at pack 2; S2 wants [5, 7, 4] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 222 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 222,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 7,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":222,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,7],"initial_stock":0,"unit_cost":8,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,7,4],"initial_stock":2,"unit_cost":4,"holding_cost":1,"shortage_cost":14,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":195.0,"gold_bound":195.0,"gold_solution":{"family":"inventory","status":"optimal","objective":195.0,"bound":195.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":7},{"sku_id":"S2","period":3,"qty":4}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"a2c2cf9f0e528f38","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-027","family":"inventory","split":"test","interactive":false,"difficulty":"medium","language":"en","template_id":"T-A","seed":25027,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 200. On-hand stock across SKUs cannot exceed 29. S1 wants [4, 5, 2] at pack 1; S2 wants [4, 8, 2] at pack 2; S3 wants [2, 6, 6] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 200 و سقف موجودی کل 29 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 200,\n \"warehouse_capacity\": 29,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 4,\n 5,\n 2\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 8,\n 2\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 2,\n 6,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 6,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":200,"warehouse_capacity":29,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[4,5,2],"initial_stock":3,"unit_cost":5,"holding_cost":1,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,8,2],"initial_stock":2,"unit_cost":3,"holding_cost":2,"shortage_cost":12,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[2,6,6],"initial_stock":3,"unit_cost":9,"holding_cost":1,"shortage_cost":6,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":143.0,"gold_bound":143.0,"gold_solution":{"family":"inventory","status":"optimal","objective":143.0,"bound":143.0,"orders":[{"sku_id":"S1","period":1,"qty":1},{"sku_id":"S1","period":2,"qty":5},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S2","period":1,"qty":2},{"sku_id":"S2","period":2,"qty":8},{"sku_id":"S2","period":3,"qty":2},{"sku_id":"S3","period":1,"qty":0},{"sku_id":"S3","period":2,"qty":0},{"sku_id":"S3","period":3,"qty":0}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"58e2d8d2872c433a","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-028","family":"inventory","split":"test","interactive":true,"difficulty":"hard","language":"fa","template_id":"T-B","seed":25028,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket), S4 (filter) over a 4-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 417. On-hand stock across SKUs cannot exceed 48. S1 wants [2, 6, 5, 4] at pack 2; S2 wants [6, 2, 5, 6] at pack 3; S3 wants [3, 2, 7, 5] at pack 1; S4 wants [7, 3, 4, 4] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر) در افق 4 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 417 و سقف موجودی کل 48 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 4,\n \"budget\": 417,\n \"warehouse_capacity\": 48,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 6,\n 5,\n 4\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 2,\n 5,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 3,\n 2,\n 7,\n 5\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 7,\n 3,\n 4,\n 4\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":417,"warehouse_capacity":48,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,6,5,4],"initial_stock":1,"unit_cost":5,"holding_cost":3,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,2,5,6],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[3,2,7,5],"initial_stock":0,"unit_cost":8,"holding_cost":3,"shortage_cost":9,"pack_size":1,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[7,3,4,4],"initial_stock":3,"unit_cost":6,"holding_cost":1,"shortage_cost":9,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":422.0,"gold_bound":422.0,"gold_solution":{"family":"inventory","status":"optimal","objective":422.0,"bound":422.0,"orders":[{"sku_id":"S1","period":1,"qty":2},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S1","period":4,"qty":4},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S2","period":4,"qty":6},{"sku_id":"S3","period":1,"qty":3},{"sku_id":"S3","period":2,"qty":2},{"sku_id":"S3","period":3,"qty":7},{"sku_id":"S3","period":4,"qty":5},{"sku_id":"S4","period":1,"qty":6},{"sku_id":"S4","period":2,"qty":3},{"sku_id":"S4","period":3,"qty":3},{"sku_id":"S4","period":4,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"d4b291056d53e1b6","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-029","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":25029,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 205. On-hand stock across SKUs cannot exceed 25. S1 wants [7, 6, 3] at pack 3; S2 wants [6, 4, 5] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 205 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 205,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 6,\n 3\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 4,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":205,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,6,3],"initial_stock":0,"unit_cost":8,"holding_cost":1,"shortage_cost":14,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,4,5],"initial_stock":2,"unit_cost":4,"holding_cost":1,"shortage_cost":10,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":186.0,"gold_bound":186.0,"gold_solution":{"family":"inventory","status":"optimal","objective":186.0,"bound":186.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":4},{"sku_id":"S2","period":2,"qty":4},{"sku_id":"S2","period":3,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"df4a252d2ab08ed3","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-030","family":"inventory","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":25030,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 174. On-hand stock across SKUs cannot exceed 25. S1 wants [3, 3, 2] at pack 1; S2 wants [6, 2, 7] at pack 2; S3 wants [8, 3, 2] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 174 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 174,\n \"warehouse_capacity\": 25,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 3,\n 2\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 2,\n 7\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 8,\n 3,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":174,"warehouse_capacity":25,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,3,2],"initial_stock":0,"unit_cost":7,"holding_cost":1,"shortage_cost":9,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,2,7],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[8,3,2],"initial_stock":1,"unit_cost":3,"holding_cost":2,"shortage_cost":12,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":160.0,"gold_bound":160.0,"gold_solution":{"family":"inventory","status":"optimal","objective":160.0,"bound":160.0,"orders":[{"sku_id":"S1","period":1,"qty":3},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S2","period":1,"qty":4},{"sku_id":"S2","period":2,"qty":2},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":8},{"sku_id":"S3","period":2,"qty":2},{"sku_id":"S3","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7ab02a4b652b205f","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-031","family":"inventory","split":"test","interactive":true,"difficulty":"easy","language":"en","template_id":"T-A","seed":25031,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 178. On-hand stock across SKUs cannot exceed 25. S1 wants [7, 6, 5] at pack 1; S2 wants [2, 5, 5] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 178 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 178,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 6,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 5,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 7,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":178,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,6,5],"initial_stock":2,"unit_cost":6,"holding_cost":1,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,5,5],"initial_stock":2,"unit_cost":7,"holding_cost":3,"shortage_cost":9,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":166.0,"gold_bound":166.0,"gold_solution":{"family":"inventory","status":"optimal","objective":166.0,"bound":166.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":5},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":5},{"sku_id":"S2","period":3,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"17d8f21147efad41","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-032","family":"inventory","split":"test","interactive":false,"difficulty":"infeasible","language":"fa","template_id":"T-B","seed":25032,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 49. On-hand stock across SKUs cannot exceed 47. S1 wants [3, 8, 6] at pack 1; S2 wants [8, 3, 6] at pack 2; S3 wants [5, 3, 5] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 49 و سقف موجودی کل 47 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 49,\n \"warehouse_capacity\": 47,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 8,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 3,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 5,\n 3,\n 5\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":49,"warehouse_capacity":47,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,8,6],"initial_stock":0,"unit_cost":3,"holding_cost":2,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,3,6],"initial_stock":0,"unit_cost":4,"holding_cost":1,"shortage_cost":14,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[5,3,5],"initial_stock":0,"unit_cost":9,"holding_cost":2,"shortage_cost":10,"pack_size":2,"lead_time":0}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"inventory","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"a81392c6044cd7df","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-033","family":"inventory","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-A","seed":25033,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 42. On-hand stock across SKUs cannot exceed 41. S1 wants [3, 3, 3] at pack 2; S2 wants [4, 7, 7] at pack 2; S3 wants [3, 7, 4] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 42 و سقف موجودی کل 41 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 42,\n \"warehouse_capacity\": 41,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 3,\n 3\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 7,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 3,\n 7,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":42,"warehouse_capacity":41,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,3,3],"initial_stock":0,"unit_cost":5,"holding_cost":3,"shortage_cost":11,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,7,7],"initial_stock":0,"unit_cost":4,"holding_cost":2,"shortage_cost":6,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[3,7,4],"initial_stock":0,"unit_cost":6,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"inventory","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"ea9231d0be843484","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-034","family":"inventory","split":"test","interactive":true,"difficulty":"infeasible","language":"fa","template_id":"T-B","seed":25034,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 56. On-hand stock across SKUs cannot exceed 52. S1 wants [4, 7, 6] at pack 2; S2 wants [8, 3, 8] at pack 1; S3 wants [6, 3, 7] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 56 و سقف موجودی کل 52 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 56,\n \"warehouse_capacity\": 52,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 4,\n 7,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 3,\n 8\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 6,\n 3,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 2,\n \"shortage_cost\": 8,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":56,"warehouse_capacity":52,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[4,7,6],"initial_stock":0,"unit_cost":9,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,3,8],"initial_stock":0,"unit_cost":3,"holding_cost":3,"shortage_cost":9,"pack_size":1,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[6,3,7],"initial_stock":0,"unit_cost":4,"holding_cost":2,"shortage_cost":8,"pack_size":2,"lead_time":0}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"inventory","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"da716bb0cb346fe1","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"ASN-001","family":"assignment","split":"development","interactive":true,"difficulty":"easy","language":"fa","template_id":"D-A","seed":50001,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills lift/weld, T2 size 1 skills inspect, T3 size 2 skills pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 40}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 13}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills lift/weld, T2 size 1 skills inspect, T3 size 2 skills pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 40}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 13}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 38\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["lift","weld"],"penalty":40},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect"],"penalty":22},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack"],"penalty":40},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":38}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A3","cost":12},{"task_id":"T4","agent_id":"A1","cost":11},{"task_id":"T4","agent_id":"A2","cost":7},{"task_id":"T4","agent_id":"A3","cost":13}]},"gold_status":"optimal","gold_objective":35.0,"gold_bound":35.0,"gold_solution":{"family":"assignment","status":"optimal","objective":35.0,"bound":35.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"1cddcd6462c5befc","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-002","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":50002,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 11}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 11}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 37\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["weld"],"penalty":37},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":34},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack","weld"],"penalty":22},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":37}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":11},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":11},{"task_id":"T3","agent_id":"A1","cost":6},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":17},{"task_id":"T4","agent_id":"A2","cost":9},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":26.0,"gold_bound":26.0,"gold_solution":{"family":"assignment","status":"optimal","objective":26.0,"bound":26.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"d2c2d3e77c899e5b","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-003","family":"assignment","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":50003,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills inspect/lift, T2 size 2 skills inspect/lift, T3 size 2 skills pack/weld, T4 size 2 skills pack/weld, T5 size 1 skills inspect/lift, T6 size 2 skills inspect/lift\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 31}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills inspect/lift, T2 size 2 skills inspect/lift, T3 size 2 skills pack/weld, T4 size 2 skills pack/weld, T5 size 1 skills inspect/lift, T6 size 2 skills inspect/lift\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 31}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 25\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["inspect","lift"],"penalty":31},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift"],"penalty":25},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack","weld"],"penalty":28},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["pack","weld"],"penalty":39},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","lift"],"penalty":38},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","lift"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":6},{"task_id":"T1","agent_id":"A2","cost":18},{"task_id":"T1","agent_id":"A3","cost":17},{"task_id":"T2","agent_id":"A1","cost":8},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":13},{"task_id":"T3","agent_id":"A1","cost":9},{"task_id":"T3","agent_id":"A2","cost":8},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A1","cost":15},{"task_id":"T4","agent_id":"A2","cost":8},{"task_id":"T4","agent_id":"A3","cost":12},{"task_id":"T5","agent_id":"A1","cost":6},{"task_id":"T5","agent_id":"A2","cost":9},{"task_id":"T5","agent_id":"A3","cost":18},{"task_id":"T6","agent_id":"A1","cost":5},{"task_id":"T6","agent_id":"A2","cost":16},{"task_id":"T6","agent_id":"A3","cost":14}]},"gold_status":"optimal","gold_objective":39.0,"gold_bound":39.0,"gold_solution":{"family":"assignment","status":"optimal","objective":39.0,"bound":39.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A1"},{"task_id":"T6","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7cb9463c065ed495","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-004","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":50004,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/weld, T2 size 3 skills inspect, T3 size 3 skills lift/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/weld, T2 size 3 skills inspect, T3 size 3 skills lift/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 37\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","weld"],"penalty":40},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect"],"penalty":22},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift","pack"],"penalty":31},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["lift","weld"],"penalty":37}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":14},{"task_id":"T1","agent_id":"A2","cost":15},{"task_id":"T1","agent_id":"A3","cost":6},{"task_id":"T2","agent_id":"A2","cost":16},{"task_id":"T2","agent_id":"A3","cost":8},{"task_id":"T3","agent_id":"A3","cost":15},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A3","cost":16}]},"gold_status":"optimal","gold_objective":44.0,"gold_bound":44.0,"gold_solution":{"family":"assignment","status":"optimal","objective":44.0,"bound":44.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"617e65bd9540551c","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-005","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":50005,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills pack/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 24}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills pack/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 24}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 34\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["pack","weld"],"penalty":24},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","weld"],"penalty":33},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack"],"penalty":32},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["inspect","weld"],"penalty":34}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":14},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A1","cost":11},{"task_id":"T2","agent_id":"A2","cost":11},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A2","cost":5},{"task_id":"T4","agent_id":"A3","cost":16}]},"gold_status":"optimal","gold_objective":30.0,"gold_bound":30.0,"gold_solution":{"family":"assignment","status":"optimal","objective":30.0,"bound":30.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"313df2be239a5ae9","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-006","family":"assignment","split":"development","interactive":true,"difficulty":"medium","language":"en","template_id":"D-C","seed":50006,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills lift, T4 size 1 skills inspect, T5 size 2 skills lift/pack, T6 size 2 skills lift\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 5 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 20}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 27}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 40}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills lift, T4 size 1 skills inspect, T5 size 2 skills lift/pack, T6 size 2 skills lift\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 5 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 20}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 27}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 40}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 38\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift"],"penalty":20},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":27},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift"],"penalty":28},{"task_id":"T4","name":"job-4","size":1,"required":true,"skills":["inspect"],"penalty":39},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["lift","pack"],"penalty":40},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["lift"],"penalty":38}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":11},{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A1","cost":8},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":9},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":11},{"task_id":"T4","agent_id":"A2","cost":18},{"task_id":"T4","agent_id":"A3","cost":14},{"task_id":"T5","agent_id":"A2","cost":15},{"task_id":"T5","agent_id":"A3","cost":7},{"task_id":"T6","agent_id":"A3","cost":11}]},"gold_status":"optimal","gold_objective":48.0,"gold_bound":48.0,"gold_solution":{"family":"assignment","status":"optimal","objective":48.0,"bound":48.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"633fec80b9b681c9","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-007","family":"assignment","split":"development","interactive":false,"difficulty":"hard","language":"fa","template_id":"D-A","seed":50007,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills inspect/lift, T4 size 2 skills lift/pack, T5 size 1 skills inspect/weld, T6 size 1 skills pack, T7 size 1 skills inspect/pack, T8 size 1 skills lift/weld\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 29}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 30}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 22}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 23}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T8\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 8}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills inspect/lift, T4 size 2 skills lift/pack, T5 size 1 skills inspect/weld, T6 size 1 skills pack, T7 size 1 skills inspect/pack, T8 size 1 skills lift/weld\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 29}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 30}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 22}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 23}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T8\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 8}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 23\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 8\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["inspect","lift"],"penalty":21},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":29},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift"],"penalty":30},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["lift","pack"],"penalty":22},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","weld"],"penalty":21},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["pack"],"penalty":32},{"task_id":"T7","name":"job-7","size":1,"required":true,"skills":["inspect","pack"],"penalty":23},{"task_id":"T8","name":"job-8","size":1,"required":true,"skills":["lift","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A2","cost":12},{"task_id":"T1","agent_id":"A3","cost":12},{"task_id":"T1","agent_id":"A4","cost":7},{"task_id":"T2","agent_id":"A1","cost":11},{"task_id":"T2","agent_id":"A2","cost":18},{"task_id":"T2","agent_id":"A3","cost":18},{"task_id":"T2","agent_id":"A4","cost":14},{"task_id":"T3","agent_id":"A1","cost":4},{"task_id":"T3","agent_id":"A2","cost":6},{"task_id":"T3","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A4","cost":5},{"task_id":"T4","agent_id":"A2","cost":13},{"task_id":"T4","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A4","cost":17},{"task_id":"T5","agent_id":"A1","cost":10},{"task_id":"T5","agent_id":"A2","cost":9},{"task_id":"T5","agent_id":"A4","cost":18},{"task_id":"T6","agent_id":"A2","cost":12},{"task_id":"T6","agent_id":"A3","cost":7},{"task_id":"T6","agent_id":"A4","cost":5},{"task_id":"T7","agent_id":"A1","cost":14},{"task_id":"T7","agent_id":"A2","cost":15},{"task_id":"T7","agent_id":"A3","cost":13},{"task_id":"T7","agent_id":"A4","cost":5},{"task_id":"T8","agent_id":"A1","cost":17},{"task_id":"T8","agent_id":"A3","cost":18},{"task_id":"T8","agent_id":"A4","cost":8}]},"gold_status":"optimal","gold_objective":55.0,"gold_bound":55.0,"gold_solution":{"family":"assignment","status":"optimal","objective":55.0,"bound":55.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A4"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A2"},{"task_id":"T6","agent_id":"A4"},{"task_id":"T7","agent_id":"A4"},{"task_id":"T8","agent_id":"A4"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"4d73d8bdc819ff4a","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-008","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":50008,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 1 skills inspect/pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 26}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 1 skills inspect/pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 26}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 26\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["lift","weld"],"penalty":34},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","weld"],"penalty":33},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":26}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A1","cost":4},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A2","cost":8},{"task_id":"T3","agent_id":"A3","cost":13},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A2","cost":17},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":31.0,"gold_bound":31.0,"gold_solution":{"family":"assignment","status":"optimal","objective":31.0,"bound":31.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"0e4781ed5b25d32c","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-009","family":"assignment","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":50009,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/lift, T2 size 2 skills lift/pack, T3 size 2 skills pack, T4 size 1 skills inspect/lift, T5 size 3 skills inspect/weld, T6 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 32}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 9}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/lift, T2 size 2 skills lift/pack, T3 size 2 skills pack, T4 size 1 skills inspect/lift, T5 size 3 skills inspect/weld, T6 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 32}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 9}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 25\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 32\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 9\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["lift","pack"],"penalty":30},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack"],"penalty":20},{"task_id":"T4","name":"job-4","size":1,"required":true,"skills":["inspect","lift"],"penalty":25},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["inspect","weld"],"penalty":32},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["lift","weld"],"penalty":32}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":14},{"task_id":"T1","agent_id":"A2","cost":4},{"task_id":"T1","agent_id":"A3","cost":15},{"task_id":"T2","agent_id":"A2","cost":14},{"task_id":"T2","agent_id":"A3","cost":6},{"task_id":"T3","agent_id":"A2","cost":7},{"task_id":"T3","agent_id":"A3","cost":12},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A2","cost":9},{"task_id":"T4","agent_id":"A3","cost":15},{"task_id":"T5","agent_id":"A1","cost":11},{"task_id":"T5","agent_id":"A2","cost":16},{"task_id":"T5","agent_id":"A3","cost":6},{"task_id":"T6","agent_id":"A1","cost":17},{"task_id":"T6","agent_id":"A3","cost":9}]},"gold_status":"optimal","gold_objective":51.0,"gold_bound":51.0,"gold_solution":{"family":"assignment","status":"optimal","objective":51.0,"bound":51.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2ed0462d809cf9b4","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-010","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":50010,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 4 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 39}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 20}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 17}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 4 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 39}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 20}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 17}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 20\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":40},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":38},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack"],"penalty":39},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["inspect","weld"],"penalty":20}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":15},{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":13},{"task_id":"T3","agent_id":"A3","cost":7},{"task_id":"T4","agent_id":"A1","cost":8},{"task_id":"T4","agent_id":"A2","cost":8},{"task_id":"T4","agent_id":"A3","cost":17}]},"gold_status":"optimal","gold_objective":24.0,"gold_bound":24.0,"gold_solution":{"family":"assignment","status":"optimal","objective":24.0,"bound":24.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f1b67e1305aef3ad","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-011","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":50011,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills pack/weld, T2 size 3 skills inspect/weld, T3 size 3 skills lift/pack, T4 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 5}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills pack/weld, T2 size 3 skills inspect/weld, T3 size 3 skills lift/pack, T4 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 5}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["pack","weld"],"penalty":30},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","weld"],"penalty":34},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift","pack"],"penalty":38},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["lift","weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":8},{"task_id":"T1","agent_id":"A3","cost":10},{"task_id":"T2","agent_id":"A1","cost":10},{"task_id":"T2","agent_id":"A2","cost":12},{"task_id":"T2","agent_id":"A3","cost":8},{"task_id":"T3","agent_id":"A3","cost":8},{"task_id":"T4","agent_id":"A1","cost":17},{"task_id":"T4","agent_id":"A3","cost":5}]},"gold_status":"optimal","gold_objective":29.0,"gold_bound":29.0,"gold_solution":{"family":"assignment","status":"optimal","objective":29.0,"bound":29.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"6e546d67a8410d0f","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-012","family":"assignment","split":"development","interactive":true,"difficulty":"medium","language":"en","template_id":"D-C","seed":50012,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/lift, T3 size 1 skills inspect/lift, T4 size 3 skills inspect, T5 size 2 skills inspect, T6 size 3 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"pack\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 40}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 35}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 36}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/lift, T3 size 1 skills inspect/lift, T4 size 3 skills inspect, T5 size 2 skills inspect, T6 size 3 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"pack\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 40}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 35}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 36}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 36\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift","pack"],"penalty":37},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift"],"penalty":34},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","lift"],"penalty":32},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["inspect"],"penalty":40},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["inspect"],"penalty":35},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["lift","weld"],"penalty":36}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":18},{"task_id":"T1","agent_id":"A2","cost":17},{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A1","cost":7},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A1","cost":15},{"task_id":"T3","agent_id":"A2","cost":9},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":4},{"task_id":"T4","agent_id":"A2","cost":8},{"task_id":"T4","agent_id":"A3","cost":7},{"task_id":"T5","agent_id":"A1","cost":17},{"task_id":"T5","agent_id":"A2","cost":15},{"task_id":"T5","agent_id":"A3","cost":10},{"task_id":"T6","agent_id":"A1","cost":15},{"task_id":"T6","agent_id":"A3","cost":11}]},"gold_status":"optimal","gold_objective":47.0,"gold_bound":47.0,"gold_solution":{"family":"assignment","status":"optimal","objective":47.0,"bound":47.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2b47606bb2a45436","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-013","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":50013,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills lift/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 24}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 18}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills lift/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 24}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 18}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":21},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack"],"penalty":24},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["inspect","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A3","cost":10},{"task_id":"T2","agent_id":"A2","cost":14},{"task_id":"T2","agent_id":"A3","cost":7},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A1","cost":15},{"task_id":"T4","agent_id":"A2","cost":13},{"task_id":"T4","agent_id":"A3","cost":18}]},"gold_status":"optimal","gold_objective":35.0,"gold_bound":35.0,"gold_solution":{"family":"assignment","status":"optimal","objective":35.0,"bound":35.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"04a6ab674fa9c7ce","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-014","family":"assignment","split":"development","interactive":false,"difficulty":"hard","language":"en","template_id":"D-B","seed":50014,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills inspect/pack, T2 size 3 skills inspect/lift, T3 size 2 skills inspect/pack, T4 size 2 skills inspect/lift, T5 size 1 skills inspect/pack, T6 size 3 skills inspect/weld, T7 size 1 skills inspect/lift, T8 size 3 skills lift\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills lift/pack, A4 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 40}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 35}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 22}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills inspect/pack, T2 size 3 skills inspect/lift, T3 size 2 skills inspect/pack, T4 size 2 skills inspect/lift, T5 size 1 skills inspect/pack, T6 size 3 skills inspect/weld, T7 size 1 skills inspect/lift, T8 size 3 skills lift\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills lift/pack, A4 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 40}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 35}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 22}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 28\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": 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\"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 11\n }\n 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intersection is the eligibility rule"} +{"problem_id":"ASN-015","family":"assignment","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":50015,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect, T2 size 2 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 2 skills inspect, T5 size 2 skills inspect, T6 size 1 skills inspect/lift/weld\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 31}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 23}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 27}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 10}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect, T2 size 2 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 2 skills inspect, T5 size 2 skills inspect, T6 size 1 skills inspect/lift/weld\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 31}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 23}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 27}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 10}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 23\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 27\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","weld"],"penalty":31},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack","weld"],"penalty":23},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["inspect","lift","weld"],"penalty":27}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":6},{"task_id":"T1","agent_id":"A2","cost":4},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A1","cost":12},{"task_id":"T2","agent_id":"A2","cost":13},{"task_id":"T2","agent_id":"A3","cost":14},{"task_id":"T3","agent_id":"A1","cost":17},{"task_id":"T3","agent_id":"A2","cost":6},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":8},{"task_id":"T4","agent_id":"A2","cost":11},{"task_id":"T4","agent_id":"A3","cost":6},{"task_id":"T5","agent_id":"A1","cost":12},{"task_id":"T5","agent_id":"A2","cost":12},{"task_id":"T5","agent_id":"A3","cost":10},{"task_id":"T6","agent_id":"A1","cost":14},{"task_id":"T6","agent_id":"A2","cost":18},{"task_id":"T6","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":47.0,"gold_bound":47.0,"gold_solution":{"family":"assignment","status":"optimal","objective":47.0,"bound":47.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A2"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"d507c6d1a92b00e1","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-016","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":50016,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills weld, T2 size 3 skills inspect/weld, T3 size 2 skills inspect/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 25}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills weld, T2 size 3 skills inspect/weld, T3 size 2 skills inspect/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 25}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 25\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":27},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","weld"],"penalty":32},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["inspect","pack"],"penalty":25},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["lift","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":8},{"task_id":"T1","agent_id":"A3","cost":12},{"task_id":"T2","agent_id":"A1","cost":10},{"task_id":"T2","agent_id":"A2","cost":18},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A2","cost":9},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":12},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":28.0,"gold_bound":28.0,"gold_solution":{"family":"assignment","status":"optimal","objective":28.0,"bound":28.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f9b263c3d202188e","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-017","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":50017,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills lift/weld, T2 size 2 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 37}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills lift/weld, T2 size 2 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 37}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":22},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift"],"penalty":37},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack","weld"],"penalty":32},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":33}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A2","cost":11},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A1","cost":10},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A2","cost":11},{"task_id":"T4","agent_id":"A3","cost":14}]},"gold_status":"optimal","gold_objective":28.0,"gold_bound":28.0,"gold_solution":{"family":"assignment","status":"optimal","objective":28.0,"bound":28.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f515c7358f0c6201","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-018","family":"assignment","split":"development","interactive":true,"difficulty":"medium","language":"en","template_id":"D-C","seed":50018,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills inspect, T2 size 2 skills inspect/lift/weld, T3 size 3 skills inspect/lift/weld, T4 size 3 skills weld, T5 size 1 skills inspect, T6 size 2 skills lift/pack\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 24}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills inspect, T2 size 2 skills inspect/lift/weld, T3 size 3 skills inspect/lift/weld, T4 size 3 skills weld, T5 size 1 skills inspect, T6 size 2 skills lift/pack\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 24}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 37\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["inspect"],"penalty":27},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift","weld"],"penalty":30},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift","weld"],"penalty":33},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["weld"],"penalty":37},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect"],"penalty":24},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["lift","pack"],"penalty":37}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":17},{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":4},{"task_id":"T2","agent_id":"A1","cost":8},{"task_id":"T2","agent_id":"A2","cost":16},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A1","cost":18},{"task_id":"T3","agent_id":"A2","cost":18},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":12},{"task_id":"T4","agent_id":"A3","cost":4},{"task_id":"T5","agent_id":"A1","cost":17},{"task_id":"T5","agent_id":"A2","cost":16},{"task_id":"T5","agent_id":"A3","cost":14},{"task_id":"T6","agent_id":"A2","cost":17},{"task_id":"T6","agent_id":"A3","cost":6}]},"gold_status":"optimal","gold_objective":58.0,"gold_bound":58.0,"gold_solution":{"family":"assignment","status":"optimal","objective":58.0,"bound":58.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A2"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"aa2a372f888bbc65","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-019","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":50019,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 35}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 29}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 35}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 29}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 33\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["weld"],"penalty":35},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":38},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack","weld"],"penalty":29},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["lift","weld"],"penalty":33}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":12},{"task_id":"T3","agent_id":"A1","cost":16},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A3","cost":6}]},"gold_status":"optimal","gold_objective":20.0,"gold_bound":20.0,"gold_solution":{"family":"assignment","status":"optimal","objective":20.0,"bound":20.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"94619056bf241dce","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-020","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":50020,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect, T3 size 1 skills pack/weld, T4 size 2 skills weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 26}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"weld\"], \"penalty\": 40}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect, T3 size 1 skills pack/weld, T4 size 2 skills weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 26}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"weld\"], \"penalty\": 40}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 40\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":39},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect"],"penalty":26},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack","weld"],"penalty":32},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["weld"],"penalty":40}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A2","cost":14},{"task_id":"T2","agent_id":"A3","cost":14},{"task_id":"T3","agent_id":"A1","cost":8},{"task_id":"T3","agent_id":"A3","cost":8},{"task_id":"T4","agent_id":"A1","cost":5},{"task_id":"T4","agent_id":"A3","cost":16}]},"gold_status":"optimal","gold_objective":34.0,"gold_bound":34.0,"gold_solution":{"family":"assignment","status":"optimal","objective":34.0,"bound":34.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"a70e0db3d846416a","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-021","family":"assignment","split":"test","interactive":false,"difficulty":"hard","language":"fa","template_id":"T-A","seed":50021,"prompt_en":"A service desk has technicians A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/pack, T3 size 1 skills lift, T4 size 2 skills lift/pack, T5 size 1 skills lift/weld, T6 size 2 skills inspect/weld, T7 size 3 skills lift/weld, T8 size 2 skills pack/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/pack, T3 size 1 skills lift, T4 size 2 skills lift/pack, T5 size 1 skills lift/weld, T6 size 2 skills inspect/weld, T7 size 3 skills lift/weld, T8 size 2 skills pack/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 9\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift","pack"],"penalty":32},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":29},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["lift"],"penalty":33},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["lift","pack"],"penalty":28},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["lift","weld"],"penalty":40},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","weld"],"penalty":32},{"task_id":"T7","name":"job-7","size":3,"required":true,"skills":["lift","weld"],"penalty":38},{"task_id":"T8","name":"job-8","size":2,"required":true,"skills":["pack","weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":10},{"task_id":"T1","agent_id":"A2","cost":4},{"task_id":"T1","agent_id":"A3","cost":12},{"task_id":"T1","agent_id":"A4","cost":9},{"task_id":"T2","agent_id":"A1","cost":13},{"task_id":"T2","agent_id":"A2","cost":15},{"task_id":"T2","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A4","cost":15},{"task_id":"T3","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A4","cost":15},{"task_id":"T4","agent_id":"A2","cost":14},{"task_id":"T4","agent_id":"A3","cost":16},{"task_id":"T4","agent_id":"A4","cost":7},{"task_id":"T5","agent_id":"A1","cost":18},{"task_id":"T5","agent_id":"A3","cost":16},{"task_id":"T5","agent_id":"A4","cost":9},{"task_id":"T6","agent_id":"A1","cost":15},{"task_id":"T6","agent_id":"A2","cost":7},{"task_id":"T6","agent_id":"A4","cost":17},{"task_id":"T7","agent_id":"A1","cost":4},{"task_id":"T7","agent_id":"A3","cost":6},{"task_id":"T7","agent_id":"A4","cost":17},{"task_id":"T8","agent_id":"A1","cost":16},{"task_id":"T8","agent_id":"A2","cost":6},{"task_id":"T8","agent_id":"A3","cost":4},{"task_id":"T8","agent_id":"A4","cost":9}]},"gold_status":"optimal","gold_objective":63.0,"gold_bound":63.0,"gold_solution":{"family":"assignment","status":"optimal","objective":63.0,"bound":63.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A2"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A4"},{"task_id":"T4","agent_id":"A4"},{"task_id":"T5","agent_id":"A4"},{"task_id":"T6","agent_id":"A2"},{"task_id":"T7","agent_id":"A1"},{"task_id":"T8","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"68e49e596eb52a85","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-022","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":50022,"prompt_en":"A service desk has technicians A1 cap 4 skills weld, A2 cap 4 skills inspect, A3 cap 6 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills lift/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills lift/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 4 skills weld, A2 cap 4 skills inspect, A3 cap 6 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills lift/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills lift/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":36},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","weld"],"penalty":22},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack"],"penalty":27},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["lift","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A3","cost":11},{"task_id":"T2","agent_id":"A1","cost":16},{"task_id":"T2","agent_id":"A2","cost":15},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":10},{"task_id":"T4","agent_id":"A3","cost":18}]},"gold_status":"optimal","gold_objective":53.0,"gold_bound":53.0,"gold_solution":{"family":"assignment","status":"optimal","objective":53.0,"bound":53.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"91d5d0f2a7cdb2b3","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-023","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50023,"prompt_en":"A service desk has technicians A1 cap 3 skills weld, A2 cap 4 skills inspect, A3 cap 7 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 1 skills inspect/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 3 skills weld, A2 cap 4 skills inspect, A3 cap 7 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 1 skills inspect/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":29},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","weld"],"penalty":22},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack","weld"],"penalty":36},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["inspect","weld"],"penalty":33}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A3","cost":18},{"task_id":"T2","agent_id":"A1","cost":18},{"task_id":"T2","agent_id":"A2","cost":8},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A1","cost":10},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":4},{"task_id":"T4","agent_id":"A2","cost":14},{"task_id":"T4","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":21.0,"gold_bound":21.0,"gold_solution":{"family":"assignment","status":"optimal","objective":21.0,"bound":21.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"616463a38483d3aa","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-024","family":"assignment","split":"test","interactive":true,"difficulty":"medium","language":"en","template_id":"T-B","seed":50024,"prompt_en":"A service desk has technicians A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 9 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills weld, T2 size 3 skills pack, T3 size 3 skills lift/weld, T4 size 3 skills inspect/lift, T5 size 3 skills pack, T6 size 2 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 9 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills weld, T2 size 3 skills pack, T3 size 3 skills lift/weld, T4 size 3 skills inspect/lift, T5 size 3 skills pack, T6 size 2 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 9,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n }\n 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intersection is the eligibility rule"} +{"problem_id":"ASN-025","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50025,"prompt_en":"A service desk has technicians A1 cap 5 skills weld, A2 cap 6 skills inspect, A3 cap 5 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/pack, T3 size 1 skills inspect/pack, T4 size 2 skills weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 5 skills weld, A2 cap 6 skills inspect, A3 cap 5 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/pack, T3 size 1 skills inspect/pack, T4 size 2 skills weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","weld"],"penalty":39},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","pack"],"penalty":36},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","pack"],"penalty":26},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":10},{"task_id":"T1","agent_id":"A2","cost":11},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A2","cost":12},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A2","cost":18},{"task_id":"T3","agent_id":"A3","cost":12},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":34.0,"gold_bound":34.0,"gold_solution":{"family":"assignment","status":"optimal","objective":34.0,"bound":34.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2d5e70242c82e1c7","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-026","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":50026,"prompt_en":"A service desk has technicians A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills pack/weld, T2 size 2 skills inspect/pack, T3 size 2 skills inspect/pack, T4 size 3 skills lift/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills pack/weld, T2 size 2 skills inspect/pack, T3 size 2 skills inspect/pack, T4 size 3 skills lift/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["pack","weld"],"penalty":32},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["lift","weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":15},{"task_id":"T1","agent_id":"A3","cost":10},{"task_id":"T2","agent_id":"A2","cost":10},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A2","cost":16},{"task_id":"T3","agent_id":"A3","cost":18},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A3","cost":14}]},"gold_status":"optimal","gold_objective":46.0,"gold_bound":46.0,"gold_solution":{"family":"assignment","status":"optimal","objective":46.0,"bound":46.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"9cf7363994177683","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-027","family":"assignment","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-A","seed":50027,"prompt_en":"A service desk has technicians A1 cap 3 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect, T2 size 3 skills inspect, T3 size 1 skills inspect/lift/weld, T4 size 2 skills weld, T5 size 1 skills inspect/weld, T6 size 1 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 3 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect, T2 size 3 skills inspect, T3 size 1 skills inspect/lift/weld, T4 size 2 skills weld, T5 size 1 skills inspect/weld, T6 size 1 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 35\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","lift","weld"],"penalty":34},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["weld"],"penalty":32},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","weld"],"penalty":20},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["inspect","lift"],"penalty":35}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A2","cost":16},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A1","cost":9},{"task_id":"T2","agent_id":"A2","cost":8},{"task_id":"T2","agent_id":"A3","cost":6},{"task_id":"T3","agent_id":"A1","cost":8},{"task_id":"T3","agent_id":"A2","cost":18},{"task_id":"T3","agent_id":"A3","cost":14},{"task_id":"T4","agent_id":"A1","cost":14},{"task_id":"T4","agent_id":"A3","cost":14},{"task_id":"T5","agent_id":"A1","cost":14},{"task_id":"T5","agent_id":"A2","cost":18},{"task_id":"T5","agent_id":"A3","cost":18},{"task_id":"T6","agent_id":"A1","cost":11},{"task_id":"T6","agent_id":"A2","cost":5},{"task_id":"T6","agent_id":"A3","cost":6}]},"gold_status":"optimal","gold_objective":63.0,"gold_bound":63.0,"gold_solution":{"family":"assignment","status":"optimal","objective":63.0,"bound":63.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A1"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"75c4dedc90aa87db","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-028","family":"assignment","split":"test","interactive":false,"difficulty":"hard","language":"en","template_id":"T-B","seed":50028,"prompt_en":"A service desk has technicians A1 cap 4 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 4 skills lift/pack, A4 cap 6 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills inspect/pack, T2 size 1 skills inspect/weld, T3 size 3 skills inspect/lift/weld, T4 size 1 skills inspect/lift/pack, T5 size 1 skills weld, T6 size 2 skills inspect/weld, T7 size 2 skills pack, T8 size 3 skills lift/pack. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 4 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 4 skills lift/pack, A4 cap 6 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills inspect/pack, T2 size 1 skills inspect/weld, T3 size 3 skills inspect/lift/weld, T4 size 1 skills inspect/lift/pack, T5 size 1 skills weld, T6 size 2 skills inspect/weld, T7 size 2 skills pack, T8 size 3 skills lift/pack. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 39\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 4,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["inspect","pack"],"penalty":29},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","weld"],"penalty":40},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift","weld"],"penalty":32},{"task_id":"T4","name":"job-4","size":1,"required":true,"skills":["inspect","lift","pack"],"penalty":28},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["weld"],"penalty":33},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","weld"],"penalty":29},{"task_id":"T7","name":"job-7","size":2,"required":true,"skills":["pack"],"penalty":29},{"task_id":"T8","name":"job-8","size":3,"required":true,"skills":["lift","pack"],"penalty":39}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":4,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":15},{"task_id":"T1","agent_id":"A4","cost":15},{"task_id":"T2","agent_id":"A1","cost":9},{"task_id":"T2","agent_id":"A2","cost":11},{"task_id":"T2","agent_id":"A4","cost":17},{"task_id":"T3","agent_id":"A1","cost":11},{"task_id":"T3","agent_id":"A2","cost":10},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T3","agent_id":"A4","cost":18},{"task_id":"T4","agent_id":"A1","cost":13},{"task_id":"T4","agent_id":"A2","cost":6},{"task_id":"T4","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A4","cost":6},{"task_id":"T5","agent_id":"A1","cost":8},{"task_id":"T5","agent_id":"A4","cost":15},{"task_id":"T6","agent_id":"A1","cost":11},{"task_id":"T6","agent_id":"A2","cost":9},{"task_id":"T6","agent_id":"A4","cost":18},{"task_id":"T7","agent_id":"A2","cost":7},{"task_id":"T7","agent_id":"A3","cost":6},{"task_id":"T7","agent_id":"A4","cost":5},{"task_id":"T8","agent_id":"A2","cost":13},{"task_id":"T8","agent_id":"A3","cost":18},{"task_id":"T8","agent_id":"A4","cost":14}]},"gold_status":"optimal","gold_objective":59.0,"gold_bound":59.0,"gold_solution":{"family":"assignment","status":"optimal","objective":59.0,"bound":59.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A1"},{"task_id":"T6","agent_id":"A2"},{"task_id":"T7","agent_id":"A4"},{"task_id":"T8","agent_id":"A4"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"33e8008ea9f0e332","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-029","family":"assignment","split":"test","interactive":true,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50029,"prompt_en":"A service desk has technicians A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills pack/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills pack/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 25\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","weld"],"penalty":26},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","lift"],"penalty":36},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack"],"penalty":33},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["pack","weld"],"penalty":25}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":15},{"task_id":"T1","agent_id":"A2","cost":14},{"task_id":"T1","agent_id":"A3","cost":8},{"task_id":"T2","agent_id":"A2","cost":7},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A3","cost":10},{"task_id":"T4","agent_id":"A1","cost":13},{"task_id":"T4","agent_id":"A3","cost":12}]},"gold_status":"optimal","gold_objective":34.0,"gold_bound":34.0,"gold_solution":{"family":"assignment","status":"optimal","objective":34.0,"bound":34.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"a37065772aa4dfbf","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-030","family":"assignment","split":"test","interactive":false,"difficulty":"medium","language":"en","template_id":"T-B","seed":50030,"prompt_en":"A service desk has technicians A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 2 skills lift, T4 size 2 skills weld, T5 size 2 skills inspect, T6 size 1 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 2 skills lift, T4 size 2 skills weld, T5 size 2 skills inspect, T6 size 1 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 28\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["inspect","weld"],"penalty":35},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["lift"],"penalty":39},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["weld"],"penalty":22},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["inspect"],"penalty":30},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["inspect","lift"],"penalty":28}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":18},{"task_id":"T1","agent_id":"A2","cost":16},{"task_id":"T1","agent_id":"A3","cost":4},{"task_id":"T2","agent_id":"A1","cost":9},{"task_id":"T2","agent_id":"A2","cost":18},{"task_id":"T2","agent_id":"A3","cost":9},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":4},{"task_id":"T4","agent_id":"A3","cost":15},{"task_id":"T5","agent_id":"A1","cost":8},{"task_id":"T5","agent_id":"A2","cost":6},{"task_id":"T5","agent_id":"A3","cost":4},{"task_id":"T6","agent_id":"A1","cost":15},{"task_id":"T6","agent_id":"A2","cost":5},{"task_id":"T6","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":29.999999999999996,"gold_bound":29.999999999999996,"gold_solution":{"family":"assignment","status":"optimal","objective":29.999999999999996,"bound":29.999999999999996,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"ae3cf299b843c92f","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-031","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50031,"prompt_en":"A service desk has technicians A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills pack/weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack, T4 size 3 skills lift/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills pack/weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack, T4 size 3 skills lift/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 23\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 34\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["pack","weld"],"penalty":23},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack"],"penalty":24},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["lift","weld"],"penalty":34}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":7},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A2","cost":7},{"task_id":"T2","agent_id":"A3","cost":7},{"task_id":"T3","agent_id":"A3","cost":13},{"task_id":"T4","agent_id":"A1","cost":10},{"task_id":"T4","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":37.0,"gold_bound":37.0,"gold_solution":{"family":"assignment","status":"optimal","objective":37.0,"bound":37.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"1b6764eba2517c16","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-032","family":"assignment","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-B","seed":50032,"prompt_en":"A service desk has technicians A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack. Work orders: T1 size 3 skills pack, T2 size 3 skills inspect, T3 size 3 skills pack, T4 size 3 skills weld, T5 size 3 skills inspect, T6 size 3 skills weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack را دارد. سفارش‌ها: T1 size 3 skills pack, T2 size 3 skills inspect, T3 size 3 skills pack, T4 size 3 skills weld, T5 size 3 skills inspect, T6 size 3 skills weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 28\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 1,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["pack"],"penalty":37},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect"],"penalty":37},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack"],"penalty":39},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["weld"],"penalty":27},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["inspect"],"penalty":30},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["weld"],"penalty":28}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":1,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":1,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":1,"skills":["lift","pack"]}],"costs":[{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A1","cost":6},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T3","agent_id":"A2","cost":7},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T5","agent_id":"A1","cost":15},{"task_id":"T5","agent_id":"A2","cost":6},{"task_id":"T6","agent_id":"A1","cost":10}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"assignment","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"2c4f1aa24275210a","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-033","family":"assignment","split":"test","interactive":true,"difficulty":"infeasible","language":"fa","template_id":"T-A","seed":50033,"prompt_en":"A service desk has technicians A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack. Work orders: T1 size 3 skills lift, T2 size 3 skills pack, T3 size 3 skills inspect/lift, T4 size 3 skills inspect/pack, T5 size 3 skills pack, T6 size 3 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack را دارد. سفارش‌ها: T1 size 3 skills lift, T2 size 3 skills pack, T3 size 3 skills inspect/lift, T4 size 3 skills inspect/pack, T5 size 3 skills pack, T6 size 3 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 20\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 1,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["lift"],"penalty":36},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["pack"],"penalty":30},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift"],"penalty":28},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["inspect","pack"],"penalty":34},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["pack"],"penalty":20},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["inspect","lift"],"penalty":20}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":1,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":1,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":1,"skills":["lift","pack"]}],"costs":[{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A2","cost":7},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A1","cost":5},{"task_id":"T3","agent_id":"A2","cost":8},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":14},{"task_id":"T4","agent_id":"A2","cost":10},{"task_id":"T4","agent_id":"A3","cost":8},{"task_id":"T5","agent_id":"A2","cost":7},{"task_id":"T5","agent_id":"A3","cost":11},{"task_id":"T6","agent_id":"A1","cost":9},{"task_id":"T6","agent_id":"A2","cost":18},{"task_id":"T6","agent_id":"A3","cost":17}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"assignment","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"483125be5eebd870","notes":"skill intersection is the eligibility rule"} +{"problem_id":"SCH-001","family":"scheduling","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":75001,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 5 rel 2 due 8, J2 dur 2 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 2 rel 2 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 2, \"due\": 8, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 5 rel 2 due 8, J2 dur 2 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 2 rel 2 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 2, \"due\": 8, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 8,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 20\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":2,"due":8,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":10,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":14,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":2,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":20},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":7},{"job_id":"J2","machine_id":"M1","start":0,"end":2},{"job_id":"J3","machine_id":"M1","start":7,"end":10},{"job_id":"J4","machine_id":"M1","start":10,"end":12}],"message":"OPTIMAL"},"structural_key":"f3b26ff82b5918fb","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-002","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75002,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 5 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 5 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 10, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 24}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 5 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 5 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 10, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 24}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 4,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 19,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 24\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":4,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":5,"release":0,"due":10,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":19,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":24},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":3,"end":8},{"job_id":"J3","machine_id":"M1","start":8,"end":11},{"job_id":"J4","machine_id":"M1","start":11,"end":16}],"message":"OPTIMAL"},"structural_key":"d340539d914c97df","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-003","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75003,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 1 due 6, J2 dur 3 rel 2 due 7, J3 dur 4 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 3 rel 0 due 20, J6 dur 2 rel 0 due 21\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 21, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 26}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 1 due 6, J2 dur 3 rel 2 due 7, J3 dur 4 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 3 rel 0 due 20, J6 dur 2 rel 0 due 21\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 21, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 26}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 7,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 26\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":1,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":3,"release":2,"due":7,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":13,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":20,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":0,"due":21,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":26},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":2,"end":5},{"job_id":"J2","machine_id":"M1","start":3,"end":6},{"job_id":"J3","machine_id":"M2","start":5,"end":9},{"job_id":"J4","machine_id":"M1","start":0,"end":3},{"job_id":"J5","machine_id":"M1","start":6,"end":9},{"job_id":"J6","machine_id":"M2","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"8d93269a62953269","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-004","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":75004,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 3 rel 2 due 10, J3 dur 4 rel 0 due 15, J4 dur 4 rel 0 due 18\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 10, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 18, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 3 rel 2 due 10, J3 dur 4 rel 0 due 15, J4 dur 4 rel 0 due 18\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 10, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 18, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 10,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 18,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 23\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":2,"due":10,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":15,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":18,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":23},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":4,"end":7},{"job_id":"J3","machine_id":"M1","start":11,"end":15},{"job_id":"J4","machine_id":"M1","start":7,"end":11}],"message":"OPTIMAL"},"structural_key":"ab08e0ff4cbe98a0","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-005","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75005,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 5 rel 0 due 6, J2 dur 3 rel 1 due 12, J3 dur 4 rel 2 due 16, J4 dur 2 rel 2 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 5 rel 0 due 6, J2 dur 3 rel 1 due 12, J3 dur 4 rel 2 due 16, J4 dur 2 rel 2 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 12,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":1,"due":12,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":2,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":2,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":5},{"job_id":"J2","machine_id":"M1","start":7,"end":10},{"job_id":"J3","machine_id":"M1","start":10,"end":14},{"job_id":"J4","machine_id":"M1","start":5,"end":7}],"message":"OPTIMAL"},"structural_key":"3a19f6671a25fbea","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-006","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75006,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 5 rel 1 due 11, J3 dur 2 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 5 rel 0 due 21, J6 dur 2 rel 1 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 1, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 0, \"due\": 21, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 5 rel 1 due 11, J3 dur 2 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 5 rel 0 due 21, J6 dur 2 rel 1 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 1, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 0, \"due\": 21, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 11,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 22,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":6,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":5,"release":1,"due":11,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":13,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":17,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":0,"due":21,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":1,"due":22,"weight":2,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":3},{"job_id":"J2","machine_id":"M2","start":5,"end":10},{"job_id":"J3","machine_id":"M1","start":5,"end":7},{"job_id":"J4","machine_id":"M1","start":7,"end":10},{"job_id":"J5","machine_id":"M1","start":0,"end":5},{"job_id":"J6","machine_id":"M2","start":3,"end":5}],"message":"OPTIMAL"},"structural_key":"28f92c4b29421b9e","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-007","family":"scheduling","split":"development","interactive":true,"difficulty":"hard","language":"en","template_id":"D-A","seed":75007,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3, J2->J5). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 5 rel 0 due 11, J3 dur 2 rel 1 due 15, J4 dur 2 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 4 rel 0 due 22, J7 dur 2 rel 1 due 22, J8 dur 3 rel 2 due 25\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 4, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 3, \"release\": 2, \"due\": 25, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 32}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3, J2->J5) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 5 rel 0 due 11, J3 dur 2 rel 1 due 15, J4 dur 2 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 4 rel 0 due 22, J7 dur 2 rel 1 due 22, J8 dur 3 rel 2 due 25\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 4, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 3, \"release\": 2, \"due\": 25, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 32}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 22,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 22,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 25,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 32\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":5,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":1,"due":15,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":17,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":0,"due":17,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":4,"release":0,"due":22,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J7","name":"op-7","duration":2,"release":1,"due":22,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":3,"release":2,"due":25,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":32},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":0,"end":5},{"job_id":"J3","machine_id":"M2","start":4,"end":6},{"job_id":"J4","machine_id":"M2","start":8,"end":10},{"job_id":"J5","machine_id":"M2","start":6,"end":8},{"job_id":"J6","machine_id":"M1","start":5,"end":9},{"job_id":"J7","machine_id":"M2","start":10,"end":12},{"job_id":"J8","machine_id":"M1","start":9,"end":12}],"message":"OPTIMAL"},"structural_key":"050bb292957ce323","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-008","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75008,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 1 due 6, J2 dur 4 rel 0 due 12, J3 dur 4 rel 0 due 15, J4 dur 5 rel 1 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 1, \"due\": 19, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 25}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 1 due 6, J2 dur 4 rel 0 due 12, J3 dur 4 rel 0 due 15, J4 dur 5 rel 1 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 1, \"due\": 19, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 25}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 19,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 25\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":1,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":12,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":1,"due":19,"weight":3,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":25},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":1,"end":5},{"job_id":"J2","machine_id":"M1","start":5,"end":9},{"job_id":"J3","machine_id":"M1","start":9,"end":13},{"job_id":"J4","machine_id":"M1","start":13,"end":18}],"message":"OPTIMAL"},"structural_key":"98f68288cc66b7e8","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-009","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75009,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 2 rel 2 due 6, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 11, J5 dur 5 rel 1 due 18, J6 dur 2 rel 0 due 20\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 2, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 1, \"due\": 18, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 20, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 24}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 2 rel 2 due 6, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 11, J5 dur 5 rel 1 due 18, J6 dur 2 rel 0 due 20\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 2, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 1, \"due\": 18, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 20, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 24}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 18,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 24\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":2,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":11,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":1,"due":18,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":0,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":24},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":2,"end":4},{"job_id":"J3","machine_id":"M1","start":4,"end":7},{"job_id":"J4","machine_id":"M2","start":0,"end":2},{"job_id":"J5","machine_id":"M2","start":4,"end":9},{"job_id":"J6","machine_id":"M2","start":2,"end":4}],"message":"OPTIMAL"},"structural_key":"a82fa38af8e40896","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-010","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":75010,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 5, J2 dur 2 rel 1 due 9, J3 dur 2 rel 0 due 12, J4 dur 4 rel 1 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 1, \"due\": 9, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 5, J2 dur 2 rel 1 due 9, J3 dur 2 rel 0 due 12, J4 dur 4 rel 1 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 1, \"due\": 9, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 5,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 9,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 14,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 20\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":5,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":9,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":12,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":1,"due":14,"weight":3,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":20},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":4,"end":6},{"job_id":"J3","machine_id":"M1","start":10,"end":12},{"job_id":"J4","machine_id":"M1","start":6,"end":10}],"message":"OPTIMAL"},"structural_key":"44defd099664afa8","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-011","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75011,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 4 rel 0 due 7, J3 dur 3 rel 0 due 11, J4 dur 4 rel 0 due 16\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 4 rel 0 due 7, J3 dur 3 rel 0 due 11, J4 dur 4 rel 0 due 16\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 21\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":6,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":7,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":11,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":21},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":2,"end":6},{"job_id":"J3","machine_id":"M1","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":9,"end":13}],"message":"OPTIMAL"},"structural_key":"1f2e26b801fa687e","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-012","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75012,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 6, J2 dur 2 rel 0 due 10, J3 dur 3 rel 1 due 12, J4 dur 3 rel 2 due 15, J5 dur 3 rel 0 due 16, J6 dur 2 rel 2 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 6, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 2, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 25}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 6, J2 dur 2 rel 0 due 10, J3 dur 3 rel 1 due 12, J4 dur 3 rel 2 due 15, J5 dur 3 rel 0 due 16, J6 dur 2 rel 2 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 6, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 2, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 25}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 15,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 19,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 25\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":6,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":10,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":1,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":2,"due":15,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":2,"due":19,"weight":2,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":25},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":0,"end":2},{"job_id":"J3","machine_id":"M2","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":2,"end":5},{"job_id":"J5","machine_id":"M1","start":5,"end":8},{"job_id":"J6","machine_id":"M2","start":4,"end":6}],"message":"OPTIMAL"},"structural_key":"e309923760f6714b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-013","family":"scheduling","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":75013,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 5 rel 2 due 11, J3 dur 4 rel 1 due 14, J4 dur 2 rel 1 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 2, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 5 rel 2 due 11, J3 dur 4 rel 1 due 14, J4 dur 2 rel 1 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 2, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 11,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 14,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 21\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":6,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":5,"release":2,"due":11,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":1,"due":14,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":1,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":21},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":6,"end":11},{"job_id":"J3","machine_id":"M1","start":2,"end":6},{"job_id":"J4","machine_id":"M1","start":11,"end":13}],"message":"OPTIMAL"},"structural_key":"fa5346efc4f12de7","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-014","family":"scheduling","split":"development","interactive":false,"difficulty":"hard","language":"en","template_id":"D-B","seed":75014,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3, J2->J5). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 3, J2 dur 4 rel 1 due 8, J3 dur 4 rel 0 due 11, J4 dur 4 rel 2 due 16, J5 dur 3 rel 0 due 21, J6 dur 3 rel 1 due 23, J7 dur 3 rel 0 due 24, J8 dur 5 rel 0 due 31\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 3, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 8, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 21, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 3, \"release\": 1, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 3, \"release\": 0, \"due\": 24, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 5, \"release\": 0, \"due\": 31, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 36}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3, J2->J5) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 3, J2 dur 4 rel 1 due 8, J3 dur 4 rel 0 due 11, J4 dur 4 rel 2 due 16, J5 dur 3 rel 0 due 21, J6 dur 3 rel 1 due 23, J7 dur 3 rel 0 due 24, J8 dur 5 rel 0 due 31\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 3, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 8, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 21, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 3, \"release\": 1, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 3, \"release\": 0, \"due\": 24, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 5, \"release\": 0, \"due\": 31, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 36}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 3,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 8,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 23,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 24,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 31,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 36\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":3,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":8,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":2,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":21,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":1,"due":23,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J7","name":"op-7","duration":3,"release":0,"due":24,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":5,"release":0,"due":31,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":36},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":3,"end":7},{"job_id":"J3","machine_id":"M1","start":7,"end":11},{"job_id":"J4","machine_id":"M2","start":2,"end":6},{"job_id":"J5","machine_id":"M1","start":11,"end":14},{"job_id":"J6","machine_id":"M2","start":11,"end":14},{"job_id":"J7","machine_id":"M1","start":0,"end":3},{"job_id":"J8","machine_id":"M2","start":6,"end":11}],"message":"OPTIMAL"},"structural_key":"c4077ee842dab620","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-015","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75015,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 4 rel 1 due 11, J3 dur 3 rel 0 due 12, J4 dur 3 rel 1 due 15, J5 dur 3 rel 0 due 20, J6 dur 5 rel 2 due 23\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 11, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 12, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 1, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 2, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 29}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 4 rel 1 due 11, J3 dur 3 rel 0 due 12, J4 dur 3 rel 1 due 15, J5 dur 3 rel 0 due 20, J6 dur 5 rel 2 due 23\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 11, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 12, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 1, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 2, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 29}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 4,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 11,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 23,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 29\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":4,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":11,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":12,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":3,"release":1,"due":15,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":20,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":5,"release":2,"due":23,"weight":4,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":29},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":3,"end":7},{"job_id":"J3","machine_id":"M1","start":7,"end":10},{"job_id":"J4","machine_id":"M2","start":3,"end":6},{"job_id":"J5","machine_id":"M2","start":0,"end":3},{"job_id":"J6","machine_id":"M2","start":6,"end":11}],"message":"OPTIMAL"},"structural_key":"f3cab51cd91813b0","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-016","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":75016,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 2 due 5, J2 dur 3 rel 0 due 10, J3 dur 3 rel 2 due 12, J4 dur 5 rel 0 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 2, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 2, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 2 due 5, J2 dur 3 rel 0 due 10, J3 dur 3 rel 2 due 12, J4 dur 5 rel 0 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 2, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 2, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 5,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 12,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":2,"due":5,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":2,"due":12,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":15,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":2.0,"gold_bound":2.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":2.0,"bound":2.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":3,"end":6},{"job_id":"J2","machine_id":"M1","start":0,"end":3},{"job_id":"J3","machine_id":"M1","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":9,"end":14}],"message":"OPTIMAL"},"structural_key":"77c5ca9a6efec0ce","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-017","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75017,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 3 rel 1 due 7, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 13\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 19}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 3 rel 1 due 7, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 13\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 19}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 7,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 19\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":6,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":1,"due":7,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":13,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":19},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":3,"end":6},{"job_id":"J3","machine_id":"M1","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":9,"end":11}],"message":"OPTIMAL"},"structural_key":"321dcec5bcc2ab1a","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-018","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75018,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 4, J2 dur 4 rel 0 due 10, J3 dur 2 rel 0 due 9, J4 dur 3 rel 2 due 14, J5 dur 4 rel 0 due 17, J6 dur 5 rel 0 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 9, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 14, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 4, \"release\": 0, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 4, J2 dur 4 rel 0 due 10, J3 dur 2 rel 0 due 9, J4 dur 3 rel 2 due 14, J5 dur 4 rel 0 due 17, J6 dur 5 rel 0 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 9, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 14, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 4, \"release\": 0, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 4,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 22,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":4,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":9,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":2,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":0,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J6","name":"op-6","duration":5,"release":0,"due":22,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":4,"end":8},{"job_id":"J3","machine_id":"M2","start":2,"end":4},{"job_id":"J4","machine_id":"M2","start":4,"end":7},{"job_id":"J5","machine_id":"M1","start":0,"end":4},{"job_id":"J6","machine_id":"M1","start":8,"end":13}],"message":"OPTIMAL"},"structural_key":"0a25d991b8ebc99b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-019","family":"scheduling","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":75019,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 5 rel 0 due 7, J2 dur 4 rel 0 due 13, J3 dur 4 rel 1 due 17, J4 dur 2 rel 0 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 5 rel 0 due 7, J2 dur 4 rel 0 due 13, J3 dur 4 rel 1 due 17, J4 dur 2 rel 0 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 17,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 23\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":13,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":1,"due":17,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":23},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":7},{"job_id":"J2","machine_id":"M1","start":7,"end":11},{"job_id":"J3","machine_id":"M1","start":11,"end":15},{"job_id":"J4","machine_id":"M1","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"21a2617ee4fc356c","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-020","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75020,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 1 due 7, J2 dur 4 rel 2 due 8, J3 dur 4 rel 1 due 13, J4 dur 4 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 2, \"due\": 8, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 13, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 1 due 7, J2 dur 4 rel 2 due 8, J3 dur 4 rel 1 due 13, J4 dur 4 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 2, \"due\": 8, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 13, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 8,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 13,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 19,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 23\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":1,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":2,"due":8,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":1,"due":13,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":19,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":23},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":1,"end":4},{"job_id":"J2","machine_id":"M1","start":4,"end":8},{"job_id":"J3","machine_id":"M1","start":8,"end":12},{"job_id":"J4","machine_id":"M1","start":12,"end":16}],"message":"OPTIMAL"},"structural_key":"76ab27078c9e56ec","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-021","family":"scheduling","split":"test","interactive":false,"difficulty":"hard","language":"fa","template_id":"T-A","seed":75021,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 3 rel 0 due 7, J2 dur 2 rel 0 due 9, J3 dur 2 rel 0 due 9, J4 dur 5 rel 0 due 16, J5 dur 4 rel 2 due 20, J6 dur 4 rel 0 due 23, J7 dur 3 rel 2 due 27, J8 dur 2 rel 0 due 26. Precedence: J1->J3, J2->J5. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 3 rel 0 due 7, J2 dur 2 rel 0 due 9, J3 dur 2 rel 0 due 9, J4 dur 5 rel 0 due 16, J5 dur 4 rel 2 due 20, J6 dur 4 rel 0 due 23, J7 dur 3 rel 2 due 27, J8 dur 2 rel 0 due 26. تقدم: J1->J3, J2->J5. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 16,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 23,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 27,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 26,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 33\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":7,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":9,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":9,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":16,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":2,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J6","name":"op-6","duration":4,"release":0,"due":23,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J7","name":"op-7","duration":3,"release":2,"due":27,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":2,"release":0,"due":26,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":33},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":2,"end":5},{"job_id":"J2","machine_id":"M2","start":0,"end":2},{"job_id":"J3","machine_id":"M1","start":6,"end":8},{"job_id":"J4","machine_id":"M2","start":8,"end":13},{"job_id":"J5","machine_id":"M1","start":2,"end":6},{"job_id":"J6","machine_id":"M1","start":8,"end":12},{"job_id":"J7","machine_id":"M2","start":5,"end":8},{"job_id":"J8","machine_id":"M1","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"88a4981fddb98a2b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-022","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":75022,"prompt_en":"A shop has machines M1. Jobs: J1 dur 5 rel 0 due 9, J2 dur 3 rel 0 due 10, J3 dur 4 rel 2 due 13, J4 dur 2 rel 1 due 17. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 5 rel 0 due 9, J2 dur 3 rel 0 due 10, J3 dur 4 rel 2 due 13, J4 dur 2 rel 1 due 17. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 13,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":9,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":2,"due":13,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":1,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":3,"end":8},{"job_id":"J2","machine_id":"M1","start":0,"end":3},{"job_id":"J3","machine_id":"M1","start":8,"end":12},{"job_id":"J4","machine_id":"M1","start":12,"end":14}],"message":"OPTIMAL"},"structural_key":"fc27c47c78ea227c","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-023","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":75023,"prompt_en":"A shop has machines M1. Jobs: J1 dur 3 rel 0 due 7, J2 dur 2 rel 1 due 6, J3 dur 2 rel 0 due 10, J4 dur 2 rel 2 due 11. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 3 rel 0 due 7, J2 dur 2 rel 1 due 6, J3 dur 2 rel 0 due 10, J4 dur 2 rel 2 due 11. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 17\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":7,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":10,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":2,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":17},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":4,"end":7},{"job_id":"J2","machine_id":"M1","start":2,"end":4},{"job_id":"J3","machine_id":"M1","start":0,"end":2},{"job_id":"J4","machine_id":"M1","start":7,"end":9}],"message":"OPTIMAL"},"structural_key":"5dfdc5a6705389ef","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-024","family":"scheduling","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":75024,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 5 rel 2 due 7, J2 dur 3 rel 2 due 11, J3 dur 2 rel 0 due 14, J4 dur 3 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 5 rel 0 due 24. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 5 rel 2 due 7, J2 dur 3 rel 2 due 11, J3 dur 2 rel 0 due 14, J4 dur 3 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 5 rel 0 due 24. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 11,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 24,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":2,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":3,"release":2,"due":11,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":5,"release":0,"due":24,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":2,"end":7},{"job_id":"J2","machine_id":"M2","start":7,"end":10},{"job_id":"J3","machine_id":"M1","start":8,"end":10},{"job_id":"J4","machine_id":"M1","start":0,"end":3},{"job_id":"J5","machine_id":"M2","start":0,"end":2},{"job_id":"J6","machine_id":"M1","start":3,"end":8}],"message":"OPTIMAL"},"structural_key":"1a960892242a07ff","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-025","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":75025,"prompt_en":"A shop has machines M1. Jobs: J1 dur 4 rel 1 due 5, J2 dur 4 rel 0 due 12, J3 dur 2 rel 1 due 12, J4 dur 2 rel 0 due 14. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 4 rel 1 due 5, J2 dur 4 rel 0 due 12, J3 dur 2 rel 1 due 12, J4 dur 2 rel 0 due 14. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 5,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 12,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 20\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":1,"due":5,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":1,"due":12,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":20},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":1,"end":5},{"job_id":"J2","machine_id":"M1","start":5,"end":9},{"job_id":"J3","machine_id":"M1","start":9,"end":11},{"job_id":"J4","machine_id":"M1","start":11,"end":13}],"message":"OPTIMAL"},"structural_key":"754a69c12ebd799b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-026","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":75026,"prompt_en":"A shop has machines M1. Jobs: J1 dur 5 rel 0 due 9, J2 dur 2 rel 1 due 10, J3 dur 4 rel 0 due 14, J4 dur 2 rel 0 due 15. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 5 rel 0 due 9, J2 dur 2 rel 1 due 10, J3 dur 4 rel 0 due 14, J4 dur 2 rel 0 due 15. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 10,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 21\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":9,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":10,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":15,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":21},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":4,"end":9},{"job_id":"J2","machine_id":"M1","start":2,"end":4},{"job_id":"J3","machine_id":"M1","start":9,"end":13},{"job_id":"J4","machine_id":"M1","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"cec5818c37927030","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-027","family":"scheduling","split":"test","interactive":true,"difficulty":"medium","language":"fa","template_id":"T-A","seed":75027,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 3 rel 0 due 5, J2 dur 2 rel 1 due 8, J3 dur 3 rel 0 due 10, J4 dur 4 rel 1 due 14, J5 dur 4 rel 0 due 20, J6 dur 3 rel 0 due 22. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 3 rel 0 due 5, J2 dur 2 rel 1 due 8, J3 dur 3 rel 0 due 10, J4 dur 4 rel 1 due 14, J5 dur 4 rel 0 due 20, J6 dur 3 rel 0 due 22. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 5,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 8,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 22,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 27\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":5,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":8,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":10,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":4,"release":1,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":0,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":0,"due":22,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":27},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":1,"end":3},{"job_id":"J3","machine_id":"M1","start":3,"end":6},{"job_id":"J4","machine_id":"M2","start":6,"end":10},{"job_id":"J5","machine_id":"M1","start":6,"end":10},{"job_id":"J6","machine_id":"M2","start":3,"end":6}],"message":"OPTIMAL"},"structural_key":"94894e246dcfd2a7","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-028","family":"scheduling","split":"test","interactive":false,"difficulty":"hard","language":"en","template_id":"T-B","seed":75028,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 5 rel 0 due 9, J2 dur 2 rel 0 due 8, J3 dur 2 rel 0 due 12, J4 dur 4 rel 0 due 17, J5 dur 5 rel 0 due 20, J6 dur 3 rel 2 due 22, J7 dur 4 rel 0 due 26, J8 dur 4 rel 2 due 32. Precedence: J1->J3, J2->J5. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 5 rel 0 due 9, J2 dur 2 rel 0 due 8, J3 dur 2 rel 0 due 12, J4 dur 4 rel 0 due 17, J5 dur 5 rel 0 due 20, J6 dur 3 rel 2 due 22, J7 dur 4 rel 0 due 26, J8 dur 4 rel 2 due 32. تقدم: J1->J3, J2->J5. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 8,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 22,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 26,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 32,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 37\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":9,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":8,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":17,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":0,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":2,"due":22,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J7","name":"op-7","duration":4,"release":0,"due":26,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":4,"release":2,"due":32,"weight":1,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":37},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":4,"end":9},{"job_id":"J2","machine_id":"M2","start":0,"end":2},{"job_id":"J3","machine_id":"M1","start":9,"end":11},{"job_id":"J4","machine_id":"M1","start":0,"end":4},{"job_id":"J5","machine_id":"M2","start":6,"end":11},{"job_id":"J6","machine_id":"M2","start":11,"end":14},{"job_id":"J7","machine_id":"M1","start":11,"end":15},{"job_id":"J8","machine_id":"M2","start":2,"end":6}],"message":"OPTIMAL"},"structural_key":"786d201a96694b14","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-029","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":75029,"prompt_en":"A shop has machines M1. Jobs: J1 dur 4 rel 2 due 6, J2 dur 2 rel 2 due 9, J3 dur 4 rel 2 due 14, J4 dur 4 rel 2 due 15. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 4 rel 2 due 6, J2 dur 2 rel 2 due 9, J3 dur 4 rel 2 due 14, J4 dur 4 rel 2 due 15. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 6,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 9,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 14,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 15,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":2,"due":6,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":2,"due":9,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":2,"due":14,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":2,"due":15,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":2.0,"gold_bound":2.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":2.0,"bound":2.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":6},{"job_id":"J2","machine_id":"M1","start":6,"end":8},{"job_id":"J3","machine_id":"M1","start":8,"end":12},{"job_id":"J4","machine_id":"M1","start":12,"end":16}],"message":"OPTIMAL"},"structural_key":"c1def371d6464506","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-030","family":"scheduling","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":75030,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 2 rel 2 due 4, J2 dur 4 rel 0 due 10, J3 dur 4 rel 0 due 11, J4 dur 3 rel 0 due 15, J5 dur 4 rel 1 due 21, J6 dur 4 rel 2 due 22. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 2 rel 2 due 4, J2 dur 4 rel 0 due 10, J3 dur 4 rel 0 due 11, J4 dur 3 rel 0 due 15, J5 dur 4 rel 1 due 21, J6 dur 4 rel 2 due 22. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 4,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 21,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 22,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 29\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":2,"due":4,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":1,"due":21,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":4,"release":2,"due":22,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":29},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":4},{"job_id":"J2","machine_id":"M2","start":0,"end":4},{"job_id":"J3","machine_id":"M2","start":4,"end":8},{"job_id":"J4","machine_id":"M1","start":8,"end":11},{"job_id":"J5","machine_id":"M2","start":8,"end":12},{"job_id":"J6","machine_id":"M1","start":4,"end":8}],"message":"OPTIMAL"},"structural_key":"d614e5ebef3872d6","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-031","family":"scheduling","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-A","seed":75031,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 3 rel 0 due 2 hard, J2 dur 5 rel 1 due 5 hard, J3 dur 2 rel 0 due 14, J4 dur 4 rel 0 due 18, J5 dur 5 rel 0 due 21, J6 dur 3 rel 0 due 26. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 3 rel 0 due 2 hard, J2 dur 5 rel 1 due 5 hard, J3 dur 2 rel 0 due 14, J4 dur 4 rel 0 due 18, J5 dur 5 rel 0 due 21, J6 dur 3 rel 0 due 26. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 2,\n \"weight\": 4,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 5,\n \"weight\": 1,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 18,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 26,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 30\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":2,"weight":4,"hard_due":true,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":5,"release":1,"due":5,"weight":1,"hard_due":true,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":18,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":0,"due":21,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":0,"due":26,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":30},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"scheduling","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"1a1b4b4a5a920dbe","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-032","family":"scheduling","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-B","seed":75032,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 2 rel 1 due 2 hard, J2 dur 4 rel 1 due 4 hard, J3 dur 3 rel 2 due 12, J4 dur 2 rel 0 due 13, J5 dur 2 rel 1 due 15, J6 dur 3 rel 1 due 18. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 2 rel 1 due 2 hard, J2 dur 4 rel 1 due 4 hard, J3 dur 3 rel 2 due 12, J4 dur 2 rel 0 due 13, J5 dur 2 rel 1 due 15, J6 dur 3 rel 1 due 18. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 2,\n \"weight\": 2,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 4,\n \"weight\": 2,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 18,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 24\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":1,"due":2,"weight":2,"hard_due":true,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":4,"weight":2,"hard_due":true,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":2,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":13,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":1,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":1,"due":18,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":24},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"scheduling","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"56a2b20635ec8a65","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-033","family":"scheduling","split":"test","interactive":true,"difficulty":"infeasible","language":"fa","template_id":"T-A","seed":75033,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 4 rel 0 due 3 hard, J2 dur 4 rel 1 due 4 hard, J3 dur 3 rel 0 due 12, J4 dur 5 rel 0 due 17, J5 dur 2 rel 1 due 19, J6 dur 2 rel 0 due 21. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 4 rel 0 due 3 hard, J2 dur 4 rel 1 due 4 hard, J3 dur 3 rel 0 due 12, J4 dur 5 rel 0 due 17, J5 dur 2 rel 1 due 19, J6 dur 2 rel 0 due 21. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 3,\n \"weight\": 2,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 4,\n \"weight\": 4,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 19,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":3,"weight":2,"hard_due":true,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":4,"weight":4,"hard_due":true,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":12,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":1,"due":19,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J6","name":"op-6","duration":2,"release":0,"due":21,"weight":4,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"scheduling","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"dde60fb92fe4b1f3","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} diff --git a/data/protocol.md b/data/protocol.md new file mode 100644 index 0000000000000000000000000000000000000000..ff47013be4ad9a79eaef15e1ef9594474afb3640 --- /dev/null +++ b/data/protocol.md @@ -0,0 +1,13 @@ +# ORBench reproduction protocol v1 + +Seed: 25. Code version: 0.1.0. Solver: OR-Tools CP-SAT, 1 thread, 6–8 seconds. + +1. Generate the catalog with `python scripts/build_artifacts.py`. +2. Each problem stores `schema_payload`, bilingual prompts, `gold_status`, `gold_objective`, and `gold_solution`. +3. Evaluated methods: `structured-solver`, `heuristic`, `json-extractor+solver`, `template-extractor+solver`, `naive-direct`. +4. Listed but not run: `Qwen/Qwen3-4B-Instruct-2507`, `Qwen/Qwen3.8-27B`, `moonshotai/Kimi-K3`, `zai-org/GLM-5.3`, `deepseek-ai/DeepSeek-V4.1-Flash`. Cells are `not_evaluated`. +5. Gap = max(0, (method_obj − gold_obj) / max(1, |gold_obj|)) only if gold status is optimal and the method plan is feasible. +6. Paid APIs stay off. Do not substitute a second paid provider when the first is missing. +7. Synthetic results in this dataset are not customer data. + +Run `pytest tests/test_pipeline.py` after generation. A passing suite is the acceptance check for constraint validation, split hygiene, and honest unevaluated cells. diff --git a/data/results.jsonl b/data/results.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..a41bd3c4ddeb6cf6db49e642d5300e0bfade4fea --- /dev/null +++ b/data/results.jsonl @@ -0,0 +1,1000 @@ +{"problem_id":"INV-001","method_id":"structured-solver","method_kind":"structured-solver","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":159.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0038488999707624316,"cost_usd":0.0,"violated":[],"notes":"schema entered the solver without an LLM","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"heuristic","method_kind":"heuristic","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"heuristic","feasible":true,"optimality_gap":0.11949685534591195,"objective":178.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.000054100004490464926,"cost_usd":0.0,"violated":[],"notes":"lot-for-lot pack-rounded","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"json-extractor+solver","method_kind":"text-to-schema","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":159.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.003551199974026531,"cost_usd":0.0,"violated":[],"notes":"JSON extracted from the prompt","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"template-extractor+solver","method_kind":"text-to-schema","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":159.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0035841999924741685,"cost_usd":0.0,"violated":[],"notes":"labeled fields or SCHEMA_BEGIN block","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"naive-direct","method_kind":"direct-answer","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"invalid","feasible":false,"optimality_gap":null,"objective":211.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.00002640002639964223,"cost_usd":0.0,"violated":["pack","budget"],"notes":"naive-direct: order raw demand, ignore pack/budget/capacity","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"Qwen/Qwen3-4B-Instruct-2507","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"Paid/local LLM inference is off. No batch was run.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"Qwen/Qwen3.8-27B","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"Not hosted on this CPU Space. No API batch.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"moonshotai/Kimi-K3","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"API optional and disabled. Not evaluated.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"zai-org/GLM-5.3","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"API optional and disabled. Not evaluated.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"deepseek-ai/DeepSeek-V4.1-Flash","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"API optional and disabled. Not evaluated.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"structured-solver","method_kind":"structured-solver","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":93.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.006716199975926429,"cost_usd":0.0,"violated":[],"notes":"schema entered the solver without an LLM","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"heuristic","method_kind":"heuristic","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"heuristic","feasible":true,"optimality_gap":0.1935483870967742,"objective":111.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.000055100012104958296,"cost_usd":0.0,"violated":[],"notes":"lot-for-lot pack-rounded","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"json-extractor+solver","method_kind":"text-to-schema","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":93.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.006304699985776097,"cost_usd":0.0,"violated":[],"notes":"JSON extracted from the prompt","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"template-extractor+solver","method_kind":"text-to-schema","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":93.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.006902099994476885,"cost_usd":0.0,"violated":[],"notes":"labeled fields or SCHEMA_BEGIN block","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"naive-direct","method_kind":"direct-answer","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"invalid","feasible":false,"optimality_gap":null,"objective":149.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.00004730001091957092,"cost_usd":0.0,"violated":["pack","pack","pack","pack"],"notes":"naive-direct: order raw demand, ignore pack/budget/capacity","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"Qwen/Qwen3-4B-Instruct-2507","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":93.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"Paid/local LLM inference is off. 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Not evaluated.","precomputed":true,"family":"scheduling","split":"test","language":"fa","difficulty":"infeasible"} diff --git a/data/sample_preview.json b/data/sample_preview.json new file mode 100644 index 0000000000000000000000000000000000000000..981735ce13efbc2b732655ce3352031a70691292 --- /dev/null +++ b/data/sample_preview.json @@ -0,0 +1,17 @@ +{ + "run_id": "orbench-eccc1a511a", + "status": "optimal", + "kpis": { + "n_problems": 100, + "structured_feasible": 0.92, + "heuristic_gap": 0.031919404673584915, + "template_fidelity": 0.6, + "n_methods_evaluated": 5, + "n_methods_listed": 10 + }, + "kpi_html": "

Problems in view

100

interactive subset or filtered catalog

Structured-solver feasible

92%

share of valid plans after independent checks

Heuristic mean gap

3.2%

only where gold status is proven optimal

Template fidelity

60%

atomic constraint facts recovered from text

Methods evaluated

5/10

evaluated / listed — unevaluated is not zero

", + "precomputed": true, + "n_problems": 100, + "n_eval_rows": 1000, + "interactive": "INV-001" +} \ No newline at end of file diff --git a/data/splits.json b/data/splits.json new file mode 100644 index 0000000000000000000000000000000000000000..1738082edae4893beaa89f49583619ec633a57b2 --- /dev/null +++ b/data/splits.json @@ -0,0 +1,128 @@ +{ + "development": [ + "INV-001", + "INV-002", + "INV-003", + "INV-004", + "INV-005", + "INV-006", + "INV-007", + "INV-008", + "INV-009", + "INV-010", + "INV-011", + "INV-012", + "INV-013", + "INV-014", + "INV-015", + "INV-016", + "INV-017", + "INV-018", + "INV-019", + "INV-020", + "ASN-001", + "ASN-002", + "ASN-003", + "ASN-004", + "ASN-005", + "ASN-006", + "ASN-007", + "ASN-008", + "ASN-009", + "ASN-010", + "ASN-011", + "ASN-012", + "ASN-013", + "ASN-014", + "ASN-015", + "ASN-016", + "ASN-017", + "ASN-018", + "ASN-019", + "ASN-020", + "SCH-001", + "SCH-002", + "SCH-003", + "SCH-004", + "SCH-005", + "SCH-006", + "SCH-007", + "SCH-008", + "SCH-009", + "SCH-010", + "SCH-011", + "SCH-012", + "SCH-013", + "SCH-014", + "SCH-015", + "SCH-016", + "SCH-017", + "SCH-018", + "SCH-019", + "SCH-020" + ], + "test": [ + "INV-021", + "INV-022", + "INV-023", + "INV-024", + "INV-025", + "INV-026", + "INV-027", + "INV-028", + "INV-029", + "INV-030", + "INV-031", + "INV-032", + "INV-033", + "INV-034", + "ASN-021", + "ASN-022", + "ASN-023", + "ASN-024", + "ASN-025", + "ASN-026", + "ASN-027", + "ASN-028", + "ASN-029", + "ASN-030", + "ASN-031", + "ASN-032", + "ASN-033", + "SCH-021", + "SCH-022", + "SCH-023", + "SCH-024", + "SCH-025", + "SCH-026", + "SCH-027", + "SCH-028", + "SCH-029", + "SCH-030", + "SCH-031", + "SCH-032", + "SCH-033" + ], + "interactive": [ + "INV-001", + "INV-008", + "INV-014", + "INV-021", + "INV-028", + "INV-031", + "INV-034", + "ASN-001", + "ASN-006", + "ASN-012", + "ASN-018", + "ASN-024", + "ASN-029", + "ASN-033", + "SCH-001", + "SCH-007", + "SCH-013", + "SCH-019", + "SCH-027", + "SCH-033" + ] +} \ No newline at end of file diff --git a/demo/.gitattributes b/demo/.gitattributes new file mode 100644 index 0000000000000000000000000000000000000000..9174e16e4139bd5eb0a540a3c342b05538b8442e --- /dev/null +++ b/demo/.gitattributes @@ -0,0 +1,8 @@ +* text=auto eol=lf +*.py text eol=lf +*.md text eol=lf +*.csv text eol=lf +*.json text eol=lf +*.jsonl text eol=lf +*.html text eol=lf +*.txt text eol=lf diff --git a/demo/.gitignore b/demo/.gitignore new file mode 100644 index 0000000000000000000000000000000000000000..4a6a3b2a35f6e1d07ecce477de82571e69c6995a --- /dev/null +++ b/demo/.gitignore @@ -0,0 +1,6 @@ +__pycache__/ +.pytest_cache/ +.venv/ +*.pyc +.gradio/ +tmp/ diff --git a/demo/README.md b/demo/README.md new file mode 100644 index 0000000000000000000000000000000000000000..1df9490fa5c768d543d8c4bbff30915b55922514 --- /dev/null +++ b/demo/README.md @@ -0,0 +1,55 @@ +--- +title: ORBench Solver and Agent Benchmark +emoji: 🧪 +colorFrom: indigo +colorTo: purple +sdk: gradio +sdk_version: 6.15.1 +app_file: app.py +fullWidth: true +python_version: "3.12" +short_description: Compare OR solvers and agents on 100 small problems +pinned: true +license: apache-2.0 +tags: + - model-benchmarking + - operations-research + - structured-generation + - evaluation + - data-visualization +datasets: + - AriaAICompany/or-bench-problems +--- + +# ORBench — Solver and Agent Decision Benchmark + +**Aria AI** research prototype. Teams want to know whether a new model can recover constraints and produce a *valid* decision. A fluent paragraph is not a feasible plan. The numeric validator is the judge. + +The MVP is 100 small synthetic instances from inventory, assignment, and scheduling, with a 60/40 development–test split and 20 interactive samples. Three comparison paths are recorded: structured form + CP-SAT, text → schema → solver, and a fixed heuristic. A naive direct answer is included only as a labeled benchmark, not as an operational planner. + +## What you can do + +1. Load one of the 20 interactive problems (English or Persian). +2. Compare CP-SAT, lot-for-lot / greedy / EDD, JSON extraction, template extraction, and a naive direct answer. +3. Hide a hard constraint in the prompt and watch fidelity drop. +4. Filter the recorded 100-problem table by family, split, language, or difficulty. +5. Download the comparison CSV and the JSON report. + +CPU only. No paid API. Named Hub models (Qwen, Kimi, GLM, DeepSeek) stay **not_evaluated**. That cell is not a zero and not a rank. + +## Hosting + +- Live app: this Space (`alirezaaminzadeh/or-bench` if organization Gradio quota is 0). +- Organization card: [AriaAICompany/or-bench](https://huggingface.co/spaces/AriaAICompany/or-bench). +- Dataset: [AriaAICompany/or-bench-problems](https://huggingface.co/datasets/AriaAICompany/or-bench-problems). +- Collection: [Aria AI — OR + LLM Evaluation](https://huggingface.co/collections/AriaAICompany/aria-ai-or-llm-evaluation). + +## Persian + +اوربنچ روش‌های ساخت تصمیم را روی مسئله‌های کوچک موجودی، تخصیص و زمان‌بندی مقایسه می‌کند. داور validator عددی است. خانه مدل اجرا‌نشده «ارزیابی نشده» است، نه صفر. + +## Links + +- [AriaAICompany](https://huggingface.co/AriaAICompany) +- [aria-ai.ir](https://aria-ai.ir/) +- Roadmap project 25 of 25 diff --git a/demo/app.py b/demo/app.py new file mode 100644 index 0000000000000000000000000000000000000000..f9b0a16f136898f16b20d83a851114a23f09c2d3 --- /dev/null +++ b/demo/app.py @@ -0,0 +1,8 @@ +import gradio as gr + +from src.ui import CSS, build_demo + +demo = build_demo() + +if __name__ == "__main__": + demo.launch(theme=gr.themes.Soft(primary_hue="indigo", secondary_hue="purple"), css=CSS) diff --git a/demo/examples/leaderboard.csv b/demo/examples/leaderboard.csv new file mode 100644 index 0000000000000000000000000000000000000000..da5c871df63efc150667ce9f2b5fe5b424d1816c --- /dev/null +++ b/demo/examples/leaderboard.csv @@ -0,0 +1,11 @@ +method_id,evaluated,n,parse_rate,feasible_rate,infeasible_agreement,mean_gap,mean_fidelity,mean_seconds,mean_cost_usd,n_optimal +heuristic,True,100,1.0,0.91,0.0,0.031919404673584915,1.0,7.628599880263209e-05,0.0,0 +json-extractor+solver,True,100,1.0,0.92,1.0,2.613101900343095e-18,1.0,0.004290478996699676,0.0,92 +naive-direct,True,100,1.0,0.22,0.0,0.0,1.0,4.173900291789323e-05,0.0,0 +structured-solver,True,100,1.0,0.92,1.0,2.613101900343095e-18,1.0,0.004329786997986957,0.0,92 +template-extractor+solver,True,100,0.6,0.6,0.0,2.033026425636911e-18,0.6,0.0030710569996153935,0.0,60 +Qwen/Qwen3-4B-Instruct-2507,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated +Qwen/Qwen3.8-27B,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated +deepseek-ai/DeepSeek-V4.1-Flash,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated +moonshotai/Kimi-K3,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated +zai-org/GLM-5.3,False,100,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated,not_evaluated diff --git a/demo/examples/problems.jsonl b/demo/examples/problems.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..e65cd18f38cfd6d5607922547f2ef5ef7ace10c6 --- /dev/null +++ b/demo/examples/problems.jsonl @@ -0,0 +1,100 @@ +{"problem_id":"INV-001","family":"inventory","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":25001,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 192 currency units. Storage holds at most 19 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 192\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=6,4,6 pack=1 cost=9 hold=1 short=8 stock=2\nSKU S2 demand=2,7,2 pack=2 cost=5 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 192, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 4, 6], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 7, 2], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 192 واحد پول و ظرفیت انبار 19 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 192\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=6,4,6 pack=1 cost=9 hold=1 short=8 stock=2\nSKU S2 demand=2,7,2 pack=2 cost=5 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 192, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 4, 6], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 7, 2], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 192,\n \"warehouse_capacity\": 19,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 4,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 8,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 7,\n 2\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":192,"warehouse_capacity":19,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,4,6],"initial_stock":2,"unit_cost":9,"holding_cost":1,"shortage_cost":8,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,7,2],"initial_stock":2,"unit_cost":5,"holding_cost":1,"shortage_cost":7,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":159.0,"gold_bound":159.0,"gold_solution":{"family":"inventory","status":"optimal","objective":159.0,"bound":159.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"c064f38a5aa2b27c","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-002","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":25002,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 111 currency units. Storage holds at most 19 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 111\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,3 pack=3 cost=4 hold=3 short=9 stock=2\nSKU S2 demand=7,4,3 pack=2 cost=4 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 111, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 3], \"initial_stock\": 2, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 111 واحد پول و ظرفیت انبار 19 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 111\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,3 pack=3 cost=4 hold=3 short=9 stock=2\nSKU S2 demand=7,4,3 pack=2 cost=4 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 111, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 3], \"initial_stock\": 2, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 111,\n \"warehouse_capacity\": 19,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 4,\n 3\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 4,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 7,\n 4,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 4,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":111,"warehouse_capacity":19,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,4,3],"initial_stock":2,"unit_cost":4,"holding_cost":3,"shortage_cost":9,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[7,4,3],"initial_stock":3,"unit_cost":4,"holding_cost":3,"shortage_cost":8,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":93.0,"gold_bound":93.0,"gold_solution":{"family":"inventory","status":"optimal","objective":93.0,"bound":93.0,"orders":[{"sku_id":"S1","period":1,"qty":3},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":4},{"sku_id":"S2","period":2,"qty":4},{"sku_id":"S2","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"5c4c80b9b28d8fdd","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-003","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"en","template_id":"D-C","seed":25003,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 311 currency units. Storage holds at most 31 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 311\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=2,6,6 pack=1 cost=8 hold=3 short=14 stock=2\nSKU S2 demand=8,3,3 pack=1 cost=9 hold=3 short=12 stock=3\nSKU S3 demand=7,8,6 pack=2 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 311, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 6, 6], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 3, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 6], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 311 واحد پول و ظرفیت انبار 31 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 311\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=2,6,6 pack=1 cost=8 hold=3 short=14 stock=2\nSKU S2 demand=8,3,3 pack=1 cost=9 hold=3 short=12 stock=3\nSKU S3 demand=7,8,6 pack=2 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 311, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 6, 6], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 3, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 6], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 311,\n \"warehouse_capacity\": 31,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 6,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 3,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 8,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":311,"warehouse_capacity":31,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,6,6],"initial_stock":2,"unit_cost":8,"holding_cost":3,"shortage_cost":14,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,3,3],"initial_stock":3,"unit_cost":9,"holding_cost":3,"shortage_cost":12,"pack_size":1,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,8,6],"initial_stock":2,"unit_cost":5,"holding_cost":3,"shortage_cost":11,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":296.0,"gold_bound":296.0,"gold_solution":{"family":"inventory","status":"optimal","objective":296.0,"bound":296.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":5},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3},{"sku_id":"S3","period":1,"qty":4},{"sku_id":"S3","period":2,"qty":8},{"sku_id":"S3","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"b8ded0d56a7c873c","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-004","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":25004,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 208 currency units. Storage holds at most 21 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 208\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=3,3,6 pack=3 cost=5 hold=2 short=13 stock=0\nSKU S2 demand=2,5,7 pack=1 cost=9 hold=3 short=14 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 208, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 3, 6], \"initial_stock\": 0, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 5, 7], \"initial_stock\": 0, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 208 واحد پول و ظرفیت انبار 21 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 208\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=3,3,6 pack=3 cost=5 hold=2 short=13 stock=0\nSKU S2 demand=2,5,7 pack=1 cost=9 hold=3 short=14 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 208, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 3, 6], \"initial_stock\": 0, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 5, 7], \"initial_stock\": 0, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 208,\n \"warehouse_capacity\": 21,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 3,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 5,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 5,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":208,"warehouse_capacity":21,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,3,6],"initial_stock":0,"unit_cost":5,"holding_cost":2,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,5,7],"initial_stock":0,"unit_cost":9,"holding_cost":3,"shortage_cost":14,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":186.0,"gold_bound":186.0,"gold_solution":{"family":"inventory","status":"optimal","objective":186.0,"bound":186.0,"orders":[{"sku_id":"S1","period":1,"qty":3},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":2},{"sku_id":"S2","period":2,"qty":5},{"sku_id":"S2","period":3,"qty":7}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"224e408bade9beae","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-005","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":25005,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 224 currency units. Storage holds at most 28 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 224\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=6,5,8 pack=3 cost=6 hold=3 short=13 stock=2\nSKU S2 demand=6,7,6 pack=3 cost=6 hold=2 short=6 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 224, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 5, 8], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 7, 6], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 224 واحد پول و ظرفیت انبار 28 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 224\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=6,5,8 pack=3 cost=6 hold=3 short=13 stock=2\nSKU S2 demand=6,7,6 pack=3 cost=6 hold=2 short=6 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 224, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 5, 8], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 7, 6], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 224,\n \"warehouse_capacity\": 28,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 5,\n 8\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 7,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":224,"warehouse_capacity":28,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,5,8],"initial_stock":2,"unit_cost":6,"holding_cost":3,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,7,6],"initial_stock":3,"unit_cost":6,"holding_cost":2,"shortage_cost":6,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":232.99999999999997,"gold_bound":232.99999999999997,"gold_solution":{"family":"inventory","status":"optimal","objective":232.99999999999997,"bound":232.99999999999997,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":9},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":9},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"df2f98c85b303667","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-006","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":25006,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 336 currency units. Storage holds at most 37 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 336\nCAPACITY: 37\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,2 pack=2 cost=9 hold=3 short=7 stock=1\nSKU S2 demand=6,4,8 pack=3 cost=6 hold=2 short=9 stock=1\nSKU S3 demand=5,3,4 pack=3 cost=6 hold=2 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 336, \"warehouse_capacity\": 37, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 4, 8], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [5, 3, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 336 واحد پول و ظرفیت انبار 37 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 336\nCAPACITY: 37\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,2 pack=2 cost=9 hold=3 short=7 stock=1\nSKU S2 demand=6,4,8 pack=3 cost=6 hold=2 short=9 stock=1\nSKU S3 demand=5,3,4 pack=3 cost=6 hold=2 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 336, \"warehouse_capacity\": 37, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 4, 8], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [5, 3, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 336,\n \"warehouse_capacity\": 37,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 8,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 4,\n 8\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 9,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 5,\n 3,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 11,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":336,"warehouse_capacity":37,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,8,2],"initial_stock":1,"unit_cost":9,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,4,8],"initial_stock":1,"unit_cost":6,"holding_cost":2,"shortage_cost":9,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[5,3,4],"initial_stock":2,"unit_cost":6,"holding_cost":2,"shortage_cost":11,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":280.0,"gold_bound":280.0,"gold_solution":{"family":"inventory","status":"optimal","objective":280.0,"bound":280.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":3},{"sku_id":"S3","period":2,"qty":3},{"sku_id":"S3","period":3,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"37b860c2e403d2c5","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-007","family":"inventory","split":"development","interactive":false,"difficulty":"hard","language":"en","template_id":"D-A","seed":25007,"prompt_en":"A B2B warehouse plans 4 weeks for 4 SKUs: S1 (bearing), S2 (seal), S3 (gasket), S4 (filter). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 596 currency units. Storage holds at most 56 units in total. Minimize purchase + holding + shortage.\nPERIODS: 4\nBUDGET: 596\nCAPACITY: 56\nCOVER_REQUIRED: 1\nSKU S1 demand=5,4,8,4 pack=1 cost=8 hold=2 short=6 stock=0\nSKU S2 demand=4,7,6,5 pack=1 cost=8 hold=3 short=7 stock=3\nSKU S3 demand=8,4,2,5 pack=3 cost=9 hold=1 short=11 stock=3\nSKU S4 demand=2,5,5,4 pack=1 cost=6 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 596, \"warehouse_capacity\": 56, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8, 4], \"initial_stock\": 0, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 7, 6, 5], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [8, 4, 2, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [2, 5, 5, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 4 هفته و 4 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 596 واحد پول و ظرفیت انبار 56 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 4\nBUDGET: 596\nCAPACITY: 56\nCOVER_REQUIRED: 1\nSKU S1 demand=5,4,8,4 pack=1 cost=8 hold=2 short=6 stock=0\nSKU S2 demand=4,7,6,5 pack=1 cost=8 hold=3 short=7 stock=3\nSKU S3 demand=8,4,2,5 pack=3 cost=9 hold=1 short=11 stock=3\nSKU S4 demand=2,5,5,4 pack=1 cost=6 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 596, \"warehouse_capacity\": 56, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8, 4], \"initial_stock\": 0, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 7, 6, 5], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [8, 4, 2, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [2, 5, 5, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 4,\n \"budget\": 596,\n \"warehouse_capacity\": 56,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 4,\n 8,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 7,\n 6,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 8,\n 4,\n 2,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 11,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 2,\n 5,\n 5,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":596,"warehouse_capacity":56,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,4,8,4],"initial_stock":0,"unit_cost":8,"holding_cost":2,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,7,6,5],"initial_stock":3,"unit_cost":8,"holding_cost":3,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[8,4,2,5],"initial_stock":3,"unit_cost":9,"holding_cost":1,"shortage_cost":11,"pack_size":3,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[2,5,5,4],"initial_stock":2,"unit_cost":6,"holding_cost":2,"shortage_cost":12,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":570.0,"gold_bound":570.0,"gold_solution":{"family":"inventory","status":"optimal","objective":570.0,"bound":570.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":8},{"sku_id":"S1","period":4,"qty":4},{"sku_id":"S2","period":1,"qty":1},{"sku_id":"S2","period":2,"qty":7},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S2","period":4,"qty":5},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":3},{"sku_id":"S3","period":3,"qty":3},{"sku_id":"S3","period":4,"qty":6},{"sku_id":"S4","period":1,"qty":0},{"sku_id":"S4","period":2,"qty":5},{"sku_id":"S4","period":3,"qty":5},{"sku_id":"S4","period":4,"qty":4}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"3e101f0e29677e33","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-008","family":"inventory","split":"development","interactive":true,"difficulty":"easy","language":"fa","template_id":"D-B","seed":25008,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 175 currency units. Storage holds at most 24 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 175\nCAPACITY: 24\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,4 pack=1 cost=8 hold=3 short=12 stock=1\nSKU S2 demand=2,4,3 pack=2 cost=4 hold=3 short=7 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 175, \"warehouse_capacity\": 24, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 4], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 175 واحد پول و ظرفیت انبار 24 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 175\nCAPACITY: 24\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,4 pack=1 cost=8 hold=3 short=12 stock=1\nSKU S2 demand=2,4,3 pack=2 cost=4 hold=3 short=7 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 175, \"warehouse_capacity\": 24, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 4], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 175,\n \"warehouse_capacity\": 24,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 8,\n 4\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 4,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 4,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":175,"warehouse_capacity":24,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,8,4],"initial_stock":1,"unit_cost":8,"holding_cost":3,"shortage_cost":12,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,4,3],"initial_stock":3,"unit_cost":4,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":166.0,"gold_bound":166.0,"gold_solution":{"family":"inventory","status":"optimal","objective":166.0,"bound":166.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":8},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":4},{"sku_id":"S2","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f2dfa9f008318786","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-009","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"en","template_id":"D-C","seed":25009,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 287 currency units. Storage holds at most 42 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 287\nCAPACITY: 42\nCOVER_REQUIRED: 0\nSKU S1 demand=8,4,4 pack=2 cost=3 hold=2 short=10 stock=0\nSKU S2 demand=5,8,6 pack=3 cost=6 hold=1 short=12 stock=0\nSKU S3 demand=7,8,7 pack=3 cost=4 hold=1 short=13 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 287, \"warehouse_capacity\": 42, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 4], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 8, 6], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 12, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 7], \"initial_stock\": 0, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 287 واحد پول و ظرفیت انبار 42 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 287\nCAPACITY: 42\nCOVER_REQUIRED: 0\nSKU S1 demand=8,4,4 pack=2 cost=3 hold=2 short=10 stock=0\nSKU S2 demand=5,8,6 pack=3 cost=6 hold=1 short=12 stock=0\nSKU S3 demand=7,8,7 pack=3 cost=4 hold=1 short=13 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 287, \"warehouse_capacity\": 42, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 4], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 8, 6], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 12, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 7], \"initial_stock\": 0, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 287,\n \"warehouse_capacity\": 42,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 8,\n 4,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 8,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 12,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 8,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":287,"warehouse_capacity":42,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[8,4,4],"initial_stock":0,"unit_cost":3,"holding_cost":2,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,8,6],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":12,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,8,7],"initial_stock":0,"unit_cost":4,"holding_cost":1,"shortage_cost":13,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":267.0,"gold_bound":267.0,"gold_solution":{"family":"inventory","status":"optimal","objective":267.0,"bound":267.0,"orders":[{"sku_id":"S1","period":1,"qty":8},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":9},{"sku_id":"S3","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"caebc391dc3f21a3","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-010","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":25010,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 240 currency units. Storage holds at most 28 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 240\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=8,4,6 pack=1 cost=8 hold=1 short=6 stock=1\nSKU S2 demand=2,6,8 pack=1 cost=7 hold=3 short=12 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 240, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 6], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 6, 8], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 240 واحد پول و ظرفیت انبار 28 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 240\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=8,4,6 pack=1 cost=8 hold=1 short=6 stock=1\nSKU S2 demand=2,6,8 pack=1 cost=7 hold=3 short=12 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 240, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 6], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 6, 8], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 240,\n \"warehouse_capacity\": 28,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 8,\n 4,\n 6\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 6,\n 8\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 3,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":240,"warehouse_capacity":28,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[8,4,6],"initial_stock":1,"unit_cost":8,"holding_cost":1,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,6,8],"initial_stock":3,"unit_cost":7,"holding_cost":3,"shortage_cost":12,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":230.0,"gold_bound":230.0,"gold_solution":{"family":"inventory","status":"optimal","objective":230.0,"bound":230.0,"orders":[{"sku_id":"S1","period":1,"qty":7},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":5},{"sku_id":"S2","period":3,"qty":8}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f482821b43520a57","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-011","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":25011,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 167 currency units. Storage holds at most 16 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 167\nCAPACITY: 16\nCOVER_REQUIRED: 0\nSKU S1 demand=2,5,4 pack=2 cost=8 hold=2 short=11 stock=3\nSKU S2 demand=8,4,2 pack=3 cost=7 hold=1 short=14 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 167, \"warehouse_capacity\": 16, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 5, 4], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 4, 2], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 14, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 167 واحد پول و ظرفیت انبار 16 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 167\nCAPACITY: 16\nCOVER_REQUIRED: 0\nSKU S1 demand=2,5,4 pack=2 cost=8 hold=2 short=11 stock=3\nSKU S2 demand=8,4,2 pack=3 cost=7 hold=1 short=14 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 167, \"warehouse_capacity\": 16, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 5, 4], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 4, 2], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 14, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 167,\n \"warehouse_capacity\": 16,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 5,\n 4\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 4,\n 2\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":167,"warehouse_capacity":16,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,5,4],"initial_stock":3,"unit_cost":8,"holding_cost":2,"shortage_cost":11,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,4,2],"initial_stock":3,"unit_cost":7,"holding_cost":1,"shortage_cost":14,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":152.0,"gold_bound":152.0,"gold_solution":{"family":"inventory","status":"optimal","objective":152.0,"bound":152.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"8ad0f8164e7ede31","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-012","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":25012,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 277 currency units. Storage holds at most 31 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,2 pack=3 cost=6 hold=3 short=11 stock=1\nSKU S2 demand=7,8,2 pack=3 cost=6 hold=2 short=10 stock=3\nSKU S3 demand=6,3,5 pack=1 cost=5 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 2], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 8, 2], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 3, 5], \"initial_stock\": 3, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 277 واحد پول و ظرفیت انبار 31 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,2 pack=3 cost=6 hold=3 short=11 stock=1\nSKU S2 demand=7,8,2 pack=3 cost=6 hold=2 short=10 stock=3\nSKU S3 demand=6,3,5 pack=1 cost=5 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 2], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 8, 2], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 3, 5], \"initial_stock\": 3, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 277,\n \"warehouse_capacity\": 31,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 8,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 7,\n 8,\n 2\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 6,\n 3,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":277,"warehouse_capacity":31,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,8,2],"initial_stock":1,"unit_cost":6,"holding_cost":3,"shortage_cost":11,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[7,8,2],"initial_stock":3,"unit_cost":6,"holding_cost":2,"shortage_cost":10,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[6,3,5],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":8,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":253.0,"gold_bound":253.0,"gold_solution":{"family":"inventory","status":"optimal","objective":253.0,"bound":253.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":9},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":9},{"sku_id":"S2","period":3,"qty":0},{"sku_id":"S3","period":1,"qty":3},{"sku_id":"S3","period":2,"qty":3},{"sku_id":"S3","period":3,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"3827beb73596c516","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-013","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":25013,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 256 currency units. Storage holds at most 21 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 256\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,3 pack=3 cost=9 hold=2 short=7 stock=3\nSKU S2 demand=3,6,4 pack=2 cost=9 hold=2 short=6 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 256, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 6, 4], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 256 واحد پول و ظرفیت انبار 21 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 256\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,3 pack=3 cost=9 hold=2 short=7 stock=3\nSKU S2 demand=3,6,4 pack=2 cost=9 hold=2 short=6 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 256, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 6, 4], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 256,\n \"warehouse_capacity\": 21,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 8,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 7,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 3,\n 6,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":256,"warehouse_capacity":21,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,8,3],"initial_stock":3,"unit_cost":9,"holding_cost":2,"shortage_cost":7,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[3,6,4],"initial_stock":2,"unit_cost":9,"holding_cost":2,"shortage_cost":6,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":171.0,"gold_bound":171.0,"gold_solution":{"family":"inventory","status":"optimal","objective":171.0,"bound":171.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":0},{"sku_id":"S2","period":3,"qty":0}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"1a72f172d379cd66","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-014","family":"inventory","split":"development","interactive":true,"difficulty":"hard","language":"fa","template_id":"D-B","seed":25014,"prompt_en":"A B2B warehouse plans 4 weeks for 4 SKUs: S1 (bearing), S2 (seal), S3 (gasket), S4 (filter). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 451 currency units. Storage holds at most 57 units in total. Minimize purchase + holding + shortage.\nPERIODS: 4\nBUDGET: 451\nCAPACITY: 57\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,2,4 pack=2 cost=7 hold=3 short=7 stock=2\nSKU S2 demand=6,6,8,2 pack=2 cost=5 hold=2 short=9 stock=1\nSKU S3 demand=7,2,5,8 pack=2 cost=5 hold=2 short=13 stock=2\nSKU S4 demand=3,8,4,3 pack=1 cost=8 hold=3 short=10 stock=3\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 451, \"warehouse_capacity\": 57, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 2, 4], \"initial_stock\": 2, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 2, 5, 8], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [3, 8, 4, 3], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 4 هفته و 4 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 451 واحد پول و ظرفیت انبار 57 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 4\nBUDGET: 451\nCAPACITY: 57\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,2,4 pack=2 cost=7 hold=3 short=7 stock=2\nSKU S2 demand=6,6,8,2 pack=2 cost=5 hold=2 short=9 stock=1\nSKU S3 demand=7,2,5,8 pack=2 cost=5 hold=2 short=13 stock=2\nSKU S4 demand=3,8,4,3 pack=1 cost=8 hold=3 short=10 stock=3\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 451, \"warehouse_capacity\": 57, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 2, 4], \"initial_stock\": 2, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 2, 5, 8], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [3, 8, 4, 3], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 4,\n \"budget\": 451,\n \"warehouse_capacity\": 57,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 2,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 7,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 6,\n 8,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 5,\n \"holding_cost\": 2,\n \"shortage_cost\": 9,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 2,\n 5,\n 8\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 3,\n 8,\n 4,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 10,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":451,"warehouse_capacity":57,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,2,4],"initial_stock":2,"unit_cost":7,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,6,8,2],"initial_stock":1,"unit_cost":5,"holding_cost":2,"shortage_cost":9,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,2,5,8],"initial_stock":2,"unit_cost":5,"holding_cost":2,"shortage_cost":13,"pack_size":2,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[3,8,4,3],"initial_stock":3,"unit_cost":8,"holding_cost":3,"shortage_cost":10,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":443.0,"gold_bound":443.0,"gold_solution":{"family":"inventory","status":"optimal","objective":443.0,"bound":443.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S1","period":4,"qty":4},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":8},{"sku_id":"S2","period":4,"qty":2},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":2},{"sku_id":"S3","period":3,"qty":4},{"sku_id":"S3","period":4,"qty":8},{"sku_id":"S4","period":1,"qty":0},{"sku_id":"S4","period":2,"qty":8},{"sku_id":"S4","period":3,"qty":4},{"sku_id":"S4","period":4,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"220c39206c2443c2","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-015","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"en","template_id":"D-C","seed":25015,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 277 currency units. Storage holds at most 27 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 27\nCOVER_REQUIRED: 1\nSKU S1 demand=3,4,2 pack=1 cost=9 hold=2 short=10 stock=2\nSKU S2 demand=4,2,5 pack=2 cost=6 hold=1 short=10 stock=2\nSKU S3 demand=7,6,7 pack=1 cost=8 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 27, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 4, 2], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 2, 5], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 6, 7], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 277 واحد پول و ظرفیت انبار 27 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 27\nCOVER_REQUIRED: 1\nSKU S1 demand=3,4,2 pack=1 cost=9 hold=2 short=10 stock=2\nSKU S2 demand=4,2,5 pack=2 cost=6 hold=1 short=10 stock=2\nSKU S3 demand=7,6,7 pack=1 cost=8 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 27, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 4, 2], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 2, 5], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 6, 7], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 277,\n \"warehouse_capacity\": 27,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 4,\n 2\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 2,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 6,\n 7\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":277,"warehouse_capacity":27,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,4,2],"initial_stock":2,"unit_cost":9,"holding_cost":2,"shortage_cost":10,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,2,5],"initial_stock":2,"unit_cost":6,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,6,7],"initial_stock":2,"unit_cost":8,"holding_cost":2,"shortage_cost":12,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":268.0,"gold_bound":268.0,"gold_solution":{"family":"inventory","status":"optimal","objective":268.0,"bound":268.0,"orders":[{"sku_id":"S1","period":1,"qty":1},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S2","period":1,"qty":2},{"sku_id":"S2","period":2,"qty":2},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":5},{"sku_id":"S3","period":2,"qty":6},{"sku_id":"S3","period":3,"qty":7}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"06a75306f2f713c8","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-016","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":25016,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 148 currency units. Storage holds at most 27 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 148\nCAPACITY: 27\nCOVER_REQUIRED: 0\nSKU S1 demand=2,8,8 pack=1 cost=3 hold=3 short=14 stock=0\nSKU S2 demand=4,5,5 pack=3 cost=7 hold=1 short=13 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 148, \"warehouse_capacity\": 27, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 8, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 5, 5], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 148 واحد پول و ظرفیت انبار 27 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 148\nCAPACITY: 27\nCOVER_REQUIRED: 0\nSKU S1 demand=2,8,8 pack=1 cost=3 hold=3 short=14 stock=0\nSKU S2 demand=4,5,5 pack=3 cost=7 hold=1 short=13 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 148, \"warehouse_capacity\": 27, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 8, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 5, 5], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 148,\n \"warehouse_capacity\": 27,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 8,\n 8\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 3,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 5,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":148,"warehouse_capacity":27,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,8,8],"initial_stock":0,"unit_cost":3,"holding_cost":3,"shortage_cost":14,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,5,5],"initial_stock":3,"unit_cost":7,"holding_cost":1,"shortage_cost":13,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":141.0,"gold_bound":141.0,"gold_solution":{"family":"inventory","status":"optimal","objective":141.0,"bound":141.0,"orders":[{"sku_id":"S1","period":1,"qty":2},{"sku_id":"S1","period":2,"qty":8},{"sku_id":"S1","period":3,"qty":8},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7c84e87cc10f3c05","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-017","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":25017,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 182 currency units. Storage holds at most 23 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 182\nCAPACITY: 23\nCOVER_REQUIRED: 0\nSKU S1 demand=7,2,5 pack=3 cost=4 hold=1 short=10 stock=1\nSKU S2 demand=8,2,6 pack=2 cost=7 hold=1 short=9 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 182, \"warehouse_capacity\": 23, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 2, 5], \"initial_stock\": 1, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 2, 6], \"initial_stock\": 0, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 182 واحد پول و ظرفیت انبار 23 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 182\nCAPACITY: 23\nCOVER_REQUIRED: 0\nSKU S1 demand=7,2,5 pack=3 cost=4 hold=1 short=10 stock=1\nSKU S2 demand=8,2,6 pack=2 cost=7 hold=1 short=9 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 182, \"warehouse_capacity\": 23, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 2, 5], \"initial_stock\": 1, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 2, 6], \"initial_stock\": 0, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 182,\n \"warehouse_capacity\": 23,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 2,\n 5\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 2,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":182,"warehouse_capacity":23,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,2,5],"initial_stock":1,"unit_cost":4,"holding_cost":1,"shortage_cost":10,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,2,6],"initial_stock":0,"unit_cost":7,"holding_cost":1,"shortage_cost":9,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":171.0,"gold_bound":171.0,"gold_solution":{"family":"inventory","status":"optimal","objective":171.0,"bound":171.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":8},{"sku_id":"S2","period":2,"qty":2},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7315654a4c498e83","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-018","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":25018,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 209 currency units. Storage holds at most 28 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 209\nCAPACITY: 28\nCOVER_REQUIRED: 0\nSKU S1 demand=4,4,4 pack=1 cost=6 hold=1 short=7 stock=0\nSKU S2 demand=3,3,3 pack=3 cost=6 hold=1 short=7 stock=0\nSKU S3 demand=6,4,7 pack=1 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 209, \"warehouse_capacity\": 28, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [4, 4, 4], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 3, 3], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 4, 7], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 209 واحد پول و ظرفیت انبار 28 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 209\nCAPACITY: 28\nCOVER_REQUIRED: 0\nSKU S1 demand=4,4,4 pack=1 cost=6 hold=1 short=7 stock=0\nSKU S2 demand=3,3,3 pack=3 cost=6 hold=1 short=7 stock=0\nSKU S3 demand=6,4,7 pack=1 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 209, \"warehouse_capacity\": 28, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [4, 4, 4], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 3, 3], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 4, 7], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 209,\n \"warehouse_capacity\": 28,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 4,\n 4,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 3,\n 3,\n 3\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 6,\n 4,\n 7\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":209,"warehouse_capacity":28,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[4,4,4],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[3,3,3],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":7,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[6,4,7],"initial_stock":2,"unit_cost":5,"holding_cost":3,"shortage_cost":11,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":201.0,"gold_bound":201.0,"gold_solution":{"family":"inventory","status":"optimal","objective":201.0,"bound":201.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3},{"sku_id":"S3","period":1,"qty":4},{"sku_id":"S3","period":2,"qty":4},{"sku_id":"S3","period":3,"qty":7}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2db06bd39b73849d","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-019","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":25019,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 169 currency units. Storage holds at most 25 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 169\nCAPACITY: 25\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,8 pack=1 cost=3 hold=1 short=6 stock=0\nSKU S2 demand=4,4,5 pack=2 cost=9 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 169, \"warehouse_capacity\": 25, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 4, 5], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 169 واحد پول و ظرفیت انبار 25 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 169\nCAPACITY: 25\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,8 pack=1 cost=3 hold=1 short=6 stock=0\nSKU S2 demand=4,4,5 pack=2 cost=9 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 169, \"warehouse_capacity\": 25, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 4, 5], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 169,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 4,\n 8\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 1,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 4,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":169,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,4,8],"initial_stock":0,"unit_cost":3,"holding_cost":1,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,4,5],"initial_stock":2,"unit_cost":9,"holding_cost":1,"shortage_cost":7,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":128.0,"gold_bound":128.0,"gold_solution":{"family":"inventory","status":"optimal","objective":128.0,"bound":128.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":8},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":0},{"sku_id":"S2","period":3,"qty":0}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"5a0bc130cf4da2cb","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-020","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":25020,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 191 currency units. Storage holds at most 20 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 191\nCAPACITY: 20\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,5 pack=1 cost=9 hold=2 short=13 stock=3\nSKU S2 demand=5,3,4 pack=3 cost=6 hold=3 short=8 stock=1\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 191, \"warehouse_capacity\": 20, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 3, 4], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 191 واحد پول و ظرفیت انبار 20 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 191\nCAPACITY: 20\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,5 pack=1 cost=9 hold=2 short=13 stock=3\nSKU S2 demand=5,3,4 pack=3 cost=6 hold=3 short=8 stock=1\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 191, \"warehouse_capacity\": 20, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 3, 4], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 191,\n \"warehouse_capacity\": 20,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 3,\n 4\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":191,"warehouse_capacity":20,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,5],"initial_stock":3,"unit_cost":9,"holding_cost":2,"shortage_cost":13,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,3,4],"initial_stock":1,"unit_cost":6,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":195.0,"gold_bound":195.0,"gold_solution":{"family":"inventory","status":"optimal","objective":195.0,"bound":195.0,"orders":[{"sku_id":"S1","period":1,"qty":2},{"sku_id":"S1","period":2,"qty":5},{"sku_id":"S1","period":3,"qty":5},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7504669a6087b21d","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-021","family":"inventory","split":"test","interactive":true,"difficulty":"hard","language":"en","template_id":"T-A","seed":25021,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket), S4 (filter) over a 4-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 667. On-hand stock across SKUs cannot exceed 56. S1 wants [6, 5, 5, 6] at pack 1; S2 wants [5, 3, 7, 4] at pack 3; S3 wants [8, 5, 4, 8] at pack 2; S4 wants [2, 8, 5, 5] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر) در افق 4 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 667 و سقف موجودی کل 56 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 4,\n \"budget\": 667,\n \"warehouse_capacity\": 56,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 5,\n 5,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 7,\n \"holding_cost\": 2,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 3,\n 7,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 8,\n 5,\n 4,\n 8\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 2,\n 8,\n 5,\n 5\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":667,"warehouse_capacity":56,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,5,5,6],"initial_stock":2,"unit_cost":7,"holding_cost":2,"shortage_cost":14,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,3,7,4],"initial_stock":2,"unit_cost":8,"holding_cost":2,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[8,5,4,8],"initial_stock":3,"unit_cost":9,"holding_cost":3,"shortage_cost":9,"pack_size":2,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[2,8,5,5],"initial_stock":1,"unit_cost":8,"holding_cost":1,"shortage_cost":9,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":643.0,"gold_bound":643.0,"gold_solution":{"family":"inventory","status":"optimal","objective":643.0,"bound":643.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":5},{"sku_id":"S1","period":3,"qty":5},{"sku_id":"S1","period":4,"qty":6},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":9},{"sku_id":"S2","period":4,"qty":3},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":4},{"sku_id":"S3","period":3,"qty":4},{"sku_id":"S3","period":4,"qty":8},{"sku_id":"S4","period":1,"qty":1},{"sku_id":"S4","period":2,"qty":8},{"sku_id":"S4","period":3,"qty":5},{"sku_id":"S4","period":4,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"43f6be8e459b5009","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-022","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-B","seed":25022,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 117. On-hand stock across SKUs cannot exceed 19. S1 wants [2, 2, 3] at pack 1; S2 wants [6, 7, 7] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 117 و سقف موجودی کل 19 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 117,\n \"warehouse_capacity\": 19,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 2,\n 3\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 7,\n 7\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":117,"warehouse_capacity":19,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,2,3],"initial_stock":2,"unit_cost":3,"holding_cost":2,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,7,7],"initial_stock":1,"unit_cost":4,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":97.0,"gold_bound":97.0,"gold_solution":{"family":"inventory","status":"optimal","objective":97.0,"bound":97.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":2},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":8}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"e0b2178c1118eb1f","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-023","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":25023,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 241. On-hand stock across SKUs cannot exceed 28. S1 wants [5, 5, 7] at pack 2; S2 wants [6, 3, 5] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 241 و سقف موجودی کل 28 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 241,\n \"warehouse_capacity\": 28,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 7\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 13,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 3,\n 5\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":241,"warehouse_capacity":28,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,7],"initial_stock":1,"unit_cost":8,"holding_cost":3,"shortage_cost":13,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,3,5],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":10,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":222.0,"gold_bound":222.0,"gold_solution":{"family":"inventory","status":"optimal","objective":222.0,"bound":222.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"85786f3b3f0dfbf9","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-024","family":"inventory","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":25024,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 268. On-hand stock across SKUs cannot exceed 26. S1 wants [7, 2, 3] at pack 2; S2 wants [2, 3, 7] at pack 3; S3 wants [3, 8, 8] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 268 و سقف موجودی کل 26 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 268,\n \"warehouse_capacity\": 26,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 2,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 2,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 3,\n 7\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 3,\n 8,\n 8\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":268,"warehouse_capacity":26,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,2,3],"initial_stock":3,"unit_cost":7,"holding_cost":2,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,3,7],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[3,8,8],"initial_stock":3,"unit_cost":9,"holding_cost":1,"shortage_cost":11,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":258.0,"gold_bound":258.0,"gold_solution":{"family":"inventory","status":"optimal","objective":258.0,"bound":258.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":0},{"sku_id":"S3","period":2,"qty":8},{"sku_id":"S3","period":3,"qty":8}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"5c318f4fb63ecf81","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-025","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":25025,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 284. On-hand stock across SKUs cannot exceed 27. S1 wants [7, 5, 6] at pack 3; S2 wants [3, 4, 6] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 284 و سقف موجودی کل 27 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 284,\n \"warehouse_capacity\": 27,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 5,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 3,\n 4,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":284,"warehouse_capacity":27,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,5,6],"initial_stock":3,"unit_cost":9,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[3,4,6],"initial_stock":0,"unit_cost":9,"holding_cost":2,"shortage_cost":6,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":284.0,"gold_bound":284.0,"gold_solution":{"family":"inventory","status":"optimal","objective":284.0,"bound":284.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"34a94761719df506","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-026","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-B","seed":25026,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 222. On-hand stock across SKUs cannot exceed 25. S1 wants [5, 5, 7] at pack 2; S2 wants [5, 7, 4] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 222 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 222,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 7,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":222,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,7],"initial_stock":0,"unit_cost":8,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,7,4],"initial_stock":2,"unit_cost":4,"holding_cost":1,"shortage_cost":14,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":195.0,"gold_bound":195.0,"gold_solution":{"family":"inventory","status":"optimal","objective":195.0,"bound":195.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":7},{"sku_id":"S2","period":3,"qty":4}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"a2c2cf9f0e528f38","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-027","family":"inventory","split":"test","interactive":false,"difficulty":"medium","language":"en","template_id":"T-A","seed":25027,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 200. On-hand stock across SKUs cannot exceed 29. S1 wants [4, 5, 2] at pack 1; S2 wants [4, 8, 2] at pack 2; S3 wants [2, 6, 6] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 200 و سقف موجودی کل 29 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 200,\n \"warehouse_capacity\": 29,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 4,\n 5,\n 2\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 8,\n 2\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 2,\n 6,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 6,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":200,"warehouse_capacity":29,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[4,5,2],"initial_stock":3,"unit_cost":5,"holding_cost":1,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,8,2],"initial_stock":2,"unit_cost":3,"holding_cost":2,"shortage_cost":12,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[2,6,6],"initial_stock":3,"unit_cost":9,"holding_cost":1,"shortage_cost":6,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":143.0,"gold_bound":143.0,"gold_solution":{"family":"inventory","status":"optimal","objective":143.0,"bound":143.0,"orders":[{"sku_id":"S1","period":1,"qty":1},{"sku_id":"S1","period":2,"qty":5},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S2","period":1,"qty":2},{"sku_id":"S2","period":2,"qty":8},{"sku_id":"S2","period":3,"qty":2},{"sku_id":"S3","period":1,"qty":0},{"sku_id":"S3","period":2,"qty":0},{"sku_id":"S3","period":3,"qty":0}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"58e2d8d2872c433a","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-028","family":"inventory","split":"test","interactive":true,"difficulty":"hard","language":"fa","template_id":"T-B","seed":25028,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket), S4 (filter) over a 4-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 417. On-hand stock across SKUs cannot exceed 48. S1 wants [2, 6, 5, 4] at pack 2; S2 wants [6, 2, 5, 6] at pack 3; S3 wants [3, 2, 7, 5] at pack 1; S4 wants [7, 3, 4, 4] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر) در افق 4 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 417 و سقف موجودی کل 48 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 4,\n \"budget\": 417,\n \"warehouse_capacity\": 48,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 6,\n 5,\n 4\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 2,\n 5,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 3,\n 2,\n 7,\n 5\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 7,\n 3,\n 4,\n 4\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":417,"warehouse_capacity":48,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,6,5,4],"initial_stock":1,"unit_cost":5,"holding_cost":3,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,2,5,6],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[3,2,7,5],"initial_stock":0,"unit_cost":8,"holding_cost":3,"shortage_cost":9,"pack_size":1,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[7,3,4,4],"initial_stock":3,"unit_cost":6,"holding_cost":1,"shortage_cost":9,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":422.0,"gold_bound":422.0,"gold_solution":{"family":"inventory","status":"optimal","objective":422.0,"bound":422.0,"orders":[{"sku_id":"S1","period":1,"qty":2},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S1","period":4,"qty":4},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S2","period":4,"qty":6},{"sku_id":"S3","period":1,"qty":3},{"sku_id":"S3","period":2,"qty":2},{"sku_id":"S3","period":3,"qty":7},{"sku_id":"S3","period":4,"qty":5},{"sku_id":"S4","period":1,"qty":6},{"sku_id":"S4","period":2,"qty":3},{"sku_id":"S4","period":3,"qty":3},{"sku_id":"S4","period":4,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"d4b291056d53e1b6","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-029","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":25029,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 205. On-hand stock across SKUs cannot exceed 25. S1 wants [7, 6, 3] at pack 3; S2 wants [6, 4, 5] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 205 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 205,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 6,\n 3\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 4,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":205,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,6,3],"initial_stock":0,"unit_cost":8,"holding_cost":1,"shortage_cost":14,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,4,5],"initial_stock":2,"unit_cost":4,"holding_cost":1,"shortage_cost":10,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":186.0,"gold_bound":186.0,"gold_solution":{"family":"inventory","status":"optimal","objective":186.0,"bound":186.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":4},{"sku_id":"S2","period":2,"qty":4},{"sku_id":"S2","period":3,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"df4a252d2ab08ed3","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-030","family":"inventory","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":25030,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 174. On-hand stock across SKUs cannot exceed 25. S1 wants [3, 3, 2] at pack 1; S2 wants [6, 2, 7] at pack 2; S3 wants [8, 3, 2] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 174 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 174,\n \"warehouse_capacity\": 25,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 3,\n 2\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 2,\n 7\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 8,\n 3,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":174,"warehouse_capacity":25,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,3,2],"initial_stock":0,"unit_cost":7,"holding_cost":1,"shortage_cost":9,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,2,7],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[8,3,2],"initial_stock":1,"unit_cost":3,"holding_cost":2,"shortage_cost":12,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":160.0,"gold_bound":160.0,"gold_solution":{"family":"inventory","status":"optimal","objective":160.0,"bound":160.0,"orders":[{"sku_id":"S1","period":1,"qty":3},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S2","period":1,"qty":4},{"sku_id":"S2","period":2,"qty":2},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":8},{"sku_id":"S3","period":2,"qty":2},{"sku_id":"S3","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7ab02a4b652b205f","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-031","family":"inventory","split":"test","interactive":true,"difficulty":"easy","language":"en","template_id":"T-A","seed":25031,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 178. On-hand stock across SKUs cannot exceed 25. S1 wants [7, 6, 5] at pack 1; S2 wants [2, 5, 5] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 178 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 178,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 6,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 5,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 7,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":178,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,6,5],"initial_stock":2,"unit_cost":6,"holding_cost":1,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,5,5],"initial_stock":2,"unit_cost":7,"holding_cost":3,"shortage_cost":9,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":166.0,"gold_bound":166.0,"gold_solution":{"family":"inventory","status":"optimal","objective":166.0,"bound":166.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":5},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":5},{"sku_id":"S2","period":3,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"17d8f21147efad41","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-032","family":"inventory","split":"test","interactive":false,"difficulty":"infeasible","language":"fa","template_id":"T-B","seed":25032,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 49. On-hand stock across SKUs cannot exceed 47. S1 wants [3, 8, 6] at pack 1; S2 wants [8, 3, 6] at pack 2; S3 wants [5, 3, 5] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 49 و سقف موجودی کل 47 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 49,\n \"warehouse_capacity\": 47,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 8,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 3,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 5,\n 3,\n 5\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":49,"warehouse_capacity":47,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,8,6],"initial_stock":0,"unit_cost":3,"holding_cost":2,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,3,6],"initial_stock":0,"unit_cost":4,"holding_cost":1,"shortage_cost":14,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[5,3,5],"initial_stock":0,"unit_cost":9,"holding_cost":2,"shortage_cost":10,"pack_size":2,"lead_time":0}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"inventory","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"a81392c6044cd7df","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-033","family":"inventory","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-A","seed":25033,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 42. On-hand stock across SKUs cannot exceed 41. S1 wants [3, 3, 3] at pack 2; S2 wants [4, 7, 7] at pack 2; S3 wants [3, 7, 4] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 42 و سقف موجودی کل 41 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 42,\n \"warehouse_capacity\": 41,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 3,\n 3\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 7,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 3,\n 7,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":42,"warehouse_capacity":41,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,3,3],"initial_stock":0,"unit_cost":5,"holding_cost":3,"shortage_cost":11,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,7,7],"initial_stock":0,"unit_cost":4,"holding_cost":2,"shortage_cost":6,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[3,7,4],"initial_stock":0,"unit_cost":6,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"inventory","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"ea9231d0be843484","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"INV-034","family":"inventory","split":"test","interactive":true,"difficulty":"infeasible","language":"fa","template_id":"T-B","seed":25034,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 56. On-hand stock across SKUs cannot exceed 52. S1 wants [4, 7, 6] at pack 2; S2 wants [8, 3, 8] at pack 1; S3 wants [6, 3, 7] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 56 و سقف موجودی کل 52 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 56,\n \"warehouse_capacity\": 52,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 4,\n 7,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 3,\n 8\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 6,\n 3,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 2,\n \"shortage_cost\": 8,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":56,"warehouse_capacity":52,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[4,7,6],"initial_stock":0,"unit_cost":9,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,3,8],"initial_stock":0,"unit_cost":3,"holding_cost":3,"shortage_cost":9,"pack_size":1,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[6,3,7],"initial_stock":0,"unit_cost":4,"holding_cost":2,"shortage_cost":8,"pack_size":2,"lead_time":0}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"inventory","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"da716bb0cb346fe1","notes":"lead time is 0; units are abstract currency and pieces"} +{"problem_id":"ASN-001","family":"assignment","split":"development","interactive":true,"difficulty":"easy","language":"fa","template_id":"D-A","seed":50001,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills lift/weld, T2 size 1 skills inspect, T3 size 2 skills pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 40}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 13}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills lift/weld, T2 size 1 skills inspect, T3 size 2 skills pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 40}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 13}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 38\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["lift","weld"],"penalty":40},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect"],"penalty":22},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack"],"penalty":40},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":38}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A3","cost":12},{"task_id":"T4","agent_id":"A1","cost":11},{"task_id":"T4","agent_id":"A2","cost":7},{"task_id":"T4","agent_id":"A3","cost":13}]},"gold_status":"optimal","gold_objective":35.0,"gold_bound":35.0,"gold_solution":{"family":"assignment","status":"optimal","objective":35.0,"bound":35.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"1cddcd6462c5befc","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-002","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":50002,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 11}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 11}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 37\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["weld"],"penalty":37},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":34},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack","weld"],"penalty":22},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":37}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":11},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":11},{"task_id":"T3","agent_id":"A1","cost":6},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":17},{"task_id":"T4","agent_id":"A2","cost":9},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":26.0,"gold_bound":26.0,"gold_solution":{"family":"assignment","status":"optimal","objective":26.0,"bound":26.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"d2c2d3e77c899e5b","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-003","family":"assignment","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":50003,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills inspect/lift, T2 size 2 skills inspect/lift, T3 size 2 skills pack/weld, T4 size 2 skills pack/weld, T5 size 1 skills inspect/lift, T6 size 2 skills inspect/lift\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 31}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills inspect/lift, T2 size 2 skills inspect/lift, T3 size 2 skills pack/weld, T4 size 2 skills pack/weld, T5 size 1 skills inspect/lift, T6 size 2 skills inspect/lift\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 31}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 25\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["inspect","lift"],"penalty":31},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift"],"penalty":25},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack","weld"],"penalty":28},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["pack","weld"],"penalty":39},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","lift"],"penalty":38},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","lift"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":6},{"task_id":"T1","agent_id":"A2","cost":18},{"task_id":"T1","agent_id":"A3","cost":17},{"task_id":"T2","agent_id":"A1","cost":8},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":13},{"task_id":"T3","agent_id":"A1","cost":9},{"task_id":"T3","agent_id":"A2","cost":8},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A1","cost":15},{"task_id":"T4","agent_id":"A2","cost":8},{"task_id":"T4","agent_id":"A3","cost":12},{"task_id":"T5","agent_id":"A1","cost":6},{"task_id":"T5","agent_id":"A2","cost":9},{"task_id":"T5","agent_id":"A3","cost":18},{"task_id":"T6","agent_id":"A1","cost":5},{"task_id":"T6","agent_id":"A2","cost":16},{"task_id":"T6","agent_id":"A3","cost":14}]},"gold_status":"optimal","gold_objective":39.0,"gold_bound":39.0,"gold_solution":{"family":"assignment","status":"optimal","objective":39.0,"bound":39.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A1"},{"task_id":"T6","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7cb9463c065ed495","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-004","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":50004,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/weld, T2 size 3 skills inspect, T3 size 3 skills lift/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/weld, T2 size 3 skills inspect, T3 size 3 skills lift/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 37\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","weld"],"penalty":40},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect"],"penalty":22},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift","pack"],"penalty":31},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["lift","weld"],"penalty":37}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":14},{"task_id":"T1","agent_id":"A2","cost":15},{"task_id":"T1","agent_id":"A3","cost":6},{"task_id":"T2","agent_id":"A2","cost":16},{"task_id":"T2","agent_id":"A3","cost":8},{"task_id":"T3","agent_id":"A3","cost":15},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A3","cost":16}]},"gold_status":"optimal","gold_objective":44.0,"gold_bound":44.0,"gold_solution":{"family":"assignment","status":"optimal","objective":44.0,"bound":44.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"617e65bd9540551c","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-005","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":50005,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills pack/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 24}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills pack/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 24}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 34\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["pack","weld"],"penalty":24},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","weld"],"penalty":33},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack"],"penalty":32},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["inspect","weld"],"penalty":34}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":14},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A1","cost":11},{"task_id":"T2","agent_id":"A2","cost":11},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A2","cost":5},{"task_id":"T4","agent_id":"A3","cost":16}]},"gold_status":"optimal","gold_objective":30.0,"gold_bound":30.0,"gold_solution":{"family":"assignment","status":"optimal","objective":30.0,"bound":30.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"313df2be239a5ae9","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-006","family":"assignment","split":"development","interactive":true,"difficulty":"medium","language":"en","template_id":"D-C","seed":50006,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills lift, T4 size 1 skills inspect, T5 size 2 skills lift/pack, T6 size 2 skills lift\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 5 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 20}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 27}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 40}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills lift, T4 size 1 skills inspect, T5 size 2 skills lift/pack, T6 size 2 skills lift\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 5 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 20}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 27}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 40}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 38\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift"],"penalty":20},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":27},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift"],"penalty":28},{"task_id":"T4","name":"job-4","size":1,"required":true,"skills":["inspect"],"penalty":39},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["lift","pack"],"penalty":40},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["lift"],"penalty":38}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":11},{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A1","cost":8},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":9},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":11},{"task_id":"T4","agent_id":"A2","cost":18},{"task_id":"T4","agent_id":"A3","cost":14},{"task_id":"T5","agent_id":"A2","cost":15},{"task_id":"T5","agent_id":"A3","cost":7},{"task_id":"T6","agent_id":"A3","cost":11}]},"gold_status":"optimal","gold_objective":48.0,"gold_bound":48.0,"gold_solution":{"family":"assignment","status":"optimal","objective":48.0,"bound":48.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"633fec80b9b681c9","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-007","family":"assignment","split":"development","interactive":false,"difficulty":"hard","language":"fa","template_id":"D-A","seed":50007,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills inspect/lift, T4 size 2 skills lift/pack, T5 size 1 skills inspect/weld, T6 size 1 skills pack, T7 size 1 skills inspect/pack, T8 size 1 skills lift/weld\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 29}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 30}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 22}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 23}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T8\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 8}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills inspect/lift, T4 size 2 skills lift/pack, T5 size 1 skills inspect/weld, T6 size 1 skills pack, T7 size 1 skills inspect/pack, T8 size 1 skills lift/weld\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 29}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 30}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 22}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 23}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T8\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 8}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 23\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 8\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["inspect","lift"],"penalty":21},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":29},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift"],"penalty":30},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["lift","pack"],"penalty":22},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","weld"],"penalty":21},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["pack"],"penalty":32},{"task_id":"T7","name":"job-7","size":1,"required":true,"skills":["inspect","pack"],"penalty":23},{"task_id":"T8","name":"job-8","size":1,"required":true,"skills":["lift","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A2","cost":12},{"task_id":"T1","agent_id":"A3","cost":12},{"task_id":"T1","agent_id":"A4","cost":7},{"task_id":"T2","agent_id":"A1","cost":11},{"task_id":"T2","agent_id":"A2","cost":18},{"task_id":"T2","agent_id":"A3","cost":18},{"task_id":"T2","agent_id":"A4","cost":14},{"task_id":"T3","agent_id":"A1","cost":4},{"task_id":"T3","agent_id":"A2","cost":6},{"task_id":"T3","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A4","cost":5},{"task_id":"T4","agent_id":"A2","cost":13},{"task_id":"T4","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A4","cost":17},{"task_id":"T5","agent_id":"A1","cost":10},{"task_id":"T5","agent_id":"A2","cost":9},{"task_id":"T5","agent_id":"A4","cost":18},{"task_id":"T6","agent_id":"A2","cost":12},{"task_id":"T6","agent_id":"A3","cost":7},{"task_id":"T6","agent_id":"A4","cost":5},{"task_id":"T7","agent_id":"A1","cost":14},{"task_id":"T7","agent_id":"A2","cost":15},{"task_id":"T7","agent_id":"A3","cost":13},{"task_id":"T7","agent_id":"A4","cost":5},{"task_id":"T8","agent_id":"A1","cost":17},{"task_id":"T8","agent_id":"A3","cost":18},{"task_id":"T8","agent_id":"A4","cost":8}]},"gold_status":"optimal","gold_objective":55.0,"gold_bound":55.0,"gold_solution":{"family":"assignment","status":"optimal","objective":55.0,"bound":55.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A4"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A2"},{"task_id":"T6","agent_id":"A4"},{"task_id":"T7","agent_id":"A4"},{"task_id":"T8","agent_id":"A4"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"4d73d8bdc819ff4a","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-008","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":50008,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 1 skills inspect/pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 26}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 1 skills inspect/pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 26}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 26\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["lift","weld"],"penalty":34},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","weld"],"penalty":33},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":26}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A1","cost":4},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A2","cost":8},{"task_id":"T3","agent_id":"A3","cost":13},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A2","cost":17},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":31.0,"gold_bound":31.0,"gold_solution":{"family":"assignment","status":"optimal","objective":31.0,"bound":31.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"0e4781ed5b25d32c","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-009","family":"assignment","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":50009,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/lift, T2 size 2 skills lift/pack, T3 size 2 skills pack, T4 size 1 skills inspect/lift, T5 size 3 skills inspect/weld, T6 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 32}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 9}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/lift, T2 size 2 skills lift/pack, T3 size 2 skills pack, T4 size 1 skills inspect/lift, T5 size 3 skills inspect/weld, T6 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 32}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 9}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 25\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 32\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 9\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["lift","pack"],"penalty":30},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack"],"penalty":20},{"task_id":"T4","name":"job-4","size":1,"required":true,"skills":["inspect","lift"],"penalty":25},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["inspect","weld"],"penalty":32},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["lift","weld"],"penalty":32}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":14},{"task_id":"T1","agent_id":"A2","cost":4},{"task_id":"T1","agent_id":"A3","cost":15},{"task_id":"T2","agent_id":"A2","cost":14},{"task_id":"T2","agent_id":"A3","cost":6},{"task_id":"T3","agent_id":"A2","cost":7},{"task_id":"T3","agent_id":"A3","cost":12},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A2","cost":9},{"task_id":"T4","agent_id":"A3","cost":15},{"task_id":"T5","agent_id":"A1","cost":11},{"task_id":"T5","agent_id":"A2","cost":16},{"task_id":"T5","agent_id":"A3","cost":6},{"task_id":"T6","agent_id":"A1","cost":17},{"task_id":"T6","agent_id":"A3","cost":9}]},"gold_status":"optimal","gold_objective":51.0,"gold_bound":51.0,"gold_solution":{"family":"assignment","status":"optimal","objective":51.0,"bound":51.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2ed0462d809cf9b4","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-010","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":50010,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 4 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 39}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 20}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 17}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 4 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 39}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 20}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 17}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 20\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":40},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":38},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack"],"penalty":39},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["inspect","weld"],"penalty":20}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":15},{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":13},{"task_id":"T3","agent_id":"A3","cost":7},{"task_id":"T4","agent_id":"A1","cost":8},{"task_id":"T4","agent_id":"A2","cost":8},{"task_id":"T4","agent_id":"A3","cost":17}]},"gold_status":"optimal","gold_objective":24.0,"gold_bound":24.0,"gold_solution":{"family":"assignment","status":"optimal","objective":24.0,"bound":24.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f1b67e1305aef3ad","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-011","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":50011,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills pack/weld, T2 size 3 skills inspect/weld, T3 size 3 skills lift/pack, T4 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 5}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills pack/weld, T2 size 3 skills inspect/weld, T3 size 3 skills lift/pack, T4 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 5}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["pack","weld"],"penalty":30},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","weld"],"penalty":34},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift","pack"],"penalty":38},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["lift","weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":8},{"task_id":"T1","agent_id":"A3","cost":10},{"task_id":"T2","agent_id":"A1","cost":10},{"task_id":"T2","agent_id":"A2","cost":12},{"task_id":"T2","agent_id":"A3","cost":8},{"task_id":"T3","agent_id":"A3","cost":8},{"task_id":"T4","agent_id":"A1","cost":17},{"task_id":"T4","agent_id":"A3","cost":5}]},"gold_status":"optimal","gold_objective":29.0,"gold_bound":29.0,"gold_solution":{"family":"assignment","status":"optimal","objective":29.0,"bound":29.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"6e546d67a8410d0f","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-012","family":"assignment","split":"development","interactive":true,"difficulty":"medium","language":"en","template_id":"D-C","seed":50012,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/lift, T3 size 1 skills inspect/lift, T4 size 3 skills inspect, T5 size 2 skills inspect, T6 size 3 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"pack\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 40}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 35}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 36}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/lift, T3 size 1 skills inspect/lift, T4 size 3 skills inspect, T5 size 2 skills inspect, T6 size 3 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"pack\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 40}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 35}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 36}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 36\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift","pack"],"penalty":37},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift"],"penalty":34},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","lift"],"penalty":32},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["inspect"],"penalty":40},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["inspect"],"penalty":35},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["lift","weld"],"penalty":36}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":18},{"task_id":"T1","agent_id":"A2","cost":17},{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A1","cost":7},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A1","cost":15},{"task_id":"T3","agent_id":"A2","cost":9},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":4},{"task_id":"T4","agent_id":"A2","cost":8},{"task_id":"T4","agent_id":"A3","cost":7},{"task_id":"T5","agent_id":"A1","cost":17},{"task_id":"T5","agent_id":"A2","cost":15},{"task_id":"T5","agent_id":"A3","cost":10},{"task_id":"T6","agent_id":"A1","cost":15},{"task_id":"T6","agent_id":"A3","cost":11}]},"gold_status":"optimal","gold_objective":47.0,"gold_bound":47.0,"gold_solution":{"family":"assignment","status":"optimal","objective":47.0,"bound":47.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2b47606bb2a45436","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-013","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":50013,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills lift/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 24}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 18}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills lift/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 24}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 18}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":21},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack"],"penalty":24},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["inspect","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A3","cost":10},{"task_id":"T2","agent_id":"A2","cost":14},{"task_id":"T2","agent_id":"A3","cost":7},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A1","cost":15},{"task_id":"T4","agent_id":"A2","cost":13},{"task_id":"T4","agent_id":"A3","cost":18}]},"gold_status":"optimal","gold_objective":35.0,"gold_bound":35.0,"gold_solution":{"family":"assignment","status":"optimal","objective":35.0,"bound":35.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"04a6ab674fa9c7ce","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-014","family":"assignment","split":"development","interactive":false,"difficulty":"hard","language":"en","template_id":"D-B","seed":50014,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills inspect/pack, T2 size 3 skills inspect/lift, T3 size 2 skills inspect/pack, T4 size 2 skills inspect/lift, T5 size 1 skills inspect/pack, T6 size 3 skills inspect/weld, T7 size 1 skills inspect/lift, T8 size 3 skills lift\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills lift/pack, A4 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 40}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 35}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 22}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills inspect/pack, T2 size 3 skills inspect/lift, T3 size 2 skills inspect/pack, T4 size 2 skills inspect/lift, T5 size 1 skills inspect/pack, T6 size 3 skills inspect/weld, T7 size 1 skills inspect/lift, T8 size 3 skills lift\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills lift/pack, A4 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 40}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 35}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 22}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 28\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": 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\"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 11\n }\n 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intersection is the eligibility rule"} +{"problem_id":"ASN-015","family":"assignment","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":50015,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect, T2 size 2 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 2 skills inspect, T5 size 2 skills inspect, T6 size 1 skills inspect/lift/weld\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 31}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 23}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 27}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 10}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect, T2 size 2 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 2 skills inspect, T5 size 2 skills inspect, T6 size 1 skills inspect/lift/weld\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 31}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 23}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 27}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 10}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 23\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 27\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","weld"],"penalty":31},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack","weld"],"penalty":23},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["inspect","lift","weld"],"penalty":27}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":6},{"task_id":"T1","agent_id":"A2","cost":4},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A1","cost":12},{"task_id":"T2","agent_id":"A2","cost":13},{"task_id":"T2","agent_id":"A3","cost":14},{"task_id":"T3","agent_id":"A1","cost":17},{"task_id":"T3","agent_id":"A2","cost":6},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":8},{"task_id":"T4","agent_id":"A2","cost":11},{"task_id":"T4","agent_id":"A3","cost":6},{"task_id":"T5","agent_id":"A1","cost":12},{"task_id":"T5","agent_id":"A2","cost":12},{"task_id":"T5","agent_id":"A3","cost":10},{"task_id":"T6","agent_id":"A1","cost":14},{"task_id":"T6","agent_id":"A2","cost":18},{"task_id":"T6","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":47.0,"gold_bound":47.0,"gold_solution":{"family":"assignment","status":"optimal","objective":47.0,"bound":47.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A2"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"d507c6d1a92b00e1","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-016","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":50016,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills weld, T2 size 3 skills inspect/weld, T3 size 2 skills inspect/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 25}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills weld, T2 size 3 skills inspect/weld, T3 size 2 skills inspect/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 25}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 25\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":27},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","weld"],"penalty":32},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["inspect","pack"],"penalty":25},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["lift","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":8},{"task_id":"T1","agent_id":"A3","cost":12},{"task_id":"T2","agent_id":"A1","cost":10},{"task_id":"T2","agent_id":"A2","cost":18},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A2","cost":9},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":12},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":28.0,"gold_bound":28.0,"gold_solution":{"family":"assignment","status":"optimal","objective":28.0,"bound":28.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f9b263c3d202188e","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-017","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":50017,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills lift/weld, T2 size 2 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 37}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills lift/weld, T2 size 2 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 37}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":22},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift"],"penalty":37},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack","weld"],"penalty":32},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":33}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A2","cost":11},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A1","cost":10},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A2","cost":11},{"task_id":"T4","agent_id":"A3","cost":14}]},"gold_status":"optimal","gold_objective":28.0,"gold_bound":28.0,"gold_solution":{"family":"assignment","status":"optimal","objective":28.0,"bound":28.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f515c7358f0c6201","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-018","family":"assignment","split":"development","interactive":true,"difficulty":"medium","language":"en","template_id":"D-C","seed":50018,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills inspect, T2 size 2 skills inspect/lift/weld, T3 size 3 skills inspect/lift/weld, T4 size 3 skills weld, T5 size 1 skills inspect, T6 size 2 skills lift/pack\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 24}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills inspect, T2 size 2 skills inspect/lift/weld, T3 size 3 skills inspect/lift/weld, T4 size 3 skills weld, T5 size 1 skills inspect, T6 size 2 skills lift/pack\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 24}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 37\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["inspect"],"penalty":27},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift","weld"],"penalty":30},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift","weld"],"penalty":33},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["weld"],"penalty":37},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect"],"penalty":24},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["lift","pack"],"penalty":37}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":17},{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":4},{"task_id":"T2","agent_id":"A1","cost":8},{"task_id":"T2","agent_id":"A2","cost":16},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A1","cost":18},{"task_id":"T3","agent_id":"A2","cost":18},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":12},{"task_id":"T4","agent_id":"A3","cost":4},{"task_id":"T5","agent_id":"A1","cost":17},{"task_id":"T5","agent_id":"A2","cost":16},{"task_id":"T5","agent_id":"A3","cost":14},{"task_id":"T6","agent_id":"A2","cost":17},{"task_id":"T6","agent_id":"A3","cost":6}]},"gold_status":"optimal","gold_objective":58.0,"gold_bound":58.0,"gold_solution":{"family":"assignment","status":"optimal","objective":58.0,"bound":58.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A2"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"aa2a372f888bbc65","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-019","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":50019,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 35}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 29}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 35}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 29}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 33\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["weld"],"penalty":35},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":38},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack","weld"],"penalty":29},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["lift","weld"],"penalty":33}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":12},{"task_id":"T3","agent_id":"A1","cost":16},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A3","cost":6}]},"gold_status":"optimal","gold_objective":20.0,"gold_bound":20.0,"gold_solution":{"family":"assignment","status":"optimal","objective":20.0,"bound":20.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"94619056bf241dce","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-020","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":50020,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect, T3 size 1 skills pack/weld, T4 size 2 skills weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 26}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"weld\"], \"penalty\": 40}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect, T3 size 1 skills pack/weld, T4 size 2 skills weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 26}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"weld\"], \"penalty\": 40}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 40\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":39},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect"],"penalty":26},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack","weld"],"penalty":32},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["weld"],"penalty":40}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A2","cost":14},{"task_id":"T2","agent_id":"A3","cost":14},{"task_id":"T3","agent_id":"A1","cost":8},{"task_id":"T3","agent_id":"A3","cost":8},{"task_id":"T4","agent_id":"A1","cost":5},{"task_id":"T4","agent_id":"A3","cost":16}]},"gold_status":"optimal","gold_objective":34.0,"gold_bound":34.0,"gold_solution":{"family":"assignment","status":"optimal","objective":34.0,"bound":34.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"a70e0db3d846416a","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-021","family":"assignment","split":"test","interactive":false,"difficulty":"hard","language":"fa","template_id":"T-A","seed":50021,"prompt_en":"A service desk has technicians A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/pack, T3 size 1 skills lift, T4 size 2 skills lift/pack, T5 size 1 skills lift/weld, T6 size 2 skills inspect/weld, T7 size 3 skills lift/weld, T8 size 2 skills pack/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/pack, T3 size 1 skills lift, T4 size 2 skills lift/pack, T5 size 1 skills lift/weld, T6 size 2 skills inspect/weld, T7 size 3 skills lift/weld, T8 size 2 skills pack/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 9\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift","pack"],"penalty":32},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":29},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["lift"],"penalty":33},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["lift","pack"],"penalty":28},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["lift","weld"],"penalty":40},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","weld"],"penalty":32},{"task_id":"T7","name":"job-7","size":3,"required":true,"skills":["lift","weld"],"penalty":38},{"task_id":"T8","name":"job-8","size":2,"required":true,"skills":["pack","weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":10},{"task_id":"T1","agent_id":"A2","cost":4},{"task_id":"T1","agent_id":"A3","cost":12},{"task_id":"T1","agent_id":"A4","cost":9},{"task_id":"T2","agent_id":"A1","cost":13},{"task_id":"T2","agent_id":"A2","cost":15},{"task_id":"T2","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A4","cost":15},{"task_id":"T3","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A4","cost":15},{"task_id":"T4","agent_id":"A2","cost":14},{"task_id":"T4","agent_id":"A3","cost":16},{"task_id":"T4","agent_id":"A4","cost":7},{"task_id":"T5","agent_id":"A1","cost":18},{"task_id":"T5","agent_id":"A3","cost":16},{"task_id":"T5","agent_id":"A4","cost":9},{"task_id":"T6","agent_id":"A1","cost":15},{"task_id":"T6","agent_id":"A2","cost":7},{"task_id":"T6","agent_id":"A4","cost":17},{"task_id":"T7","agent_id":"A1","cost":4},{"task_id":"T7","agent_id":"A3","cost":6},{"task_id":"T7","agent_id":"A4","cost":17},{"task_id":"T8","agent_id":"A1","cost":16},{"task_id":"T8","agent_id":"A2","cost":6},{"task_id":"T8","agent_id":"A3","cost":4},{"task_id":"T8","agent_id":"A4","cost":9}]},"gold_status":"optimal","gold_objective":63.0,"gold_bound":63.0,"gold_solution":{"family":"assignment","status":"optimal","objective":63.0,"bound":63.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A2"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A4"},{"task_id":"T4","agent_id":"A4"},{"task_id":"T5","agent_id":"A4"},{"task_id":"T6","agent_id":"A2"},{"task_id":"T7","agent_id":"A1"},{"task_id":"T8","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"68e49e596eb52a85","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-022","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":50022,"prompt_en":"A service desk has technicians A1 cap 4 skills weld, A2 cap 4 skills inspect, A3 cap 6 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills lift/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills lift/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 4 skills weld, A2 cap 4 skills inspect, A3 cap 6 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills lift/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills lift/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":36},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","weld"],"penalty":22},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack"],"penalty":27},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["lift","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A3","cost":11},{"task_id":"T2","agent_id":"A1","cost":16},{"task_id":"T2","agent_id":"A2","cost":15},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":10},{"task_id":"T4","agent_id":"A3","cost":18}]},"gold_status":"optimal","gold_objective":53.0,"gold_bound":53.0,"gold_solution":{"family":"assignment","status":"optimal","objective":53.0,"bound":53.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"91d5d0f2a7cdb2b3","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-023","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50023,"prompt_en":"A service desk has technicians A1 cap 3 skills weld, A2 cap 4 skills inspect, A3 cap 7 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 1 skills inspect/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 3 skills weld, A2 cap 4 skills inspect, A3 cap 7 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 1 skills inspect/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":29},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","weld"],"penalty":22},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack","weld"],"penalty":36},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["inspect","weld"],"penalty":33}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A3","cost":18},{"task_id":"T2","agent_id":"A1","cost":18},{"task_id":"T2","agent_id":"A2","cost":8},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A1","cost":10},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":4},{"task_id":"T4","agent_id":"A2","cost":14},{"task_id":"T4","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":21.0,"gold_bound":21.0,"gold_solution":{"family":"assignment","status":"optimal","objective":21.0,"bound":21.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"616463a38483d3aa","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-024","family":"assignment","split":"test","interactive":true,"difficulty":"medium","language":"en","template_id":"T-B","seed":50024,"prompt_en":"A service desk has technicians A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 9 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills weld, T2 size 3 skills pack, T3 size 3 skills lift/weld, T4 size 3 skills inspect/lift, T5 size 3 skills pack, T6 size 2 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 9 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills weld, T2 size 3 skills pack, T3 size 3 skills lift/weld, T4 size 3 skills inspect/lift, T5 size 3 skills pack, T6 size 2 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 9,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n }\n 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intersection is the eligibility rule"} +{"problem_id":"ASN-025","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50025,"prompt_en":"A service desk has technicians A1 cap 5 skills weld, A2 cap 6 skills inspect, A3 cap 5 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/pack, T3 size 1 skills inspect/pack, T4 size 2 skills weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 5 skills weld, A2 cap 6 skills inspect, A3 cap 5 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/pack, T3 size 1 skills inspect/pack, T4 size 2 skills weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","weld"],"penalty":39},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","pack"],"penalty":36},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","pack"],"penalty":26},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":10},{"task_id":"T1","agent_id":"A2","cost":11},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A2","cost":12},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A2","cost":18},{"task_id":"T3","agent_id":"A3","cost":12},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":34.0,"gold_bound":34.0,"gold_solution":{"family":"assignment","status":"optimal","objective":34.0,"bound":34.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2d5e70242c82e1c7","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-026","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":50026,"prompt_en":"A service desk has technicians A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills pack/weld, T2 size 2 skills inspect/pack, T3 size 2 skills inspect/pack, T4 size 3 skills lift/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills pack/weld, T2 size 2 skills inspect/pack, T3 size 2 skills inspect/pack, T4 size 3 skills lift/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["pack","weld"],"penalty":32},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["lift","weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":15},{"task_id":"T1","agent_id":"A3","cost":10},{"task_id":"T2","agent_id":"A2","cost":10},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A2","cost":16},{"task_id":"T3","agent_id":"A3","cost":18},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A3","cost":14}]},"gold_status":"optimal","gold_objective":46.0,"gold_bound":46.0,"gold_solution":{"family":"assignment","status":"optimal","objective":46.0,"bound":46.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"9cf7363994177683","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-027","family":"assignment","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-A","seed":50027,"prompt_en":"A service desk has technicians A1 cap 3 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect, T2 size 3 skills inspect, T3 size 1 skills inspect/lift/weld, T4 size 2 skills weld, T5 size 1 skills inspect/weld, T6 size 1 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 3 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect, T2 size 3 skills inspect, T3 size 1 skills inspect/lift/weld, T4 size 2 skills weld, T5 size 1 skills inspect/weld, T6 size 1 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 35\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","lift","weld"],"penalty":34},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["weld"],"penalty":32},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","weld"],"penalty":20},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["inspect","lift"],"penalty":35}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A2","cost":16},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A1","cost":9},{"task_id":"T2","agent_id":"A2","cost":8},{"task_id":"T2","agent_id":"A3","cost":6},{"task_id":"T3","agent_id":"A1","cost":8},{"task_id":"T3","agent_id":"A2","cost":18},{"task_id":"T3","agent_id":"A3","cost":14},{"task_id":"T4","agent_id":"A1","cost":14},{"task_id":"T4","agent_id":"A3","cost":14},{"task_id":"T5","agent_id":"A1","cost":14},{"task_id":"T5","agent_id":"A2","cost":18},{"task_id":"T5","agent_id":"A3","cost":18},{"task_id":"T6","agent_id":"A1","cost":11},{"task_id":"T6","agent_id":"A2","cost":5},{"task_id":"T6","agent_id":"A3","cost":6}]},"gold_status":"optimal","gold_objective":63.0,"gold_bound":63.0,"gold_solution":{"family":"assignment","status":"optimal","objective":63.0,"bound":63.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A1"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"75c4dedc90aa87db","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-028","family":"assignment","split":"test","interactive":false,"difficulty":"hard","language":"en","template_id":"T-B","seed":50028,"prompt_en":"A service desk has technicians A1 cap 4 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 4 skills lift/pack, A4 cap 6 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills inspect/pack, T2 size 1 skills inspect/weld, T3 size 3 skills inspect/lift/weld, T4 size 1 skills inspect/lift/pack, T5 size 1 skills weld, T6 size 2 skills inspect/weld, T7 size 2 skills pack, T8 size 3 skills lift/pack. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 4 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 4 skills lift/pack, A4 cap 6 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills inspect/pack, T2 size 1 skills inspect/weld, T3 size 3 skills inspect/lift/weld, T4 size 1 skills inspect/lift/pack, T5 size 1 skills weld, T6 size 2 skills inspect/weld, T7 size 2 skills pack, T8 size 3 skills lift/pack. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 39\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 4,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["inspect","pack"],"penalty":29},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","weld"],"penalty":40},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift","weld"],"penalty":32},{"task_id":"T4","name":"job-4","size":1,"required":true,"skills":["inspect","lift","pack"],"penalty":28},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["weld"],"penalty":33},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","weld"],"penalty":29},{"task_id":"T7","name":"job-7","size":2,"required":true,"skills":["pack"],"penalty":29},{"task_id":"T8","name":"job-8","size":3,"required":true,"skills":["lift","pack"],"penalty":39}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":4,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":15},{"task_id":"T1","agent_id":"A4","cost":15},{"task_id":"T2","agent_id":"A1","cost":9},{"task_id":"T2","agent_id":"A2","cost":11},{"task_id":"T2","agent_id":"A4","cost":17},{"task_id":"T3","agent_id":"A1","cost":11},{"task_id":"T3","agent_id":"A2","cost":10},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T3","agent_id":"A4","cost":18},{"task_id":"T4","agent_id":"A1","cost":13},{"task_id":"T4","agent_id":"A2","cost":6},{"task_id":"T4","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A4","cost":6},{"task_id":"T5","agent_id":"A1","cost":8},{"task_id":"T5","agent_id":"A4","cost":15},{"task_id":"T6","agent_id":"A1","cost":11},{"task_id":"T6","agent_id":"A2","cost":9},{"task_id":"T6","agent_id":"A4","cost":18},{"task_id":"T7","agent_id":"A2","cost":7},{"task_id":"T7","agent_id":"A3","cost":6},{"task_id":"T7","agent_id":"A4","cost":5},{"task_id":"T8","agent_id":"A2","cost":13},{"task_id":"T8","agent_id":"A3","cost":18},{"task_id":"T8","agent_id":"A4","cost":14}]},"gold_status":"optimal","gold_objective":59.0,"gold_bound":59.0,"gold_solution":{"family":"assignment","status":"optimal","objective":59.0,"bound":59.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A1"},{"task_id":"T6","agent_id":"A2"},{"task_id":"T7","agent_id":"A4"},{"task_id":"T8","agent_id":"A4"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"33e8008ea9f0e332","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-029","family":"assignment","split":"test","interactive":true,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50029,"prompt_en":"A service desk has technicians A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills pack/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills pack/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 25\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","weld"],"penalty":26},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","lift"],"penalty":36},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack"],"penalty":33},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["pack","weld"],"penalty":25}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":15},{"task_id":"T1","agent_id":"A2","cost":14},{"task_id":"T1","agent_id":"A3","cost":8},{"task_id":"T2","agent_id":"A2","cost":7},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A3","cost":10},{"task_id":"T4","agent_id":"A1","cost":13},{"task_id":"T4","agent_id":"A3","cost":12}]},"gold_status":"optimal","gold_objective":34.0,"gold_bound":34.0,"gold_solution":{"family":"assignment","status":"optimal","objective":34.0,"bound":34.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"a37065772aa4dfbf","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-030","family":"assignment","split":"test","interactive":false,"difficulty":"medium","language":"en","template_id":"T-B","seed":50030,"prompt_en":"A service desk has technicians A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 2 skills lift, T4 size 2 skills weld, T5 size 2 skills inspect, T6 size 1 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 2 skills lift, T4 size 2 skills weld, T5 size 2 skills inspect, T6 size 1 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 28\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["inspect","weld"],"penalty":35},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["lift"],"penalty":39},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["weld"],"penalty":22},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["inspect"],"penalty":30},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["inspect","lift"],"penalty":28}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":18},{"task_id":"T1","agent_id":"A2","cost":16},{"task_id":"T1","agent_id":"A3","cost":4},{"task_id":"T2","agent_id":"A1","cost":9},{"task_id":"T2","agent_id":"A2","cost":18},{"task_id":"T2","agent_id":"A3","cost":9},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":4},{"task_id":"T4","agent_id":"A3","cost":15},{"task_id":"T5","agent_id":"A1","cost":8},{"task_id":"T5","agent_id":"A2","cost":6},{"task_id":"T5","agent_id":"A3","cost":4},{"task_id":"T6","agent_id":"A1","cost":15},{"task_id":"T6","agent_id":"A2","cost":5},{"task_id":"T6","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":29.999999999999996,"gold_bound":29.999999999999996,"gold_solution":{"family":"assignment","status":"optimal","objective":29.999999999999996,"bound":29.999999999999996,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"ae3cf299b843c92f","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-031","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50031,"prompt_en":"A service desk has technicians A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills pack/weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack, T4 size 3 skills lift/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills pack/weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack, T4 size 3 skills lift/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 23\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 34\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["pack","weld"],"penalty":23},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack"],"penalty":24},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["lift","weld"],"penalty":34}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":7},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A2","cost":7},{"task_id":"T2","agent_id":"A3","cost":7},{"task_id":"T3","agent_id":"A3","cost":13},{"task_id":"T4","agent_id":"A1","cost":10},{"task_id":"T4","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":37.0,"gold_bound":37.0,"gold_solution":{"family":"assignment","status":"optimal","objective":37.0,"bound":37.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"1b6764eba2517c16","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-032","family":"assignment","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-B","seed":50032,"prompt_en":"A service desk has technicians A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack. Work orders: T1 size 3 skills pack, T2 size 3 skills inspect, T3 size 3 skills pack, T4 size 3 skills weld, T5 size 3 skills inspect, T6 size 3 skills weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack را دارد. سفارش‌ها: T1 size 3 skills pack, T2 size 3 skills inspect, T3 size 3 skills pack, T4 size 3 skills weld, T5 size 3 skills inspect, T6 size 3 skills weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 28\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 1,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["pack"],"penalty":37},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect"],"penalty":37},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack"],"penalty":39},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["weld"],"penalty":27},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["inspect"],"penalty":30},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["weld"],"penalty":28}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":1,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":1,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":1,"skills":["lift","pack"]}],"costs":[{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A1","cost":6},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T3","agent_id":"A2","cost":7},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T5","agent_id":"A1","cost":15},{"task_id":"T5","agent_id":"A2","cost":6},{"task_id":"T6","agent_id":"A1","cost":10}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"assignment","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"2c4f1aa24275210a","notes":"skill intersection is the eligibility rule"} +{"problem_id":"ASN-033","family":"assignment","split":"test","interactive":true,"difficulty":"infeasible","language":"fa","template_id":"T-A","seed":50033,"prompt_en":"A service desk has technicians A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack. Work orders: T1 size 3 skills lift, T2 size 3 skills pack, T3 size 3 skills inspect/lift, T4 size 3 skills inspect/pack, T5 size 3 skills pack, T6 size 3 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack را دارد. سفارش‌ها: T1 size 3 skills lift, T2 size 3 skills pack, T3 size 3 skills inspect/lift, T4 size 3 skills inspect/pack, T5 size 3 skills pack, T6 size 3 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 20\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 1,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["lift"],"penalty":36},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["pack"],"penalty":30},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift"],"penalty":28},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["inspect","pack"],"penalty":34},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["pack"],"penalty":20},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["inspect","lift"],"penalty":20}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":1,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":1,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":1,"skills":["lift","pack"]}],"costs":[{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A2","cost":7},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A1","cost":5},{"task_id":"T3","agent_id":"A2","cost":8},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":14},{"task_id":"T4","agent_id":"A2","cost":10},{"task_id":"T4","agent_id":"A3","cost":8},{"task_id":"T5","agent_id":"A2","cost":7},{"task_id":"T5","agent_id":"A3","cost":11},{"task_id":"T6","agent_id":"A1","cost":9},{"task_id":"T6","agent_id":"A2","cost":18},{"task_id":"T6","agent_id":"A3","cost":17}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"assignment","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"483125be5eebd870","notes":"skill intersection is the eligibility rule"} +{"problem_id":"SCH-001","family":"scheduling","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":75001,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 5 rel 2 due 8, J2 dur 2 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 2 rel 2 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 2, \"due\": 8, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 5 rel 2 due 8, J2 dur 2 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 2 rel 2 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 2, \"due\": 8, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 8,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 20\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":2,"due":8,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":10,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":14,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":2,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":20},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":7},{"job_id":"J2","machine_id":"M1","start":0,"end":2},{"job_id":"J3","machine_id":"M1","start":7,"end":10},{"job_id":"J4","machine_id":"M1","start":10,"end":12}],"message":"OPTIMAL"},"structural_key":"f3b26ff82b5918fb","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-002","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75002,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 5 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 5 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 10, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 24}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 5 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 5 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 10, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 24}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 4,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 19,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 24\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":4,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":5,"release":0,"due":10,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":19,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":24},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":3,"end":8},{"job_id":"J3","machine_id":"M1","start":8,"end":11},{"job_id":"J4","machine_id":"M1","start":11,"end":16}],"message":"OPTIMAL"},"structural_key":"d340539d914c97df","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-003","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75003,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 1 due 6, J2 dur 3 rel 2 due 7, J3 dur 4 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 3 rel 0 due 20, J6 dur 2 rel 0 due 21\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 21, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 26}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 1 due 6, J2 dur 3 rel 2 due 7, J3 dur 4 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 3 rel 0 due 20, J6 dur 2 rel 0 due 21\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 21, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 26}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 7,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 26\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":1,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":3,"release":2,"due":7,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":13,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":20,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":0,"due":21,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":26},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":2,"end":5},{"job_id":"J2","machine_id":"M1","start":3,"end":6},{"job_id":"J3","machine_id":"M2","start":5,"end":9},{"job_id":"J4","machine_id":"M1","start":0,"end":3},{"job_id":"J5","machine_id":"M1","start":6,"end":9},{"job_id":"J6","machine_id":"M2","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"8d93269a62953269","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-004","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":75004,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 3 rel 2 due 10, J3 dur 4 rel 0 due 15, J4 dur 4 rel 0 due 18\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 10, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 18, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 3 rel 2 due 10, J3 dur 4 rel 0 due 15, J4 dur 4 rel 0 due 18\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 10, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 18, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 10,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 18,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 23\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":2,"due":10,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":15,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":18,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":23},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":4,"end":7},{"job_id":"J3","machine_id":"M1","start":11,"end":15},{"job_id":"J4","machine_id":"M1","start":7,"end":11}],"message":"OPTIMAL"},"structural_key":"ab08e0ff4cbe98a0","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-005","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75005,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 5 rel 0 due 6, J2 dur 3 rel 1 due 12, J3 dur 4 rel 2 due 16, J4 dur 2 rel 2 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 5 rel 0 due 6, J2 dur 3 rel 1 due 12, J3 dur 4 rel 2 due 16, J4 dur 2 rel 2 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 12,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":1,"due":12,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":2,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":2,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":5},{"job_id":"J2","machine_id":"M1","start":7,"end":10},{"job_id":"J3","machine_id":"M1","start":10,"end":14},{"job_id":"J4","machine_id":"M1","start":5,"end":7}],"message":"OPTIMAL"},"structural_key":"3a19f6671a25fbea","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-006","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75006,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 5 rel 1 due 11, J3 dur 2 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 5 rel 0 due 21, J6 dur 2 rel 1 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 1, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 0, \"due\": 21, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 5 rel 1 due 11, J3 dur 2 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 5 rel 0 due 21, J6 dur 2 rel 1 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 1, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 0, \"due\": 21, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 11,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 22,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":6,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":5,"release":1,"due":11,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":13,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":17,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":0,"due":21,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":1,"due":22,"weight":2,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":3},{"job_id":"J2","machine_id":"M2","start":5,"end":10},{"job_id":"J3","machine_id":"M1","start":5,"end":7},{"job_id":"J4","machine_id":"M1","start":7,"end":10},{"job_id":"J5","machine_id":"M1","start":0,"end":5},{"job_id":"J6","machine_id":"M2","start":3,"end":5}],"message":"OPTIMAL"},"structural_key":"28f92c4b29421b9e","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-007","family":"scheduling","split":"development","interactive":true,"difficulty":"hard","language":"en","template_id":"D-A","seed":75007,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3, J2->J5). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 5 rel 0 due 11, J3 dur 2 rel 1 due 15, J4 dur 2 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 4 rel 0 due 22, J7 dur 2 rel 1 due 22, J8 dur 3 rel 2 due 25\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 4, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 3, \"release\": 2, \"due\": 25, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 32}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3, J2->J5) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 5 rel 0 due 11, J3 dur 2 rel 1 due 15, J4 dur 2 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 4 rel 0 due 22, J7 dur 2 rel 1 due 22, J8 dur 3 rel 2 due 25\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 4, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 3, \"release\": 2, \"due\": 25, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 32}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 22,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 22,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 25,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 32\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":5,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":1,"due":15,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":17,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":0,"due":17,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":4,"release":0,"due":22,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J7","name":"op-7","duration":2,"release":1,"due":22,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":3,"release":2,"due":25,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":32},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":0,"end":5},{"job_id":"J3","machine_id":"M2","start":4,"end":6},{"job_id":"J4","machine_id":"M2","start":8,"end":10},{"job_id":"J5","machine_id":"M2","start":6,"end":8},{"job_id":"J6","machine_id":"M1","start":5,"end":9},{"job_id":"J7","machine_id":"M2","start":10,"end":12},{"job_id":"J8","machine_id":"M1","start":9,"end":12}],"message":"OPTIMAL"},"structural_key":"050bb292957ce323","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-008","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75008,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 1 due 6, J2 dur 4 rel 0 due 12, J3 dur 4 rel 0 due 15, J4 dur 5 rel 1 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 1, \"due\": 19, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 25}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 1 due 6, J2 dur 4 rel 0 due 12, J3 dur 4 rel 0 due 15, J4 dur 5 rel 1 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 1, \"due\": 19, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 25}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 19,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 25\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":1,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":12,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":1,"due":19,"weight":3,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":25},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":1,"end":5},{"job_id":"J2","machine_id":"M1","start":5,"end":9},{"job_id":"J3","machine_id":"M1","start":9,"end":13},{"job_id":"J4","machine_id":"M1","start":13,"end":18}],"message":"OPTIMAL"},"structural_key":"98f68288cc66b7e8","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-009","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75009,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 2 rel 2 due 6, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 11, J5 dur 5 rel 1 due 18, J6 dur 2 rel 0 due 20\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 2, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 1, \"due\": 18, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 20, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 24}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 2 rel 2 due 6, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 11, J5 dur 5 rel 1 due 18, J6 dur 2 rel 0 due 20\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 2, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 1, \"due\": 18, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 20, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 24}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 18,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 24\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":2,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":11,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":1,"due":18,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":0,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":24},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":2,"end":4},{"job_id":"J3","machine_id":"M1","start":4,"end":7},{"job_id":"J4","machine_id":"M2","start":0,"end":2},{"job_id":"J5","machine_id":"M2","start":4,"end":9},{"job_id":"J6","machine_id":"M2","start":2,"end":4}],"message":"OPTIMAL"},"structural_key":"a82fa38af8e40896","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-010","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":75010,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 5, J2 dur 2 rel 1 due 9, J3 dur 2 rel 0 due 12, J4 dur 4 rel 1 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 1, \"due\": 9, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 5, J2 dur 2 rel 1 due 9, J3 dur 2 rel 0 due 12, J4 dur 4 rel 1 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 1, \"due\": 9, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 5,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 9,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 14,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 20\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":5,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":9,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":12,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":1,"due":14,"weight":3,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":20},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":4,"end":6},{"job_id":"J3","machine_id":"M1","start":10,"end":12},{"job_id":"J4","machine_id":"M1","start":6,"end":10}],"message":"OPTIMAL"},"structural_key":"44defd099664afa8","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-011","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75011,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 4 rel 0 due 7, J3 dur 3 rel 0 due 11, J4 dur 4 rel 0 due 16\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 4 rel 0 due 7, J3 dur 3 rel 0 due 11, J4 dur 4 rel 0 due 16\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 21\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":6,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":7,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":11,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":21},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":2,"end":6},{"job_id":"J3","machine_id":"M1","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":9,"end":13}],"message":"OPTIMAL"},"structural_key":"1f2e26b801fa687e","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-012","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75012,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 6, J2 dur 2 rel 0 due 10, J3 dur 3 rel 1 due 12, J4 dur 3 rel 2 due 15, J5 dur 3 rel 0 due 16, J6 dur 2 rel 2 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 6, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 2, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 25}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 6, J2 dur 2 rel 0 due 10, J3 dur 3 rel 1 due 12, J4 dur 3 rel 2 due 15, J5 dur 3 rel 0 due 16, J6 dur 2 rel 2 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 6, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 2, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 25}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 15,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 19,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 25\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":6,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":10,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":1,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":2,"due":15,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":2,"due":19,"weight":2,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":25},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":0,"end":2},{"job_id":"J3","machine_id":"M2","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":2,"end":5},{"job_id":"J5","machine_id":"M1","start":5,"end":8},{"job_id":"J6","machine_id":"M2","start":4,"end":6}],"message":"OPTIMAL"},"structural_key":"e309923760f6714b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-013","family":"scheduling","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":75013,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 5 rel 2 due 11, J3 dur 4 rel 1 due 14, J4 dur 2 rel 1 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 2, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 5 rel 2 due 11, J3 dur 4 rel 1 due 14, J4 dur 2 rel 1 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 2, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 11,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 14,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 21\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":6,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":5,"release":2,"due":11,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":1,"due":14,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":1,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":21},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":6,"end":11},{"job_id":"J3","machine_id":"M1","start":2,"end":6},{"job_id":"J4","machine_id":"M1","start":11,"end":13}],"message":"OPTIMAL"},"structural_key":"fa5346efc4f12de7","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-014","family":"scheduling","split":"development","interactive":false,"difficulty":"hard","language":"en","template_id":"D-B","seed":75014,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3, J2->J5). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 3, J2 dur 4 rel 1 due 8, J3 dur 4 rel 0 due 11, J4 dur 4 rel 2 due 16, J5 dur 3 rel 0 due 21, J6 dur 3 rel 1 due 23, J7 dur 3 rel 0 due 24, J8 dur 5 rel 0 due 31\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 3, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 8, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 21, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 3, \"release\": 1, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 3, \"release\": 0, \"due\": 24, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 5, \"release\": 0, \"due\": 31, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 36}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3, J2->J5) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 3, J2 dur 4 rel 1 due 8, J3 dur 4 rel 0 due 11, J4 dur 4 rel 2 due 16, J5 dur 3 rel 0 due 21, J6 dur 3 rel 1 due 23, J7 dur 3 rel 0 due 24, J8 dur 5 rel 0 due 31\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 3, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 8, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 21, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 3, \"release\": 1, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 3, \"release\": 0, \"due\": 24, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 5, \"release\": 0, \"due\": 31, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 36}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 3,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 8,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 23,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 24,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 31,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 36\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":3,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":8,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":2,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":21,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":1,"due":23,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J7","name":"op-7","duration":3,"release":0,"due":24,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":5,"release":0,"due":31,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":36},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":3,"end":7},{"job_id":"J3","machine_id":"M1","start":7,"end":11},{"job_id":"J4","machine_id":"M2","start":2,"end":6},{"job_id":"J5","machine_id":"M1","start":11,"end":14},{"job_id":"J6","machine_id":"M2","start":11,"end":14},{"job_id":"J7","machine_id":"M1","start":0,"end":3},{"job_id":"J8","machine_id":"M2","start":6,"end":11}],"message":"OPTIMAL"},"structural_key":"c4077ee842dab620","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-015","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75015,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 4 rel 1 due 11, J3 dur 3 rel 0 due 12, J4 dur 3 rel 1 due 15, J5 dur 3 rel 0 due 20, J6 dur 5 rel 2 due 23\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 11, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 12, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 1, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 2, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 29}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 4 rel 1 due 11, J3 dur 3 rel 0 due 12, J4 dur 3 rel 1 due 15, J5 dur 3 rel 0 due 20, J6 dur 5 rel 2 due 23\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 11, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 12, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 1, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 2, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 29}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 4,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 11,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 23,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 29\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":4,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":11,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":12,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":3,"release":1,"due":15,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":20,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":5,"release":2,"due":23,"weight":4,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":29},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":3,"end":7},{"job_id":"J3","machine_id":"M1","start":7,"end":10},{"job_id":"J4","machine_id":"M2","start":3,"end":6},{"job_id":"J5","machine_id":"M2","start":0,"end":3},{"job_id":"J6","machine_id":"M2","start":6,"end":11}],"message":"OPTIMAL"},"structural_key":"f3cab51cd91813b0","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-016","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":75016,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 2 due 5, J2 dur 3 rel 0 due 10, J3 dur 3 rel 2 due 12, J4 dur 5 rel 0 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 2, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 2, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 2 due 5, J2 dur 3 rel 0 due 10, J3 dur 3 rel 2 due 12, J4 dur 5 rel 0 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 2, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 2, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 5,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 12,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":2,"due":5,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":2,"due":12,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":15,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":2.0,"gold_bound":2.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":2.0,"bound":2.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":3,"end":6},{"job_id":"J2","machine_id":"M1","start":0,"end":3},{"job_id":"J3","machine_id":"M1","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":9,"end":14}],"message":"OPTIMAL"},"structural_key":"77c5ca9a6efec0ce","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-017","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75017,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 3 rel 1 due 7, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 13\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 19}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 3 rel 1 due 7, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 13\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 19}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 7,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 19\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":6,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":1,"due":7,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":13,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":19},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":3,"end":6},{"job_id":"J3","machine_id":"M1","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":9,"end":11}],"message":"OPTIMAL"},"structural_key":"321dcec5bcc2ab1a","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-018","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75018,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 4, J2 dur 4 rel 0 due 10, J3 dur 2 rel 0 due 9, J4 dur 3 rel 2 due 14, J5 dur 4 rel 0 due 17, J6 dur 5 rel 0 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 9, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 14, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 4, \"release\": 0, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 4, J2 dur 4 rel 0 due 10, J3 dur 2 rel 0 due 9, J4 dur 3 rel 2 due 14, J5 dur 4 rel 0 due 17, J6 dur 5 rel 0 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 9, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 14, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 4, \"release\": 0, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 4,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 22,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":4,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":9,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":2,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":0,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J6","name":"op-6","duration":5,"release":0,"due":22,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":4,"end":8},{"job_id":"J3","machine_id":"M2","start":2,"end":4},{"job_id":"J4","machine_id":"M2","start":4,"end":7},{"job_id":"J5","machine_id":"M1","start":0,"end":4},{"job_id":"J6","machine_id":"M1","start":8,"end":13}],"message":"OPTIMAL"},"structural_key":"0a25d991b8ebc99b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-019","family":"scheduling","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":75019,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 5 rel 0 due 7, J2 dur 4 rel 0 due 13, J3 dur 4 rel 1 due 17, J4 dur 2 rel 0 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 5 rel 0 due 7, J2 dur 4 rel 0 due 13, J3 dur 4 rel 1 due 17, J4 dur 2 rel 0 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 17,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 23\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":13,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":1,"due":17,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":23},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":7},{"job_id":"J2","machine_id":"M1","start":7,"end":11},{"job_id":"J3","machine_id":"M1","start":11,"end":15},{"job_id":"J4","machine_id":"M1","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"21a2617ee4fc356c","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-020","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75020,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 1 due 7, J2 dur 4 rel 2 due 8, J3 dur 4 rel 1 due 13, J4 dur 4 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 2, \"due\": 8, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 13, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 1 due 7, J2 dur 4 rel 2 due 8, J3 dur 4 rel 1 due 13, J4 dur 4 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 2, \"due\": 8, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 13, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 8,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 13,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 19,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 23\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":1,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":2,"due":8,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":1,"due":13,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":19,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":23},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":1,"end":4},{"job_id":"J2","machine_id":"M1","start":4,"end":8},{"job_id":"J3","machine_id":"M1","start":8,"end":12},{"job_id":"J4","machine_id":"M1","start":12,"end":16}],"message":"OPTIMAL"},"structural_key":"76ab27078c9e56ec","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-021","family":"scheduling","split":"test","interactive":false,"difficulty":"hard","language":"fa","template_id":"T-A","seed":75021,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 3 rel 0 due 7, J2 dur 2 rel 0 due 9, J3 dur 2 rel 0 due 9, J4 dur 5 rel 0 due 16, J5 dur 4 rel 2 due 20, J6 dur 4 rel 0 due 23, J7 dur 3 rel 2 due 27, J8 dur 2 rel 0 due 26. Precedence: J1->J3, J2->J5. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 3 rel 0 due 7, J2 dur 2 rel 0 due 9, J3 dur 2 rel 0 due 9, J4 dur 5 rel 0 due 16, J5 dur 4 rel 2 due 20, J6 dur 4 rel 0 due 23, J7 dur 3 rel 2 due 27, J8 dur 2 rel 0 due 26. تقدم: J1->J3, J2->J5. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 16,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 23,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 27,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 26,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 33\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":7,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":9,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":9,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":16,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":2,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J6","name":"op-6","duration":4,"release":0,"due":23,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J7","name":"op-7","duration":3,"release":2,"due":27,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":2,"release":0,"due":26,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":33},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":2,"end":5},{"job_id":"J2","machine_id":"M2","start":0,"end":2},{"job_id":"J3","machine_id":"M1","start":6,"end":8},{"job_id":"J4","machine_id":"M2","start":8,"end":13},{"job_id":"J5","machine_id":"M1","start":2,"end":6},{"job_id":"J6","machine_id":"M1","start":8,"end":12},{"job_id":"J7","machine_id":"M2","start":5,"end":8},{"job_id":"J8","machine_id":"M1","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"88a4981fddb98a2b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-022","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":75022,"prompt_en":"A shop has machines M1. Jobs: J1 dur 5 rel 0 due 9, J2 dur 3 rel 0 due 10, J3 dur 4 rel 2 due 13, J4 dur 2 rel 1 due 17. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 5 rel 0 due 9, J2 dur 3 rel 0 due 10, J3 dur 4 rel 2 due 13, J4 dur 2 rel 1 due 17. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 13,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":9,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":2,"due":13,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":1,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":3,"end":8},{"job_id":"J2","machine_id":"M1","start":0,"end":3},{"job_id":"J3","machine_id":"M1","start":8,"end":12},{"job_id":"J4","machine_id":"M1","start":12,"end":14}],"message":"OPTIMAL"},"structural_key":"fc27c47c78ea227c","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-023","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":75023,"prompt_en":"A shop has machines M1. Jobs: J1 dur 3 rel 0 due 7, J2 dur 2 rel 1 due 6, J3 dur 2 rel 0 due 10, J4 dur 2 rel 2 due 11. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 3 rel 0 due 7, J2 dur 2 rel 1 due 6, J3 dur 2 rel 0 due 10, J4 dur 2 rel 2 due 11. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 17\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":7,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":10,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":2,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":17},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":4,"end":7},{"job_id":"J2","machine_id":"M1","start":2,"end":4},{"job_id":"J3","machine_id":"M1","start":0,"end":2},{"job_id":"J4","machine_id":"M1","start":7,"end":9}],"message":"OPTIMAL"},"structural_key":"5dfdc5a6705389ef","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-024","family":"scheduling","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":75024,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 5 rel 2 due 7, J2 dur 3 rel 2 due 11, J3 dur 2 rel 0 due 14, J4 dur 3 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 5 rel 0 due 24. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 5 rel 2 due 7, J2 dur 3 rel 2 due 11, J3 dur 2 rel 0 due 14, J4 dur 3 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 5 rel 0 due 24. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 11,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 24,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":2,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":3,"release":2,"due":11,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":5,"release":0,"due":24,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":2,"end":7},{"job_id":"J2","machine_id":"M2","start":7,"end":10},{"job_id":"J3","machine_id":"M1","start":8,"end":10},{"job_id":"J4","machine_id":"M1","start":0,"end":3},{"job_id":"J5","machine_id":"M2","start":0,"end":2},{"job_id":"J6","machine_id":"M1","start":3,"end":8}],"message":"OPTIMAL"},"structural_key":"1a960892242a07ff","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-025","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":75025,"prompt_en":"A shop has machines M1. Jobs: J1 dur 4 rel 1 due 5, J2 dur 4 rel 0 due 12, J3 dur 2 rel 1 due 12, J4 dur 2 rel 0 due 14. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 4 rel 1 due 5, J2 dur 4 rel 0 due 12, J3 dur 2 rel 1 due 12, J4 dur 2 rel 0 due 14. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 5,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 12,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 20\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":1,"due":5,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":1,"due":12,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":20},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":1,"end":5},{"job_id":"J2","machine_id":"M1","start":5,"end":9},{"job_id":"J3","machine_id":"M1","start":9,"end":11},{"job_id":"J4","machine_id":"M1","start":11,"end":13}],"message":"OPTIMAL"},"structural_key":"754a69c12ebd799b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-026","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":75026,"prompt_en":"A shop has machines M1. Jobs: J1 dur 5 rel 0 due 9, J2 dur 2 rel 1 due 10, J3 dur 4 rel 0 due 14, J4 dur 2 rel 0 due 15. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 5 rel 0 due 9, J2 dur 2 rel 1 due 10, J3 dur 4 rel 0 due 14, J4 dur 2 rel 0 due 15. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 10,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 21\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":9,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":10,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":15,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":21},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":4,"end":9},{"job_id":"J2","machine_id":"M1","start":2,"end":4},{"job_id":"J3","machine_id":"M1","start":9,"end":13},{"job_id":"J4","machine_id":"M1","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"cec5818c37927030","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-027","family":"scheduling","split":"test","interactive":true,"difficulty":"medium","language":"fa","template_id":"T-A","seed":75027,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 3 rel 0 due 5, J2 dur 2 rel 1 due 8, J3 dur 3 rel 0 due 10, J4 dur 4 rel 1 due 14, J5 dur 4 rel 0 due 20, J6 dur 3 rel 0 due 22. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 3 rel 0 due 5, J2 dur 2 rel 1 due 8, J3 dur 3 rel 0 due 10, J4 dur 4 rel 1 due 14, J5 dur 4 rel 0 due 20, J6 dur 3 rel 0 due 22. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 5,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 8,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 22,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 27\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":5,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":8,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":10,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":4,"release":1,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":0,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":0,"due":22,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":27},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":1,"end":3},{"job_id":"J3","machine_id":"M1","start":3,"end":6},{"job_id":"J4","machine_id":"M2","start":6,"end":10},{"job_id":"J5","machine_id":"M1","start":6,"end":10},{"job_id":"J6","machine_id":"M2","start":3,"end":6}],"message":"OPTIMAL"},"structural_key":"94894e246dcfd2a7","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-028","family":"scheduling","split":"test","interactive":false,"difficulty":"hard","language":"en","template_id":"T-B","seed":75028,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 5 rel 0 due 9, J2 dur 2 rel 0 due 8, J3 dur 2 rel 0 due 12, J4 dur 4 rel 0 due 17, J5 dur 5 rel 0 due 20, J6 dur 3 rel 2 due 22, J7 dur 4 rel 0 due 26, J8 dur 4 rel 2 due 32. Precedence: J1->J3, J2->J5. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 5 rel 0 due 9, J2 dur 2 rel 0 due 8, J3 dur 2 rel 0 due 12, J4 dur 4 rel 0 due 17, J5 dur 5 rel 0 due 20, J6 dur 3 rel 2 due 22, J7 dur 4 rel 0 due 26, J8 dur 4 rel 2 due 32. تقدم: J1->J3, J2->J5. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 8,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 22,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 26,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 32,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 37\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":9,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":8,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":17,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":0,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":2,"due":22,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J7","name":"op-7","duration":4,"release":0,"due":26,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":4,"release":2,"due":32,"weight":1,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":37},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":4,"end":9},{"job_id":"J2","machine_id":"M2","start":0,"end":2},{"job_id":"J3","machine_id":"M1","start":9,"end":11},{"job_id":"J4","machine_id":"M1","start":0,"end":4},{"job_id":"J5","machine_id":"M2","start":6,"end":11},{"job_id":"J6","machine_id":"M2","start":11,"end":14},{"job_id":"J7","machine_id":"M1","start":11,"end":15},{"job_id":"J8","machine_id":"M2","start":2,"end":6}],"message":"OPTIMAL"},"structural_key":"786d201a96694b14","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-029","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":75029,"prompt_en":"A shop has machines M1. Jobs: J1 dur 4 rel 2 due 6, J2 dur 2 rel 2 due 9, J3 dur 4 rel 2 due 14, J4 dur 4 rel 2 due 15. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 4 rel 2 due 6, J2 dur 2 rel 2 due 9, J3 dur 4 rel 2 due 14, J4 dur 4 rel 2 due 15. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 6,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 9,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 14,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 15,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":2,"due":6,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":2,"due":9,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":2,"due":14,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":2,"due":15,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":2.0,"gold_bound":2.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":2.0,"bound":2.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":6},{"job_id":"J2","machine_id":"M1","start":6,"end":8},{"job_id":"J3","machine_id":"M1","start":8,"end":12},{"job_id":"J4","machine_id":"M1","start":12,"end":16}],"message":"OPTIMAL"},"structural_key":"c1def371d6464506","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-030","family":"scheduling","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":75030,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 2 rel 2 due 4, J2 dur 4 rel 0 due 10, J3 dur 4 rel 0 due 11, J4 dur 3 rel 0 due 15, J5 dur 4 rel 1 due 21, J6 dur 4 rel 2 due 22. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 2 rel 2 due 4, J2 dur 4 rel 0 due 10, J3 dur 4 rel 0 due 11, J4 dur 3 rel 0 due 15, J5 dur 4 rel 1 due 21, J6 dur 4 rel 2 due 22. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 4,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 21,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 22,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 29\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":2,"due":4,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":1,"due":21,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":4,"release":2,"due":22,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":29},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":4},{"job_id":"J2","machine_id":"M2","start":0,"end":4},{"job_id":"J3","machine_id":"M2","start":4,"end":8},{"job_id":"J4","machine_id":"M1","start":8,"end":11},{"job_id":"J5","machine_id":"M2","start":8,"end":12},{"job_id":"J6","machine_id":"M1","start":4,"end":8}],"message":"OPTIMAL"},"structural_key":"d614e5ebef3872d6","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-031","family":"scheduling","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-A","seed":75031,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 3 rel 0 due 2 hard, J2 dur 5 rel 1 due 5 hard, J3 dur 2 rel 0 due 14, J4 dur 4 rel 0 due 18, J5 dur 5 rel 0 due 21, J6 dur 3 rel 0 due 26. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 3 rel 0 due 2 hard, J2 dur 5 rel 1 due 5 hard, J3 dur 2 rel 0 due 14, J4 dur 4 rel 0 due 18, J5 dur 5 rel 0 due 21, J6 dur 3 rel 0 due 26. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 2,\n \"weight\": 4,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 5,\n \"weight\": 1,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 18,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 26,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 30\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":2,"weight":4,"hard_due":true,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":5,"release":1,"due":5,"weight":1,"hard_due":true,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":18,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":0,"due":21,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":0,"due":26,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":30},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"scheduling","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"1a1b4b4a5a920dbe","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-032","family":"scheduling","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-B","seed":75032,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 2 rel 1 due 2 hard, J2 dur 4 rel 1 due 4 hard, J3 dur 3 rel 2 due 12, J4 dur 2 rel 0 due 13, J5 dur 2 rel 1 due 15, J6 dur 3 rel 1 due 18. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 2 rel 1 due 2 hard, J2 dur 4 rel 1 due 4 hard, J3 dur 3 rel 2 due 12, J4 dur 2 rel 0 due 13, J5 dur 2 rel 1 due 15, J6 dur 3 rel 1 due 18. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 2,\n \"weight\": 2,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 4,\n \"weight\": 2,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 18,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 24\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":1,"due":2,"weight":2,"hard_due":true,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":4,"weight":2,"hard_due":true,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":2,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":13,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":1,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":1,"due":18,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":24},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"scheduling","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"56a2b20635ec8a65","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} +{"problem_id":"SCH-033","family":"scheduling","split":"test","interactive":true,"difficulty":"infeasible","language":"fa","template_id":"T-A","seed":75033,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 4 rel 0 due 3 hard, J2 dur 4 rel 1 due 4 hard, J3 dur 3 rel 0 due 12, J4 dur 5 rel 0 due 17, J5 dur 2 rel 1 due 19, J6 dur 2 rel 0 due 21. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 4 rel 0 due 3 hard, J2 dur 4 rel 1 due 4 hard, J3 dur 3 rel 0 due 12, J4 dur 5 rel 0 due 17, J5 dur 2 rel 1 due 19, J6 dur 2 rel 0 due 21. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 3,\n \"weight\": 2,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 4,\n \"weight\": 4,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 19,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":3,"weight":2,"hard_due":true,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":4,"weight":4,"hard_due":true,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":12,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":1,"due":19,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J6","name":"op-6","duration":2,"release":0,"due":21,"weight":4,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"scheduling","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"dde60fb92fe4b1f3","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} diff --git a/demo/examples/protocol.md b/demo/examples/protocol.md new file mode 100644 index 0000000000000000000000000000000000000000..ff47013be4ad9a79eaef15e1ef9594474afb3640 --- /dev/null +++ b/demo/examples/protocol.md @@ -0,0 +1,13 @@ +# ORBench reproduction protocol v1 + +Seed: 25. Code version: 0.1.0. Solver: OR-Tools CP-SAT, 1 thread, 6–8 seconds. + +1. Generate the catalog with `python scripts/build_artifacts.py`. +2. Each problem stores `schema_payload`, bilingual prompts, `gold_status`, `gold_objective`, and `gold_solution`. +3. Evaluated methods: `structured-solver`, `heuristic`, `json-extractor+solver`, `template-extractor+solver`, `naive-direct`. +4. Listed but not run: `Qwen/Qwen3-4B-Instruct-2507`, `Qwen/Qwen3.8-27B`, `moonshotai/Kimi-K3`, `zai-org/GLM-5.3`, `deepseek-ai/DeepSeek-V4.1-Flash`. Cells are `not_evaluated`. +5. Gap = max(0, (method_obj − gold_obj) / max(1, |gold_obj|)) only if gold status is optimal and the method plan is feasible. +6. Paid APIs stay off. Do not substitute a second paid provider when the first is missing. +7. Synthetic results in this dataset are not customer data. + +Run `pytest tests/test_pipeline.py` after generation. A passing suite is the acceptance check for constraint validation, split hygiene, and honest unevaluated cells. diff --git a/demo/examples/results.jsonl b/demo/examples/results.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..a41bd3c4ddeb6cf6db49e642d5300e0bfade4fea --- /dev/null +++ b/demo/examples/results.jsonl @@ -0,0 +1,1000 @@ +{"problem_id":"INV-001","method_id":"structured-solver","method_kind":"structured-solver","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":159.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0038488999707624316,"cost_usd":0.0,"violated":[],"notes":"schema entered the solver without an LLM","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"heuristic","method_kind":"heuristic","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"heuristic","feasible":true,"optimality_gap":0.11949685534591195,"objective":178.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.000054100004490464926,"cost_usd":0.0,"violated":[],"notes":"lot-for-lot pack-rounded","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"json-extractor+solver","method_kind":"text-to-schema","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":159.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.003551199974026531,"cost_usd":0.0,"violated":[],"notes":"JSON extracted from the prompt","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"template-extractor+solver","method_kind":"text-to-schema","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":159.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0035841999924741685,"cost_usd":0.0,"violated":[],"notes":"labeled fields or SCHEMA_BEGIN block","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"naive-direct","method_kind":"direct-answer","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"invalid","feasible":false,"optimality_gap":null,"objective":211.0,"gold_objective":159.0,"gold_status":"optimal","seconds":0.00002640002639964223,"cost_usd":0.0,"violated":["pack","budget"],"notes":"naive-direct: order raw demand, ignore pack/budget/capacity","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"Qwen/Qwen3-4B-Instruct-2507","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"Paid/local LLM inference is off. No batch was run.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"Qwen/Qwen3.8-27B","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"Not hosted on this CPU Space. No API batch.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"moonshotai/Kimi-K3","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"API optional and disabled. Not evaluated.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"zai-org/GLM-5.3","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"API optional and disabled. Not evaluated.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-001","method_id":"deepseek-ai/DeepSeek-V4.1-Flash","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":159.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"API optional and disabled. Not evaluated.","precomputed":true,"family":"inventory","split":"development","language":"en","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"structured-solver","method_kind":"structured-solver","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":93.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.006716199975926429,"cost_usd":0.0,"violated":[],"notes":"schema entered the solver without an LLM","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"heuristic","method_kind":"heuristic","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"heuristic","feasible":true,"optimality_gap":0.1935483870967742,"objective":111.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.000055100012104958296,"cost_usd":0.0,"violated":[],"notes":"lot-for-lot pack-rounded","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"json-extractor+solver","method_kind":"text-to-schema","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":93.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.006304699985776097,"cost_usd":0.0,"violated":[],"notes":"JSON extracted from the prompt","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"template-extractor+solver","method_kind":"text-to-schema","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"optimal","feasible":true,"optimality_gap":0.0,"objective":93.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.006902099994476885,"cost_usd":0.0,"violated":[],"notes":"labeled fields or SCHEMA_BEGIN block","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"naive-direct","method_kind":"direct-answer","evaluated":true,"parse_success":true,"constraint_fidelity":1.0,"status":"invalid","feasible":false,"optimality_gap":null,"objective":149.0,"gold_objective":93.0,"gold_status":"optimal","seconds":0.00004730001091957092,"cost_usd":0.0,"violated":["pack","pack","pack","pack"],"notes":"naive-direct: order raw demand, ignore pack/budget/capacity","precomputed":true,"family":"inventory","split":"development","language":"fa","difficulty":"easy"} +{"problem_id":"INV-002","method_id":"Qwen/Qwen3-4B-Instruct-2507","method_kind":"llm-schema","evaluated":false,"parse_success":null,"constraint_fidelity":null,"status":"not_evaluated","feasible":null,"optimality_gap":null,"objective":null,"gold_objective":93.0,"gold_status":"optimal","seconds":0.0,"cost_usd":null,"violated":[],"notes":"Paid/local LLM inference is off. 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Not evaluated.","precomputed":true,"family":"scheduling","split":"test","language":"fa","difficulty":"infeasible"} diff --git a/demo/examples/sample_preview.json b/demo/examples/sample_preview.json new file mode 100644 index 0000000000000000000000000000000000000000..981735ce13efbc2b732655ce3352031a70691292 --- /dev/null +++ b/demo/examples/sample_preview.json @@ -0,0 +1,17 @@ +{ + "run_id": "orbench-eccc1a511a", + "status": "optimal", + "kpis": { + "n_problems": 100, + "structured_feasible": 0.92, + "heuristic_gap": 0.031919404673584915, + "template_fidelity": 0.6, + "n_methods_evaluated": 5, + "n_methods_listed": 10 + }, + "kpi_html": "

Problems in view

100

interactive subset or filtered catalog

Structured-solver feasible

92%

share of valid plans after independent checks

Heuristic mean gap

3.2%

only where gold status is proven optimal

Template fidelity

60%

atomic constraint facts recovered from text

Methods evaluated

5/10

evaluated / listed — unevaluated is not zero

", + "precomputed": true, + "n_problems": 100, + "n_eval_rows": 1000, + "interactive": "INV-001" +} \ No newline at end of file diff --git a/demo/examples/splits.json b/demo/examples/splits.json new file mode 100644 index 0000000000000000000000000000000000000000..1738082edae4893beaa89f49583619ec633a57b2 --- /dev/null +++ b/demo/examples/splits.json @@ -0,0 +1,128 @@ +{ + "development": [ + "INV-001", + "INV-002", + "INV-003", + "INV-004", + "INV-005", + "INV-006", + "INV-007", + "INV-008", + "INV-009", + "INV-010", + "INV-011", + "INV-012", + "INV-013", + "INV-014", + "INV-015", + "INV-016", + "INV-017", + "INV-018", + "INV-019", + "INV-020", + "ASN-001", + "ASN-002", + "ASN-003", + "ASN-004", + "ASN-005", + "ASN-006", + "ASN-007", + "ASN-008", + "ASN-009", + "ASN-010", + "ASN-011", + "ASN-012", + "ASN-013", + "ASN-014", + "ASN-015", + "ASN-016", + "ASN-017", + "ASN-018", + "ASN-019", + "ASN-020", + "SCH-001", + "SCH-002", + "SCH-003", + "SCH-004", + "SCH-005", + "SCH-006", + "SCH-007", + "SCH-008", + "SCH-009", + "SCH-010", + "SCH-011", + "SCH-012", + "SCH-013", + "SCH-014", + "SCH-015", + "SCH-016", + "SCH-017", + "SCH-018", + "SCH-019", + "SCH-020" + ], + "test": [ + "INV-021", + "INV-022", + "INV-023", + "INV-024", + "INV-025", + "INV-026", + "INV-027", + "INV-028", + "INV-029", + "INV-030", + "INV-031", + "INV-032", + "INV-033", + "INV-034", + "ASN-021", + "ASN-022", + "ASN-023", + "ASN-024", + "ASN-025", + "ASN-026", + "ASN-027", + "ASN-028", + "ASN-029", + "ASN-030", + "ASN-031", + "ASN-032", + "ASN-033", + "SCH-021", + "SCH-022", + "SCH-023", + "SCH-024", + "SCH-025", + "SCH-026", + "SCH-027", + "SCH-028", + "SCH-029", + "SCH-030", + "SCH-031", + "SCH-032", + "SCH-033" + ], + "interactive": [ + "INV-001", + "INV-008", + "INV-014", + "INV-021", + "INV-028", + "INV-031", + "INV-034", + "ASN-001", + "ASN-006", + "ASN-012", + "ASN-018", + "ASN-024", + "ASN-029", + "ASN-033", + "SCH-001", + "SCH-007", + "SCH-013", + "SCH-019", + "SCH-027", + "SCH-033" + ] +} \ No newline at end of file diff --git a/demo/requirements.txt b/demo/requirements.txt new file mode 100644 index 0000000000000000000000000000000000000000..322359b154c668f16844f4c25f81886e1abd761c --- /dev/null +++ b/demo/requirements.txt @@ -0,0 +1,5 @@ +pandas>=2.2.0,<3 +numpy>=1.26.0,<3 +pydantic>=2.6.0,<3 +ortools>=9.10,<10 +plotly>=5.24.0,<7 diff --git a/demo/src/__init__.py b/demo/src/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..00c5fa45bedce47f414c7a5d16443e29b7b8f84e --- /dev/null +++ b/demo/src/__init__.py @@ -0,0 +1 @@ +"""ORBench — reproducible comparison of solvers and structured agents.""" diff --git a/demo/src/__pycache__/__init__.cpython-312.pyc b/demo/src/__pycache__/__init__.cpython-312.pyc new file mode 100644 index 0000000000000000000000000000000000000000..e41d8e62e547530615132e31fe12238e2b98dc3b Binary files /dev/null and b/demo/src/__pycache__/__init__.cpython-312.pyc differ diff --git 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0000000000000000000000000000000000000000..00ee25638ca9e535221a4cfd7016f2edaa57f887 --- /dev/null +++ b/demo/src/baseline.py @@ -0,0 +1,181 @@ +from __future__ import annotations + +import math +import time + +from src.domain import ( + AssignmentInstance, + AssignmentRow, + Family, + InventoryInstance, + InventoryOrder, + ScheduleInstance, + ScheduleStart, + Solution, + SolveStatus, + parse_instance, +) +from src.optimizer import SolverOutcome + + +def _round_pack(qty: int, pack: int) -> int: + if qty <= 0: + return 0 + return int(math.ceil(qty / pack) * pack) + + +def heuristic_inventory(instance: InventoryInstance) -> Solution: + remaining = int(instance.budget) + orders: list[InventoryOrder] = [] + stock = {sku.sku_id: int(sku.initial_stock) for sku in instance.skus} + for t in range(1, instance.periods + 1): + for sku in sorted(instance.skus, key=lambda item: (-item.shortage_cost, item.sku_id)): + need = max(0, int(sku.demand[t - 1]) - stock[sku.sku_id]) + qty = _round_pack(need, sku.pack_size) + cost = qty * sku.unit_cost + while qty and cost > remaining: + qty = max(0, qty - sku.pack_size) + cost = qty * sku.unit_cost + projected = sum(max(0, stock[other.sku_id] - (int(other.demand[t - 1]) if other.sku_id != sku.sku_id else 0)) for other in instance.skus) + projected += max(0, stock[sku.sku_id] + qty - int(sku.demand[t - 1])) + if projected > instance.warehouse_capacity: + qty = 0 + cost = 0 + remaining -= cost + orders.append(InventoryOrder(sku_id=sku.sku_id, period=t, qty=qty)) + sold = min(stock[sku.sku_id] + qty, int(sku.demand[t - 1])) + stock[sku.sku_id] = stock[sku.sku_id] + qty - sold + return Solution(family=Family.INVENTORY, status=SolveStatus.HEURISTIC, orders=orders, message="lot-for-lot pack-rounded") + + +def heuristic_assignment(instance: AssignmentInstance) -> Solution: + costs = instance.cost_map() + remaining = {agent.agent_id: agent.capacity for agent in instance.agents} + used: set[str] = set() + rows: list[AssignmentRow] = [] + leftover: list[str] = [] + ordered = sorted(instance.tasks, key=lambda task: (not task.required, -task.penalty, task.task_id)) + for task in ordered: + candidates = [] + for agent in instance.agents: + if not instance.eligible(task, agent): + continue + if remaining[agent.agent_id] < task.size: + continue + pair = (task.task_id, agent.agent_id) + if pair not in costs: + continue + candidates.append((costs[pair], agent.agent_id)) + if not candidates: + leftover.append(task.task_id) + continue + candidates.sort() + agent_id = candidates[0][1] + rows.append(AssignmentRow(task_id=task.task_id, agent_id=agent_id)) + remaining[agent_id] -= task.size + used.add(task.task_id) + leftover.extend(task.task_id for task in instance.tasks if task.task_id not in used and task.task_id not in leftover) + return Solution( + family=Family.ASSIGNMENT, + status=SolveStatus.HEURISTIC, + assignments=rows, + unassigned=leftover, + message="cheapest eligible agent with remaining capacity", + ) + + +def heuristic_scheduling(instance: ScheduleInstance) -> Solution: + ready = {machine: 0 for machine in instance.machines} + done_end: dict[str, int] = {} + remaining = {job.job_id: job for job in instance.jobs} + starts: list[ScheduleStart] = [] + preds: dict[str, list[str]] = {job.job_id: [] for job in instance.jobs} + for edge in instance.precedences: + if edge.after in preds: + preds[edge.after].append(edge.before) + + guard = 0 + while remaining and guard < 200: + guard += 1 + ready_jobs = [ + job + for job in remaining.values() + if all(pred in done_end for pred in preds[job.job_id]) + ] + if not ready_jobs: + break + ready_jobs.sort(key=lambda job: (job.due, -job.weight, job.job_id)) + job = ready_jobs[0] + eligible = [machine for machine in instance.machines if machine in set(job.machine_eligible)] or list(instance.machines) + pred_end = max((done_end[pred] for pred in preds[job.job_id]), default=0) + machine = min(eligible, key=lambda item: (max(ready[item], job.release, pred_end), item)) + start = max(ready[machine], job.release, pred_end) + end = start + job.duration + starts.append(ScheduleStart(job_id=job.job_id, machine_id=machine, start=start, end=end)) + ready[machine] = end + done_end[job.job_id] = end + remaining.pop(job.job_id) + leftover = [job_id for job_id in remaining] + message = "earliest due date on the earliest eligible machine" + if leftover: + message += f"; leftover {leftover}" + return Solution(family=Family.SCHEDULING, status=SolveStatus.HEURISTIC, starts=starts, message=message) + + +def naive_direct(family: Family | str, payload: dict) -> Solution: + family = Family(family) + instance = parse_instance(family, payload) + if family == Family.INVENTORY: + orders = [] + for sku in instance.skus: + for t, demand in enumerate(sku.demand, start=1): + orders.append(InventoryOrder(sku_id=sku.sku_id, period=t, qty=int(demand))) + return Solution( + family=family, + status=SolveStatus.HEURISTIC, + orders=orders, + message="naive-direct: order raw demand, ignore pack/budget/capacity", + ) + if family == Family.ASSIGNMENT: + if not instance.agents: + return Solution(family=family, status=SolveStatus.HEURISTIC, message="naive-direct: no agents") + first = instance.agents[0].agent_id + rows = [AssignmentRow(task_id=task.task_id, agent_id=first) for task in instance.tasks] + return Solution( + family=family, + status=SolveStatus.HEURISTIC, + assignments=rows, + message="naive-direct: assign every task to the first agent", + ) + starts = [] + cursor = 0 + machine = instance.machines[0] if instance.machines else "M1" + for job in instance.jobs: + start = max(cursor, job.release) + starts.append(ScheduleStart(job_id=job.job_id, machine_id=machine, start=start, end=start + job.duration)) + cursor = start + job.duration + return Solution( + family=family, + status=SolveStatus.HEURISTIC, + starts=starts, + message="naive-direct: single-machine FCFS ignoring eligibility and hard dues", + ) + + +def run_heuristic(family: Family | str, payload: dict) -> SolverOutcome: + started = time.perf_counter() + family = Family(family) + instance = parse_instance(family, payload) + if family == Family.INVENTORY: + solution = heuristic_inventory(instance) + elif family == Family.ASSIGNMENT: + solution = heuristic_assignment(instance) + else: + solution = heuristic_scheduling(instance) + return SolverOutcome(solution, time.perf_counter() - started, "heuristic-v1", solution.message) + + +def run_naive(family: Family | str, payload: dict) -> SolverOutcome: + started = time.perf_counter() + solution = naive_direct(family, payload) + return SolverOutcome(solution, time.perf_counter() - started, "naive-direct-v1", solution.message) diff --git a/demo/src/budget_guard.py b/demo/src/budget_guard.py new file mode 100644 index 0000000000000000000000000000000000000000..a1b8d68942da21e77796b0e73549dc68a4321100 --- /dev/null +++ b/demo/src/budget_guard.py @@ -0,0 +1,22 @@ +from __future__ import annotations + +import os + +# Paid provider calls stay off unless a future release adds an atomic shared budget. +PAID_INFERENCE_ENABLED = False + + +def paid_inference_allowed() -> bool: + if not PAID_INFERENCE_ENABLED: + return False + if os.environ.get("ORBENCH_ALLOW_PAID") != "1": + return False + return False + + +def skip_reason() -> str: + return ( + "Live LLM APIs are disabled. Comparison cells for unnamed or unpaid " + "model runs stay not_evaluated. The free path is the CPU solver, " + "heuristics, and deterministic extractors." + ) diff --git a/demo/src/domain.py b/demo/src/domain.py new file mode 100644 index 0000000000000000000000000000000000000000..d9600b30ede41514ffefadc2115bdaf9e62ea449 --- /dev/null +++ b/demo/src/domain.py @@ -0,0 +1,297 @@ +from __future__ import annotations + +from enum import Enum +from typing import Any, Literal + +from pydantic import BaseModel, Field + +CODE_NAME = "or-bench" +CODE_VERSION = "0.1.0" +DEFAULT_SEED = 25 +DEFAULT_SOLVER_SECONDS = 8.0 +DEFAULT_THREADS = 1 +MAX_UPLOAD_MB = 10 +N_PROBLEMS = 100 +N_INVENTORY = 34 +N_ASSIGNMENT = 33 +N_SCHEDULING = 33 +N_INTERACTIVE = 20 +N_DEVELOPMENT = 60 + +SOLVER_NAME = "ortools-cpsat" +PROTOCOL_ID = "or-bench-v1" + + +class Family(str, Enum): + INVENTORY = "inventory" + ASSIGNMENT = "assignment" + SCHEDULING = "scheduling" + + +class Split(str, Enum): + DEVELOPMENT = "development" + TEST = "test" + + +class Difficulty(str, Enum): + EASY = "easy" + MEDIUM = "medium" + HARD = "hard" + INFEASIBLE = "infeasible" + + +class SolveStatus(str, Enum): + OPTIMAL = "optimal" + FEASIBLE = "feasible" + HEURISTIC = "heuristic" + INFEASIBLE = "infeasible" + TIMEOUT = "timeout" + INVALID = "invalid" + ERROR = "error" + NOT_EVALUATED = "not_evaluated" + + +class MethodKind(str, Enum): + STRUCTURED_SOLVER = "structured-solver" + HEURISTIC = "heuristic" + TEXT_TO_SCHEMA = "text-to-schema" + DIRECT_ANSWER = "direct-answer" + LLM_SCHEMA = "llm-schema" + LLM_DIRECT = "llm-direct" + + +class PromptVariant(str, Enum): + TEMPLATE = "template" + JSON = "json" + MISSING_BUDGET = "missing_constraint" + CUSTOM = "custom" + + +class InventorySku(BaseModel): + sku_id: str + name: str + demand: list[int] + initial_stock: int = Field(ge=0) + unit_cost: int = Field(ge=1) + holding_cost: int = Field(ge=0) + shortage_cost: int = Field(ge=0) + pack_size: int = Field(ge=1) + lead_time: int = Field(default=0, ge=0, le=0) + + +class InventoryInstance(BaseModel): + periods: int = Field(ge=2, le=6) + budget: int = Field(ge=0) + warehouse_capacity: int = Field(ge=0) + cover_required: bool = False + lost_sales: bool = True + skus: list[InventorySku] + + def sku_map(self) -> dict[str, InventorySku]: + return {item.sku_id: item for item in self.skus} + + +class AssignmentTask(BaseModel): + task_id: str + name: str + size: int = Field(ge=1) + required: bool = True + skills: list[str] + penalty: int = Field(ge=0) + + +class AssignmentAgent(BaseModel): + agent_id: str + name: str + capacity: int = Field(ge=0) + skills: list[str] + + +class AssignmentCost(BaseModel): + task_id: str + agent_id: str + cost: int = Field(ge=0) + + +class AssignmentInstance(BaseModel): + tasks: list[AssignmentTask] + agents: list[AssignmentAgent] + costs: list[AssignmentCost] + + def cost_map(self) -> dict[tuple[str, str], int]: + return {(row.task_id, row.agent_id): row.cost for row in self.costs} + + def eligible(self, task: AssignmentTask, agent: AssignmentAgent) -> bool: + return bool(set(task.skills) & set(agent.skills)) or not task.skills + + +class ScheduleJob(BaseModel): + job_id: str + name: str + duration: int = Field(ge=1) + release: int = Field(ge=0) + due: int = Field(ge=0) + weight: int = Field(ge=1) + hard_due: bool = False + machine_eligible: list[str] + + +class SchedulePrecedence(BaseModel): + before: str + after: str + + +class ScheduleInstance(BaseModel): + machines: list[str] + jobs: list[ScheduleJob] + precedences: list[SchedulePrecedence] + horizon: int = Field(ge=1) + + +class InventoryOrder(BaseModel): + sku_id: str + period: int + qty: int + + +class AssignmentRow(BaseModel): + task_id: str + agent_id: str + + +class ScheduleStart(BaseModel): + job_id: str + machine_id: str + start: int + end: int + + +class Solution(BaseModel): + family: Family + status: SolveStatus = SolveStatus.FEASIBLE + objective: float | None = None + bound: float | None = None + orders: list[InventoryOrder] = Field(default_factory=list) + assignments: list[AssignmentRow] = Field(default_factory=list) + unassigned: list[str] = Field(default_factory=list) + starts: list[ScheduleStart] = Field(default_factory=list) + message: str = "" + + def as_dict(self) -> dict[str, Any]: + return self.model_dump(mode="json") + + +class ProblemRecord(BaseModel): + problem_id: str + family: Family + split: Split + interactive: bool + difficulty: Difficulty + language: Literal["en", "fa"] + template_id: str + seed: int + prompt_en: str + prompt_fa: str + prompt_json: str + schema_payload: dict[str, Any] + gold_status: str + gold_objective: float | None = None + gold_bound: float | None = None + gold_solution: dict[str, Any] = Field(default_factory=dict) + structural_key: str + notes: str = "" + + def instance(self) -> InventoryInstance | AssignmentInstance | ScheduleInstance: + payload = self.schema_payload + if self.family == Family.INVENTORY: + return InventoryInstance.model_validate(payload) + if self.family == Family.ASSIGNMENT: + return AssignmentInstance.model_validate(payload) + return ScheduleInstance.model_validate(payload) + + +class ConstraintConfig(BaseModel): + solver_seconds: float = Field(default=DEFAULT_SOLVER_SECONDS, gt=1, le=30) + threads: int = Field(default=DEFAULT_THREADS, ge=1, le=2) + include_infeasible: bool = True + + +class ValidationIssue(BaseModel): + code: str + message: str + entity_id: str | None = None + passed: bool = False + + +class ValidationReport(BaseModel): + ok: bool + issues: list[ValidationIssue] + checked: list[str] + recomputed_objective: float | None = None + + def failed_codes(self) -> list[str]: + return [item.code for item in self.issues if not item.passed] + + +class ConstraintFact(BaseModel): + key: str + value: Any + source: str = "schema" + + +class MethodSpec(BaseModel): + method_id: str + display_name: str + kind: MethodKind + evaluated: bool + version: str + license: str = "apache-2.0" + cost_usd: float | None = None + notes: str = "" + reason_if_skipped: str = "" + + +class EvalRow(BaseModel): + problem_id: str + method_id: str + method_kind: str + evaluated: bool + parse_success: bool | None = None + constraint_fidelity: float | None = None + status: str + feasible: bool | None = None + optimality_gap: float | None = None + objective: float | None = None + gold_objective: float | None = None + gold_status: str + seconds: float + cost_usd: float | None = None + violated: list[str] = Field(default_factory=list) + notes: str = "" + precomputed: bool = False + family: str + split: str + language: str + difficulty: str + + +def not_evaluated_cell() -> str: + return "not_evaluated" + + +def gap(objective: float | None, gold: float | None, gold_status: str) -> float | None: + if objective is None or gold is None: + return None + if gold_status != SolveStatus.OPTIMAL.value: + return None + denom = max(1.0, abs(float(gold))) + return max(0.0, (float(objective) - float(gold)) / denom) + + +def parse_instance(family: Family | str, payload: dict[str, Any]) -> InventoryInstance | AssignmentInstance | ScheduleInstance: + family = Family(family) + if family == Family.INVENTORY: + return InventoryInstance.model_validate(payload) + if family == Family.ASSIGNMENT: + return AssignmentInstance.model_validate(payload) + return ScheduleInstance.model_validate(payload) diff --git a/demo/src/explain.py b/demo/src/explain.py new file mode 100644 index 0000000000000000000000000000000000000000..28df5883f1c19089e5a021282f9bc4091d1f7b8e --- /dev/null +++ b/demo/src/explain.py @@ -0,0 +1,81 @@ +from __future__ import annotations + +from src.domain import EvalRow, SolveStatus +from src.validation import ValidationReport + + +def status_label(status: str, lang: str = "en") -> str: + mapping = { + "en": { + "optimal": "Proven optimal (within the model)", + "feasible": "Feasible incumbent within the time limit — not proven optimal", + "heuristic": "Heuristic feasible candidate — not a proven optimum", + "infeasible": "Proven infeasible under the stated constraints", + "timeout": "No plan found before the time limit — this is not a proof of infeasibility", + "invalid": "Invalid input or schema", + "error": "Solver error", + "not_evaluated": "Not evaluated — no run, so this is not a score of 0", + }, + "fa": { + "optimal": "بهینه اثبات‌شده در مدل", + "feasible": "جواب شدنی در مهلت — بهینه بودن اثبات نشده", + "heuristic": "نامزد شدنی ابتکاری — بهینه اثبات‌شده نیست", + "infeasible": "ناممکن اثبات‌شده با قیود فعلی", + "timeout": "در مهلت جوابی پیدا نشد — این اثبات ناممکن بودن نیست", + "invalid": "ورودی یا schema نامعتبر", + "error": "خطای حل‌گر", + "not_evaluated": "ارزیابی نشده — اجرا نشده و این صفر یا رتبه نیست", + }, + } + return mapping.get(lang, mapping["en"]).get(status, status) + + +def numeric_reasons(problem, rows: list[EvalRow], report: ValidationReport | None, lang: str = "en") -> list[str]: + lines: list[str] = [] + if lang == "fa": + lines.append( + f"{problem.problem_id} خانواده {problem.family.value}، دشواری {problem.difficulty.value}، " + f"وضعیت طلایی {problem.gold_status}، هدف طلایی {problem.gold_objective}." + ) + else: + lines.append( + f"{problem.problem_id} is a {problem.difficulty.value} {problem.family.value} instance. " + f"Gold status {problem.gold_status}, gold objective {problem.gold_objective}." + ) + by_id = {row.method_id: row for row in rows if row.evaluated} + structured = by_id.get("structured-solver") + heuristic = by_id.get("heuristic") + if structured and heuristic and structured.objective is not None and heuristic.objective is not None: + delta = float(heuristic.objective) - float(structured.objective) + if lang == "fa": + lines.append(f"هدف ابتکاری {heuristic.objective} در برابر حل‌گر {structured.objective} (اختلاف {delta:+.3f}).") + else: + lines.append(f"Heuristic objective {heuristic.objective} vs solver {structured.objective} (delta {delta:+.3f}).") + extractor = by_id.get("template-extractor+solver") + if extractor and extractor.constraint_fidelity is not None: + if lang == "fa": + lines.append(f"وفاداری استخراج قالب {extractor.constraint_fidelity:.3f}؛ parse={'موفق' if extractor.parse_success else 'ناموفق'}.") + else: + lines.append(f"Template-extractor fidelity {extractor.constraint_fidelity:.3f}; parse={'ok' if extractor.parse_success else 'failed'}.") + naive = by_id.get("naive-direct") + if naive and naive.violated: + if lang == "fa": + lines.append(f"پاسخ مستقیم ساده‌لوح قیود را نقض کرد: {', '.join(naive.violated[:6])}.") + else: + lines.append(f"Naive direct answer violated: {', '.join(naive.violated[:6])}.") + if report and not report.ok: + codes = ", ".join(report.failed_codes()[:6]) + if lang == "fa": + lines.append(f"validator مستقل قیود نقض‌شده را گزارش کرد: {codes}.") + else: + lines.append(f"Independent validator flagged: {codes}.") + if problem.gold_status == SolveStatus.INFEASIBLE.value: + if lang == "fa": + lines.append("این نمونه ناممکن طراحی شده است. خانه‌های مدل اجرا‌نشده «ارزیابی نشده» می‌مانند.") + else: + lines.append("This instance is designed to be infeasible. Unevaluated model cells stay not_evaluated.") + if lang == "fa": + lines.append("امتیاز یک مدل زبانی داور نیست؛ validator عددی مرجع است. مسیر پاسخ مستقیم فقط برای بنچمارک است.") + else: + lines.append("An LLM score is not the judge. The numeric validator is the reference. Direct answers are benchmark-only.") + return lines[:8] diff --git a/demo/src/extractor.py b/demo/src/extractor.py new file mode 100644 index 0000000000000000000000000000000000000000..8fe309385148cc435ee89c297c0b4d3c58eac1ff --- /dev/null +++ b/demo/src/extractor.py @@ -0,0 +1,186 @@ +from __future__ import annotations + +import json +import re +from typing import Any + +from src.domain import Family, InventoryInstance + + +def extract_json(text: str) -> dict[str, Any] | None: + if not text or not str(text).strip(): + return None + raw = str(text).strip() + candidates = [raw] + fenced = re.findall(r"```(?:json)?\s*(\{.*?\})\s*```", raw, flags=re.S) + candidates.extend(fenced) + start = raw.find("{") + end = raw.rfind("}") + if start >= 0 and end > start: + candidates.append(raw[start : end + 1]) + for item in candidates: + try: + payload = json.loads(item) + except json.JSONDecodeError: + continue + if isinstance(payload, dict) and payload: + if "schema_payload" in payload and isinstance(payload["schema_payload"], dict): + return payload["schema_payload"] + return payload + return None + + +def extract_template(text: str, family: Family | str) -> dict[str, Any] | None: + family = Family(family) + if not text: + return None + labeled = _extract_labeled_blocks(text) + if labeled: + return labeled + if family == Family.INVENTORY: + return _extract_inventory_prose(text) + return None + + +def _extract_labeled_blocks(text: str) -> dict[str, Any] | None: + blocks = re.findall(r"SCHEMA_BEGIN\s*(\{.*?\})\s*SCHEMA_END", text, flags=re.S) + for block in blocks: + try: + payload = json.loads(block) + except json.JSONDecodeError: + continue + if isinstance(payload, dict): + return payload + return None + + +def _extract_inventory_prose(text: str) -> dict[str, Any] | None: + budget = _first_int(text, r"(?:BUDGET|budget|بودجه)\s*[:=]?\s*(\d+)") + capacity = _first_int(text, r"(?:CAPACITY|capacity|ظرفیت انبار)\s*[:=]?\s*(\d+)") + periods = _first_int(text, r"(?:PERIODS|periods|دوره)\s*[:=]?\s*(\d+)") + cover = bool(re.search(r"COVER_REQUIRED:\s*1|cover is required|پوشش کامل الزامی", text, flags=re.I)) + sku_lines = re.findall( + r"SKU\s+([A-Za-z0-9_-]+).*?demand=([0-9,]+).*?pack=(\d+).*?cost=(\d+).*?hold=(\d+).*?short=(\d+).*?stock=(\d+)", + text, + flags=re.I, + ) + if budget is None or not sku_lines: + return None + skus = [] + for sku_id, demand, pack, cost, hold, short, stock in sku_lines: + values = [int(item) for item in demand.split(",") if item.strip().isdigit()] + skus.append( + { + "sku_id": sku_id, + "name": sku_id, + "demand": values, + "initial_stock": int(stock), + "unit_cost": int(cost), + "holding_cost": int(hold), + "shortage_cost": int(short), + "pack_size": int(pack), + "lead_time": 0, + } + ) + periods = periods or (len(skus[0]["demand"]) if skus else 0) + try: + InventoryInstance.model_validate( + { + "periods": periods, + "budget": budget, + "warehouse_capacity": capacity if capacity is not None else 10**6, + "cover_required": cover, + "lost_sales": True, + "skus": skus, + } + ) + except Exception: + return None + return { + "periods": periods, + "budget": budget, + "warehouse_capacity": capacity if capacity is not None else 10**6, + "cover_required": cover, + "lost_sales": True, + "skus": skus, + } + + +def _first_int(text: str, pattern: str) -> int | None: + match = re.search(pattern, text, flags=re.I) + if not match: + return None + return int(match.group(1)) + + +def flatten_facts(family: Family | str, payload: dict) -> dict[str, str]: + family = Family(family) + facts: dict[str, str] = {} + if family == Family.INVENTORY: + facts["periods"] = str(payload.get("periods")) + facts["budget"] = str(payload.get("budget")) + facts["warehouse_capacity"] = str(payload.get("warehouse_capacity")) + facts["cover_required"] = str(bool(payload.get("cover_required"))) + for sku in payload.get("skus") or []: + key = sku.get("sku_id") + facts[f"{key}.demand"] = ",".join(str(int(v)) for v in sku.get("demand") or []) + facts[f"{key}.pack"] = str(sku.get("pack_size")) + facts[f"{key}.cost"] = str(sku.get("unit_cost")) + facts[f"{key}.stock"] = str(sku.get("initial_stock")) + facts[f"{key}.hold"] = str(sku.get("holding_cost")) + facts[f"{key}.short"] = str(sku.get("shortage_cost")) + elif family == Family.ASSIGNMENT: + facts["n_tasks"] = str(len(payload.get("tasks") or [])) + facts["n_agents"] = str(len(payload.get("agents") or [])) + for task in payload.get("tasks") or []: + facts[f"task.{task.get('task_id')}.size"] = str(task.get("size")) + facts[f"task.{task.get('task_id')}.required"] = str(bool(task.get("required"))) + facts[f"task.{task.get('task_id')}.skills"] = ",".join(sorted(task.get("skills") or [])) + for agent in payload.get("agents") or []: + facts[f"agent.{agent.get('agent_id')}.cap"] = str(agent.get("capacity")) + facts[f"agent.{agent.get('agent_id')}.skills"] = ",".join(sorted(agent.get("skills") or [])) + for row in payload.get("costs") or []: + facts[f"cost.{row.get('task_id')}.{row.get('agent_id')}"] = str(row.get("cost")) + else: + facts["machines"] = ",".join(payload.get("machines") or []) + for job in payload.get("jobs") or []: + jid = job.get("job_id") + facts[f"job.{jid}.dur"] = str(job.get("duration")) + facts[f"job.{jid}.rel"] = str(job.get("release")) + facts[f"job.{jid}.due"] = str(job.get("due")) + facts[f"job.{jid}.w"] = str(job.get("weight")) + facts[f"job.{jid}.hard"] = str(bool(job.get("hard_due"))) + facts[f"job.{jid}.m"] = ",".join(sorted(job.get("machine_eligible") or [])) + for idx, edge in enumerate(payload.get("precedences") or []): + facts[f"pred.{idx}"] = f"{edge.get('before')}->{edge.get('after')}" + return facts + + +def constraint_fidelity(family: Family | str, gold: dict, extracted: dict | None) -> float | None: + if extracted is None: + return 0.0 + gold_facts = flatten_facts(family, gold) + got = flatten_facts(family, extracted) + if not gold_facts: + return 1.0 + hits = sum(1 for key, value in gold_facts.items() if got.get(key) == value) + return hits / len(gold_facts) + + +def drop_constraint(family: Family | str, payload: dict, prompt: str) -> tuple[dict, str]: + family = Family(family) + clone = json.loads(json.dumps(payload)) + if family == Family.INVENTORY: + clone["budget"] = 10**9 + stripped = re.sub(r"(BUDGET|budget|بودجه)\s*[:=]?\s*\d+", "BUDGET omitted", prompt) + return clone, stripped + if family == Family.ASSIGNMENT: + for agent in clone.get("agents") or []: + agent["capacity"] = 10**6 + stripped = re.sub(r"(capacity|ظرفیت)\s*[:=]?\s*\d+", "capacity omitted", prompt, flags=re.I) + return clone, stripped + for job in clone.get("jobs") or []: + job["hard_due"] = False + job["due"] = job.get("due", 0) + 10**4 + stripped = re.sub(r"(hard due|موعد سخت)", "due relaxed", prompt, flags=re.I) + return clone, stripped diff --git a/demo/src/generator.py b/demo/src/generator.py new file mode 100644 index 0000000000000000000000000000000000000000..e9860460c66a09b99002c266f427a08f41d6e25d --- /dev/null +++ b/demo/src/generator.py @@ -0,0 +1,501 @@ +from __future__ import annotations + +import hashlib +import json +import random +from pathlib import Path + +from src.domain import ( + DEFAULT_SEED, + N_ASSIGNMENT, + N_INVENTORY, + N_PROBLEMS, + N_SCHEDULING, + AssignmentAgent, + AssignmentCost, + AssignmentInstance, + AssignmentTask, + Difficulty, + Family, + InventoryInstance, + InventorySku, + ProblemRecord, + ScheduleInstance, + ScheduleJob, + SchedulePrecedence, + Split, +) +from src.optimizer import solve_instance + +DEV_TEMPLATES = ("D-A", "D-B", "D-C") +TEST_TEMPLATES = ("T-A", "T-B") +SKU_NAMES = ("bearing", "seal", "gasket", "filter", "hose", "valve") +SKU_FA = ("بلبرینگ", "آب‌بند", "واشر", "فیلتر", "شیلنگ", "شیر") +TASK_SKILLS = ("weld", "inspect", "pack", "lift") +INTERACTIVE_IDS = ( + "INV-001", + "INV-008", + "INV-014", + "INV-021", + "INV-028", + "INV-031", + "INV-034", + "ASN-001", + "ASN-006", + "ASN-012", + "ASN-018", + "ASN-024", + "ASN-029", + "ASN-033", + "SCH-001", + "SCH-007", + "SCH-013", + "SCH-019", + "SCH-027", + "SCH-033", +) + + +def _split_for(index: int, n_items: int) -> Split: + # First 20 of each family → 60 development / 40 test overall. + _ = n_items + return Split.DEVELOPMENT if index <= 20 else Split.TEST + + +def _difficulty(index: int, n_items: int, infeasible_tail: int) -> Difficulty: + if index > n_items - infeasible_tail: + return Difficulty.INFEASIBLE + if index % 7 == 0: + return Difficulty.HARD + if index % 3 == 0: + return Difficulty.MEDIUM + return Difficulty.EASY + + +def _template(split: Split, index: int) -> str: + pool = DEV_TEMPLATES if split == Split.DEVELOPMENT else TEST_TEMPLATES + return pool[(index - 1) % len(pool)] + + +def _key(*parts: object) -> str: + raw = "|".join(str(item) for item in parts) + return hashlib.sha256(raw.encode("utf-8")).hexdigest()[:16] + + +def _wrap_schema(payload: dict, template_id: str) -> str: + if template_id.startswith("D-"): + return "SCHEMA_BEGIN\n" + json.dumps(payload, ensure_ascii=False) + "\nSCHEMA_END\n" + return "" + + +def _json_prompt(payload: dict) -> str: + return json.dumps(payload, ensure_ascii=False, indent=2) + + +def make_inventory(index: int, rng: random.Random) -> tuple[InventoryInstance, str]: + difficulty = _difficulty(index, N_INVENTORY, 3) + n_sku = 2 if difficulty == Difficulty.EASY else 3 if difficulty != Difficulty.HARD else 4 + periods = 3 if difficulty != Difficulty.HARD else 4 + cover = difficulty in {Difficulty.HARD, Difficulty.INFEASIBLE} or index % 5 == 0 + skus = [] + for k in range(n_sku): + demand = [rng.randint(2, 8) for _ in range(periods)] + pack = rng.choice([1, 2, 3]) + skus.append( + InventorySku( + sku_id=f"S{k + 1}", + name=SKU_NAMES[k], + demand=demand, + initial_stock=rng.randint(0, 3), + unit_cost=rng.randint(3, 9), + holding_cost=rng.randint(1, 3), + shortage_cost=rng.randint(6, 14), + pack_size=pack, + lead_time=0, + ) + ) + total_need = sum(max(0, sum(sku.demand) - sku.initial_stock) for sku in skus) + min_buy = 0 + for sku in skus: + need = max(0, sum(sku.demand) - sku.initial_stock) + packs = (need + sku.pack_size - 1) // sku.pack_size + min_buy += packs * sku.pack_size * sku.unit_cost + cap = max(8, int(total_need * 0.7) + rng.randint(2, 8)) + if difficulty == Difficulty.INFEASIBLE: + for sku in skus: + sku.initial_stock = 0 + sku.demand = [max(3, value) for value in sku.demand] + total_need = sum(sum(sku.demand) for sku in skus) + min_buy = 0 + for sku in skus: + packs = (sum(sku.demand) + sku.pack_size - 1) // sku.pack_size + min_buy += packs * sku.pack_size * sku.unit_cost + budget = max(1, min_buy // 5) + cover = True + cap = max(6, total_need) + elif difficulty == Difficulty.HARD: + budget = max(min_buy, int(min_buy * 1.05) + 2) + else: + budget = min_buy + rng.randint(8, 24) + instance = InventoryInstance( + periods=periods, + budget=int(budget), + warehouse_capacity=int(cap), + cover_required=cover, + lost_sales=True, + skus=skus, + ) + return instance, difficulty.value + + +def render_inventory(instance: InventoryInstance, template_id: str, language: str) -> tuple[str, str]: + labeled = [] + for sku in instance.skus: + labeled.append( + f"SKU {sku.sku_id} demand={','.join(str(v) for v in sku.demand)} pack={sku.pack_size} " + f"cost={sku.unit_cost} hold={sku.holding_cost} short={sku.shortage_cost} stock={sku.initial_stock}" + ) + labels = ( + f"PERIODS: {instance.periods}\nBUDGET: {instance.budget}\nCAPACITY: {instance.warehouse_capacity}\n" + f"COVER_REQUIRED: {1 if instance.cover_required else 0}\n" + "\n".join(labeled) + ) + schema_block = _wrap_schema(instance.model_dump(), template_id) + names = ", ".join(f"{sku.sku_id} ({sku.name})" for sku in instance.skus) + names_fa = ", ".join(f"{sku.sku_id} ({SKU_FA[int(sku.sku_id[1:]) - 1]})" for sku in instance.skus) + cover_en = "All demand must be covered; lost sales are forbidden." if instance.cover_required else "Lost sales are allowed and charged." + cover_fa = "پوشش کامل تقاضا الزامی است." if instance.cover_required else "کمبود مجاز است و جریمه دارد." + if template_id in {"D-A", "D-B", "D-C"}: + en = ( + f"A B2B warehouse plans {instance.periods} weeks for {len(instance.skus)} SKUs: {names}. " + f"{cover_en} Orders are pack multiples. Lead time is 0. " + f"Budget is {instance.budget} currency units. Storage holds at most {instance.warehouse_capacity} units in total. " + "Minimize purchase + holding + shortage.\n" + f"{labels}\n{schema_block}" + ) + fa = ( + f"یک انبار B2B برای {instance.periods} هفته و {len(instance.skus)} کالا برنامه می‌خرد: {names_fa}. " + f"{cover_fa} سفارش مضرب بسته است. زمان تأمین صفر است. " + f"بودجه برابر {instance.budget} واحد پول و ظرفیت انبار {instance.warehouse_capacity} واحد است. " + "هدف کمینه‌کردن خرید + نگهداری + کمبود است.\n" + f"{labels}\n{schema_block}" + ) + else: + demand_txt = "; ".join(f"{sku.sku_id} wants {sku.demand} at pack {sku.pack_size}" for sku in instance.skus) + en = ( + f"Replenish {names} over a {instance.periods}-week horizon. {cover_en} " + f"The buyer cannot spend more than {instance.budget}. On-hand stock across SKUs cannot exceed {instance.warehouse_capacity}. " + f"{demand_txt}. Costs and opening stock are in the JSON companion." + ) + fa = ( + f"برای {names_fa} در افق {instance.periods} هفته خرید کنید. {cover_fa} " + f"سقف هزینه {instance.budget} و سقف موجودی کل {instance.warehouse_capacity} است. " + "جزئیات تقاضا و بسته در فایل JSON همراه است." + ) + return en, fa + + +def make_assignment(index: int, rng: random.Random) -> tuple[AssignmentInstance, str]: + difficulty = _difficulty(index, N_ASSIGNMENT, 2) + n_tasks = 4 if difficulty == Difficulty.EASY else 6 if difficulty != Difficulty.HARD else 8 + n_agents = 3 if difficulty != Difficulty.HARD else 4 + tasks = [] + for k in range(n_tasks): + skills = [rng.choice(TASK_SKILLS)] + if difficulty != Difficulty.EASY and rng.random() < 0.35: + skills.append(rng.choice(TASK_SKILLS)) + skills = sorted(set(skills)) + tasks.append( + AssignmentTask( + task_id=f"T{k + 1}", + name=f"job-{k + 1}", + size=rng.randint(1, 3), + required=True if difficulty == Difficulty.INFEASIBLE else (k < n_tasks - 1 or difficulty != Difficulty.EASY), + skills=skills, + penalty=rng.randint(20, 40), + ) + ) + agents = [] + for k in range(n_agents): + skills = [TASK_SKILLS[k % len(TASK_SKILLS)]] + if difficulty != Difficulty.EASY: + skills.append(TASK_SKILLS[(k + 1) % len(TASK_SKILLS)]) + agents.append( + AssignmentAgent( + agent_id=f"A{k + 1}", + name=f"tech-{k + 1}", + capacity=rng.randint(3, 6) if difficulty != Difficulty.INFEASIBLE else 1, + skills=sorted(set(skills)), + ) + ) + if difficulty == Difficulty.INFEASIBLE: + for task in tasks: + task.required = True + task.size = 3 + for agent in agents: + agent.capacity = 1 + else: + for idx, task in enumerate(tasks): + agent = agents[idx % len(agents)] + if not (set(task.skills) & set(agent.skills)): + task.skills = sorted(set(task.skills + agent.skills[:1])) + required_load = sum(task.size for task in tasks if task.required) + agents[-1].skills = sorted(set(TASK_SKILLS)) + total_cap = sum(agent.capacity for agent in agents) + if required_load > total_cap: + agents[-1].capacity += required_load - total_cap + 2 + else: + agents[-1].capacity += 2 + costs = [] + for task in tasks: + for agent in agents: + if set(task.skills) & set(agent.skills) or not task.skills: + costs.append(AssignmentCost(task_id=task.task_id, agent_id=agent.agent_id, cost=rng.randint(4, 18))) + return AssignmentInstance(tasks=tasks, agents=agents, costs=costs), difficulty.value + + +def render_assignment(instance: AssignmentInstance, template_id: str) -> tuple[str, str]: + payload = instance.model_dump() + schema_block = _wrap_schema(payload, template_id) + task_txt = ", ".join(f"{task.task_id} size {task.size} skills {'/'.join(task.skills)}" for task in instance.tasks) + agent_txt = ", ".join(f"{agent.agent_id} cap {agent.capacity} skills {'/'.join(agent.skills)}" for agent in instance.agents) + if template_id.startswith("D-"): + en = ( + "Assign each required maintenance task to at most one eligible technician. " + "Do not exceed agent capacity. Optional leftover tasks pay a penalty.\n" + f"TASKS: {task_txt}\nAGENTS: {agent_txt}\n{schema_block}" + ) + fa = ( + "هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. " + "کار اختیاریِ انجام‌نشده جریمه دارد.\n" + f"TASKS: {task_txt}\nAGENTS: {agent_txt}\n{schema_block}" + ) + else: + en = ( + f"A service desk has technicians {agent_txt}. Work orders: {task_txt}. " + "A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties." + ) + fa = ( + f"میز خدمت تکنسین‌های {agent_txt} را دارد. سفارش‌ها: {task_txt}. " + "تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود." + ) + return en, fa + + +def make_schedule(index: int, rng: random.Random) -> tuple[ScheduleInstance, str]: + difficulty = _difficulty(index, N_SCHEDULING, 3) + n_jobs = 4 if difficulty == Difficulty.EASY else 6 if difficulty != Difficulty.HARD else 8 + machines = ["M1"] if difficulty == Difficulty.EASY else ["M1", "M2"] + jobs = [] + cursor = 0 + for k in range(n_jobs): + duration = rng.randint(2, 5) + release = rng.choice([0, 0, 1, 2]) + due = cursor + duration + rng.randint(1, 4) + hard = difficulty == Difficulty.INFEASIBLE and k < 2 + if difficulty == Difficulty.INFEASIBLE and k < 2: + due = release + duration - 1 + eligible = machines[:] if difficulty == Difficulty.EASY or rng.random() < 0.7 else [rng.choice(machines)] + jobs.append( + ScheduleJob( + job_id=f"J{k + 1}", + name=f"op-{k + 1}", + duration=duration, + release=release, + due=max(due, release + duration), + weight=rng.randint(1, 4), + hard_due=hard, + machine_eligible=eligible, + ) + ) + cursor += duration + if difficulty == Difficulty.INFEASIBLE and len(jobs) >= 2: + jobs[0].hard_due = True + jobs[0].due = jobs[0].release + jobs[0].duration - 1 + jobs[1].hard_due = True + jobs[1].due = jobs[1].release + jobs[1].duration - 1 + if jobs[0].due < jobs[0].release + jobs[0].duration: + pass + precedences = [] + if difficulty != Difficulty.EASY and n_jobs >= 3: + precedences.append(SchedulePrecedence(before="J1", after="J3")) + if difficulty == Difficulty.HARD and n_jobs >= 5: + precedences.append(SchedulePrecedence(before="J2", after="J5")) + horizon = sum(job.duration for job in jobs) + 8 + return ScheduleInstance(machines=machines, jobs=jobs, precedences=precedences, horizon=horizon), difficulty.value + + +def render_schedule(instance: ScheduleInstance, template_id: str) -> tuple[str, str]: + payload = instance.model_dump() + schema_block = _wrap_schema(payload, template_id) + job_txt = ", ".join( + f"{job.job_id} dur {job.duration} rel {job.release} due {job.due}{' hard' if job.hard_due else ''}" + for job in instance.jobs + ) + pred = ", ".join(f"{edge.before}->{edge.after}" for edge in instance.precedences) or "none" + if template_id.startswith("D-"): + en = ( + f"Schedule jobs on machines {', '.join(instance.machines)} without overlap. " + f"Respect release times and precedences ({pred}). Hard due dates are deadlines.\n" + f"JOBS: {job_txt}\n{schema_block}" + ) + fa = ( + f"کارها را روی ماشین‌های {', '.join(instance.machines)} بدون هم‌پوشانی زمان‌بندی کنید. " + f"زمان آزادسازی و تقدم ({pred}) رعایت شود. موعد سخت ضرب‌الاجل است.\n" + f"JOBS: {job_txt}\n{schema_block}" + ) + else: + en = ( + f"A shop has machines {', '.join(instance.machines)}. Jobs: {job_txt}. " + f"Precedence: {pred}. Minimize weighted tardiness. Do not overlap a machine." + ) + fa = ( + f"کارگاه ماشین‌های {', '.join(instance.machines)} را دارد. کارها: {job_txt}. " + f"تقدم: {pred}. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد." + ) + return en, fa + + +def _finalize( + problem_id: str, + family: Family, + index: int, + n_items: int, + instance, + difficulty: str, + template_id: str, + language: str, + seed: int, + prompt_en: str, + prompt_fa: str, + notes: str, +) -> ProblemRecord: + split = _split_for(index, n_items) + payload = instance.model_dump() + gold = solve_instance(family, payload, seconds=6.0, threads=1) + wanted = Difficulty(difficulty) + if wanted == Difficulty.INFEASIBLE and gold.solution.status.value != "infeasible": + notes = (notes + " requested infeasible; solver found a plan so the row is hard.").strip() + wanted = Difficulty.HARD + structural = _key( + family.value, + split.value, + template_id, + problem_id, + json.dumps(payload, sort_keys=True, ensure_ascii=False), + wanted.value, + ) + return ProblemRecord( + problem_id=problem_id, + family=family, + split=split, + interactive=problem_id in INTERACTIVE_IDS, + difficulty=wanted, + language=language, + template_id=template_id, + seed=seed, + prompt_en=prompt_en, + prompt_fa=prompt_fa, + prompt_json=_json_prompt(payload), + schema_payload=payload, + gold_status=gold.solution.status.value, + gold_objective=gold.solution.objective, + gold_bound=gold.solution.bound, + gold_solution=gold.solution.as_dict(), + structural_key=structural, + notes=notes, + ) + + +def generate_catalog(seed: int = DEFAULT_SEED) -> list[ProblemRecord]: + problems: list[ProblemRecord] = [] + for index in range(1, N_INVENTORY + 1): + rng = random.Random(seed * 1000 + index) + instance, difficulty = make_inventory(index, rng) + split = _split_for(index, N_INVENTORY) + template_id = _template(split, index) + language = "en" if index % 2 else "fa" + en, fa = render_inventory(instance, template_id, language) + problems.append( + _finalize( + f"INV-{index:03d}", + Family.INVENTORY, + index, + N_INVENTORY, + instance, + difficulty, + template_id, + language, + seed * 1000 + index, + en, + fa, + "lead time is 0; units are abstract currency and pieces", + ) + ) + for index in range(1, N_ASSIGNMENT + 1): + rng = random.Random(seed * 2000 + index) + instance, difficulty = make_assignment(index, rng) + split = _split_for(index, N_ASSIGNMENT) + template_id = _template(split, index) + language = "fa" if index % 2 else "en" + en, fa = render_assignment(instance, template_id) + problems.append( + _finalize( + f"ASN-{index:03d}", + Family.ASSIGNMENT, + index, + N_ASSIGNMENT, + instance, + difficulty, + template_id, + language, + seed * 2000 + index, + en, + fa, + "skill intersection is the eligibility rule", + ) + ) + for index in range(1, N_SCHEDULING + 1): + rng = random.Random(seed * 3000 + index) + instance, difficulty = make_schedule(index, rng) + split = _split_for(index, N_SCHEDULING) + template_id = _template(split, index) + language = "en" if index % 3 else "fa" + en, fa = render_schedule(instance, template_id) + problems.append( + _finalize( + f"SCH-{index:03d}", + Family.SCHEDULING, + index, + N_SCHEDULING, + instance, + difficulty, + template_id, + language, + seed * 3000 + index, + en, + fa, + "objective reported as weighted tardiness; makespan is a tie-break inside the solver only", + ) + ) + if len(problems) != N_PROBLEMS: + raise RuntimeError(f"expected {N_PROBLEMS} problems, got {len(problems)}") + return problems + + +def write_catalog(path: Path, seed: int = DEFAULT_SEED) -> list[ProblemRecord]: + problems = generate_catalog(seed) + path.parent.mkdir(parents=True, exist_ok=True) + with path.open("w", encoding="utf-8") as handle: + for row in problems: + handle.write(row.model_dump_json() + "\n") + return problems + + +def load_catalog(path: Path | None = None) -> list[ProblemRecord]: + if path and path.exists(): + rows = [] + for line in path.read_text(encoding="utf-8").splitlines(): + if line.strip(): + rows.append(ProblemRecord.model_validate_json(line)) + return rows + return generate_catalog() diff --git a/demo/src/i18n.py b/demo/src/i18n.py new file mode 100644 index 0000000000000000000000000000000000000000..24bba9c5480fa9e91107d8c92d482bbd75f993ce --- /dev/null +++ b/demo/src/i18n.py @@ -0,0 +1,112 @@ +from __future__ import annotations + +TEXTS = { + "en": { + "title": "ORBench — Solver and Agent Decision Benchmark", + "subtitle": "Compare structured solvers, heuristics, and text-to-schema agents on 100 small inventory, assignment, and scheduling tasks.", + "kind": "Research prototype · numeric validator is the judge · CPU · no paid API", + "run_sample": "Run sample", + "cancel": "Cancel run", + "reset": "Reset defaults", + "load_sample": "Load 20 interactive problems", + "language": "Language", + "problem": "Interactive problem", + "variant": "Prompt variant", + "template": "Labeled / narrative template", + "json": "JSON schema only", + "missing": "Hide a hard constraint in the text", + "time_limit": "Solver time limit (s)", + "advanced": "Advanced solver settings", + "sample_note": "Preview KPIs are a precomputed sample on the recorded 100-problem catalog. LLM rows stay not_evaluated. A fluent paragraph is not a feasible plan.", + "live_note": "Live CPU comparison: structured CP-SAT, fixed heuristic, JSON extractor, template extractor, and a naive direct answer. Named Hub models were not run.", + "kpi_n": "Problems in view", + "kpi_n_sub": "interactive subset or filtered catalog", + "kpi_feas": "Structured-solver feasible", + "kpi_feas_sub": "share of valid plans after independent checks", + "kpi_gap": "Heuristic mean gap", + "kpi_gap_sub": "only where gold status is proven optimal", + "kpi_fid": "Template fidelity", + "kpi_fid_sub": "atomic constraint facts recovered from text", + "kpi_eval": "Methods evaluated", + "kpi_eval_sub": "evaluated / listed — unevaluated is not zero", + "empty": "No live result yet. Load a sample problem and run a comparison.", + "status": "Reference status", + "upload_hint": "Edit the schema JSON only if you want a structured-solver what-if. Prompts stay synthetic. Direct-answer JSON is benchmark-only.", + "method_plot": "Parse and feasibility rates for evaluated methods", + "family_plot": "Feasibility by family for evaluated methods", + "sol_plot": "Reference CP-SAT plan", + "custom_text": "Optional custom prompt", + "custom_schema": "Editable schema JSON", + "direct_json": "Optional direct-answer JSON (benchmark only)", + "method_body": """ +ORBench is a research prototype for comparing decision-making *methods*, not a ranking of companies or a production optimizer. + +**What it decides.** For each tiny instance it records parse success, constraint fidelity, feasibility, and optimality gap versus a gold CP-SAT run. An LLM score is never the judge. + +**Three families.** Inventory (pack multiples, budget, warehouse capacity, optional hard cover), assignment (skill + capacity), and scheduling (release, precedence, optional hard due dates). Lead time is 0. Units are abstract. + +**Methods actually run.** `structured-solver`, `heuristic`, `json-extractor+solver`, `template-extractor+solver`, `naive-direct`. Development prompts include a `SCHEMA_BEGIN` block; test prompts are prose so the template extractor can fail honestly. + +**Methods listed but not run.** Qwen, Kimi, GLM, and DeepSeek cards stay `not_evaluated`. That cell is not a zero and not a rank. + +**Validator.** An independent checker recomputes inventory balance, pack, budget, capacity, assignment uniqueness/eligibility/capacity, and schedule overlap/precedence/release. Gap is reported only when gold status is optimal. + +**Limits.** 100 synthetic instances, CPU only, no paid API, no agent tool-use environment in this MVP, no claim that a fluent answer is operationally safe. Direct LLM-style answers are labeled benchmark-only. +""", + }, + "fa": { + "title": "اوربنچ — آزمایشگاه مقایسه حل‌گر و عامل تصمیم", + "subtitle": "حل‌گر ساختاریافته، ابتکاری ثابت و عامل متن‌به‌طرح را روی ۱۰۰ مسئله کوچک موجودی، تخصیص و زمان‌بندی مقایسه کنید.", + "kind": "نمونه پژوهشی · داور validator عددی است · CPU · بدون API پولی", + "run_sample": "اجرای نمونه", + "cancel": "لغو اجرا", + "reset": "بازگشت به پیش‌فرض", + "load_sample": "بارگذاری ۲۰ مسئله تعاملی", + "language": "زبان", + "problem": "مسئله تعاملی", + "variant": "نوع متن", + "template": "قالب برچسب‌دار / روایی", + "json": "فقط JSON", + "missing": "حذف یک قید سخت از متن", + "time_limit": "مهلت حل‌گر (ثانیه)", + "advanced": "تنظیمات پیشرفته حل‌گر", + "sample_note": "شاخص‌ها نمونه از پیش محاسبه‌شده روی کاتالوگ ۱۰۰ مسئله‌اند. ردیف مدل زبانی «ارزیابی نشده» است. متن روان به‌معنای برنامه شدنی نیست.", + "live_note": "مقایسه زنده CPU: CP-SAT ساختاریافته، ابتکاری ثابت، استخراج JSON، استخراج قالب، و پاسخ مستقیم ساده‌لوح. مدل‌های Hub اجرا نشده‌اند.", + "kpi_n": "مسئله در نما", + "kpi_n_sub": "زیرمجموعه تعاملی یا کاتالوگ فیلترشده", + "kpi_feas": "شدنی بودن حل‌گر ساختاریافته", + "kpi_feas_sub": "سهم برنامه معتبر پس از کنترل مستقل", + "kpi_gap": "میانگین شکاف ابتکاری", + "kpi_gap_sub": "فقط وقتی وضعیت طلایی بهینه اثبات‌شده است", + "kpi_fid": "وفاداری استخراج قالب", + "kpi_fid_sub": "حقایق اتمی قید بازیابی‌شده از متن", + "kpi_eval": "روش‌های ارزیابی‌شده", + "kpi_eval_sub": "ارزیابی‌شده / فهرست‌شده — ارزیابی‌نشده صفر نیست", + "empty": "هنوز نتیجه زنده‌ای نیست. یک مسئله نمونه را اجرا کنید.", + "status": "وضعیت مرجع", + "upload_hint": "JSON طرح را فقط برای آزمون حل‌گر ساختاریافته ویرایش کنید. پاسخ مستقیم فقط برای بنچمارک است.", + "method_plot": "نرخ تجزیه و امکان‌پذیری روش‌های ارزیابی‌شده", + "family_plot": "امکان‌پذیری به تفکیک خانواده", + "sol_plot": "برنامه مرجع CP-SAT", + "custom_text": "متن سفارشی اختیاری", + "custom_schema": "JSON طرح قابل ویرایش", + "direct_json": "JSON پاسخ مستقیم اختیاری (فقط بنچمارک)", + "method_body": """ +اوربنچ نمونه پژوهشی مقایسه *روش* است، نه رتبه‌بندی شرکت و نه بهینه‌ساز عملیاتی. + +**تصمیم.** برای هر نمونه کوچک، موفقیت تجزیه، وفاداری قید، امکان‌پذیری و شکاف بهینگی نسبت به اجرای طلایی CP-SAT ثبت می‌شود. امتیاز مدل زبانی داور نیست. + +**سه خانواده.** موجودی، تخصیص و زمان‌بندی. زمان تأمین صفر است. واحدها انتزاعی‌اند. + +**روش‌های اجراشده.** حل‌گر ساختاریافته، ابتکاری، استخراج JSON، استخراج قالب، پاسخ مستقیم ساده‌لوح. متن توسعه بلوک SCHEMA دارد؛ متن آزمون نثر است تا استخراج قالب صادقانه شکست بخورد. + +**روش‌های اجرا‌نشده.** Qwen، Kimi، GLM و DeepSeek در خانه «ارزیابی نشده» می‌مانند؛ این صفر یا رتبه نیست. + +**محدودیت.** ۱۰۰ نمونه ساختگی، فقط CPU، بدون API پولی، بدون ادعای ایمنی عملیاتی برای متن روان. +""", + }, +} + + +def t(lang: str, key: str) -> str: + return TEXTS.get(lang, TEXTS["en"]).get(key, TEXTS["en"].get(key, key)) diff --git a/demo/src/metrics.py b/demo/src/metrics.py new file mode 100644 index 0000000000000000000000000000000000000000..8824efa389ce2ae7517b9094c70314767db0a94b --- /dev/null +++ b/demo/src/metrics.py @@ -0,0 +1,201 @@ +from __future__ import annotations + +from collections import defaultdict + +import pandas as pd + +from src.domain import EvalRow, SolveStatus, gap, not_evaluated_cell +from src.model_registry import UNEVALUATED_MODELS, evaluated_ids + + +def row_from_run( + problem, + method_id: str, + method_kind: str, + parse_success: bool | None, + fidelity: float | None, + status: str, + feasible: bool | None, + objective: float | None, + seconds: float, + violated: list[str], + notes: str, + precomputed: bool = False, + cost_usd: float | None = 0.0, +) -> EvalRow: + gold_status = problem.gold_status + gold_obj = problem.gold_objective + opt_gap = gap(objective, gold_obj, gold_status) if feasible else None + return EvalRow( + problem_id=problem.problem_id, + method_id=method_id, + method_kind=method_kind, + evaluated=True, + parse_success=parse_success, + constraint_fidelity=fidelity, + status=status, + feasible=feasible, + optimality_gap=opt_gap, + objective=objective, + gold_objective=gold_obj, + gold_status=gold_status, + seconds=seconds, + cost_usd=cost_usd, + violated=violated, + notes=notes, + precomputed=precomputed, + family=problem.family.value, + split=problem.split.value, + language=problem.language, + difficulty=problem.difficulty.value, + ) + + +def skipped_rows(problem) -> list[EvalRow]: + rows = [] + for spec in UNEVALUATED_MODELS: + rows.append( + EvalRow( + problem_id=problem.problem_id, + method_id=spec.method_id, + method_kind=spec.kind.value, + evaluated=False, + parse_success=None, + constraint_fidelity=None, + status=not_evaluated_cell(), + feasible=None, + optimality_gap=None, + objective=None, + gold_objective=problem.gold_objective, + gold_status=problem.gold_status, + seconds=0.0, + cost_usd=None, + violated=[], + notes=spec.reason_if_skipped, + precomputed=True, + family=problem.family.value, + split=problem.split.value, + language=problem.language, + difficulty=problem.difficulty.value, + ) + ) + return rows + + +def summarize(rows: list[EvalRow] | pd.DataFrame) -> pd.DataFrame: + frame = rows if isinstance(rows, pd.DataFrame) else pd.DataFrame([row.model_dump() for row in rows]) + if frame.empty: + return pd.DataFrame() + out = [] + for method_id, group in frame.groupby("method_id", dropna=False): + evaluated = bool(group["evaluated"].iloc[0]) + if not evaluated: + out.append( + { + "method_id": method_id, + "evaluated": False, + "n": int(len(group)), + "parse_rate": not_evaluated_cell(), + "feasible_rate": not_evaluated_cell(), + "infeasible_agreement": not_evaluated_cell(), + "mean_gap": not_evaluated_cell(), + "mean_fidelity": not_evaluated_cell(), + "mean_seconds": not_evaluated_cell(), + "mean_cost_usd": not_evaluated_cell(), + "n_optimal": not_evaluated_cell(), + } + ) + continue + parsed = group["parse_success"].dropna() + feasible = group["feasible"].dropna() + inf_gold = group.loc[group["gold_status"] == SolveStatus.INFEASIBLE.value] + agree = None + if len(inf_gold): + agree = float((inf_gold["status"] == SolveStatus.INFEASIBLE.value).mean()) + gaps = group["optimality_gap"].dropna() + fidelity = group["constraint_fidelity"].dropna() + out.append( + { + "method_id": method_id, + "evaluated": True, + "n": int(len(group)), + "parse_rate": None if parsed.empty else float(parsed.mean()), + "feasible_rate": None if feasible.empty else float(feasible.mean()), + "infeasible_agreement": agree, + "mean_gap": None if gaps.empty else float(gaps.mean()), + "mean_fidelity": None if fidelity.empty else float(fidelity.mean()), + "mean_seconds": float(group["seconds"].mean()), + "mean_cost_usd": float(group["cost_usd"].fillna(0).mean()), + "n_optimal": int((group["status"] == SolveStatus.OPTIMAL.value).sum()), + } + ) + return pd.DataFrame(out).sort_values(["evaluated", "method_id"], ascending=[False, True]).reset_index(drop=True) + + +def family_summary(rows: list[EvalRow] | pd.DataFrame) -> pd.DataFrame: + frame = rows if isinstance(rows, pd.DataFrame) else pd.DataFrame([row.model_dump() for row in rows]) + if frame.empty: + return pd.DataFrame() + live = frame.loc[frame["evaluated"] == True] # noqa: E712 + if live.empty: + return pd.DataFrame() + records = [] + for (family, method_id), group in live.groupby(["family", "method_id"]): + feasible = group["feasible"].dropna() + gaps = group["optimality_gap"].dropna() + records.append( + { + "family": family, + "method_id": method_id, + "n": int(len(group)), + "feasible_rate": None if feasible.empty else float(feasible.mean()), + "mean_gap": None if gaps.empty else float(gaps.mean()), + } + ) + return pd.DataFrame(records).sort_values(["family", "method_id"]).reset_index(drop=True) + + +def display_cell(value) -> str: + if value is None: + return not_evaluated_cell() + if isinstance(value, float): + return f"{value:.3f}" + return str(value) + + +def kpi_snapshot(rows: list[EvalRow] | pd.DataFrame) -> dict[str, float | str | int]: + frame = rows if isinstance(rows, pd.DataFrame) else pd.DataFrame([row.model_dump() for row in rows]) + live = frame.loc[frame["method_id"].isin(evaluated_ids())] if not frame.empty else frame + structured = live.loc[live["method_id"] == "structured-solver"] if not live.empty else live + heuristic = live.loc[live["method_id"] == "heuristic"] if not live.empty else live + extractor = live.loc[live["method_id"] == "template-extractor+solver"] if not live.empty else live + return { + "n_problems": int(structured["problem_id"].nunique()) if not structured.empty else 0, + "structured_feasible": float(structured["feasible"].dropna().mean()) if not structured.empty else 0.0, + "heuristic_gap": float(heuristic["optimality_gap"].dropna().mean()) if not heuristic.empty and heuristic["optimality_gap"].notna().any() else None, + "template_fidelity": float(extractor["constraint_fidelity"].dropna().mean()) if not extractor.empty and extractor["constraint_fidelity"].notna().any() else None, + "n_methods_evaluated": int(len(evaluated_ids())), + "n_methods_listed": int(frame["method_id"].nunique()) if not frame.empty else 0, + } + + +def compare_two(rows: pd.DataFrame, left: str, right: str) -> pd.DataFrame: + if rows.empty: + return pd.DataFrame() + a = rows.loc[rows["method_id"] == left].set_index("problem_id") + b = rows.loc[rows["method_id"] == right].set_index("problem_id") + ids = sorted(set(a.index) & set(b.index)) + out = [] + for problem_id in ids: + out.append( + { + "problem_id": problem_id, + f"{left}_status": a.loc[problem_id, "status"], + f"{right}_status": b.loc[problem_id, "status"], + f"{left}_obj": a.loc[problem_id, "objective"], + f"{right}_obj": b.loc[problem_id, "objective"], + f"{left}_feasible": a.loc[problem_id, "feasible"], + f"{right}_feasible": b.loc[problem_id, "feasible"], + } + ) + return pd.DataFrame(out) diff --git a/demo/src/model_registry.py b/demo/src/model_registry.py new file mode 100644 index 0000000000000000000000000000000000000000..ac3c8b1bddb5e36d8043dede6002f185a96b0d8c --- /dev/null +++ b/demo/src/model_registry.py @@ -0,0 +1,114 @@ +from __future__ import annotations + +from src.domain import MethodKind, MethodSpec + +REGISTRY_VERSION = "2026-09-20" + +# Named Hub models are listed so the comparison table stays honest. +# None of the LLM rows were executed in this release. Cells stay +# "not_evaluated" rather than 0 or a fabricated rank. +EVALUATED_METHODS = ( + MethodSpec( + method_id="structured-solver", + display_name="Structured form + CP-SAT", + kind=MethodKind.STRUCTURED_SOLVER, + evaluated=True, + version="ortools-cpsat", + notes="Gold schema or user-edited schema enters the solver. Numeric reference.", + ), + MethodSpec( + method_id="heuristic", + display_name="Fixed heuristic (LFL / greedy / EDD)", + kind=MethodKind.HEURISTIC, + evaluated=True, + version="or-bench-heuristic-v1", + notes="Lot-for-lot inventory, cheapest-eligible assignment, earliest-due-date scheduling.", + ), + MethodSpec( + method_id="template-extractor+solver", + display_name="Template extractor → solver", + kind=MethodKind.TEXT_TO_SCHEMA, + evaluated=True, + version="or-bench-template-v1", + notes="Deterministic labeled-field parser, then CP-SAT. Not an LLM.", + ), + MethodSpec( + method_id="json-extractor+solver", + display_name="JSON extractor → solver", + kind=MethodKind.TEXT_TO_SCHEMA, + evaluated=True, + version="or-bench-json-v1", + notes="Parses a JSON object from the prompt, then CP-SAT.", + ), + MethodSpec( + method_id="naive-direct", + display_name="Naive direct answer (benchmark only)", + kind=MethodKind.DIRECT_ANSWER, + evaluated=True, + version="or-bench-naive-v1", + notes="Writes a sloppy numeric plan without a solver. Operational use is not allowed.", + ), +) + +UNEVALUATED_MODELS = ( + MethodSpec( + method_id="Qwen/Qwen3-4B-Instruct-2507", + display_name="Qwen3-4B-Instruct-2507", + kind=MethodKind.LLM_SCHEMA, + evaluated=False, + version="hub-card", + license="see model card", + reason_if_skipped="Paid/local LLM inference is off. No batch was run.", + ), + MethodSpec( + method_id="Qwen/Qwen3.8-27B", + display_name="Qwen3.8-27B", + kind=MethodKind.LLM_SCHEMA, + evaluated=False, + version="hub-card", + license="see model card", + reason_if_skipped="Not hosted on this CPU Space. No API batch.", + ), + MethodSpec( + method_id="moonshotai/Kimi-K3", + display_name="Kimi K3", + kind=MethodKind.LLM_SCHEMA, + evaluated=False, + version="hub-card", + license="see model card", + reason_if_skipped="API optional and disabled. Not evaluated.", + ), + MethodSpec( + method_id="zai-org/GLM-5.3", + display_name="GLM 5.3", + kind=MethodKind.LLM_SCHEMA, + evaluated=False, + version="hub-card", + license="see model card", + reason_if_skipped="API optional and disabled. Not evaluated.", + ), + MethodSpec( + method_id="deepseek-ai/DeepSeek-V4.1-Flash", + display_name="DeepSeek V4.1 Flash", + kind=MethodKind.LLM_SCHEMA, + evaluated=False, + version="hub-card", + license="see model card", + reason_if_skipped="API optional and disabled. Not evaluated.", + ), +) + + +def all_methods() -> list[MethodSpec]: + return list(EVALUATED_METHODS) + list(UNEVALUATED_MODELS) + + +def evaluated_ids() -> list[str]: + return [item.method_id for item in EVALUATED_METHODS] + + +def method_by_id(method_id: str) -> MethodSpec | None: + for item in all_methods(): + if item.method_id == method_id: + return item + return None diff --git a/demo/src/optimizer.py b/demo/src/optimizer.py new file mode 100644 index 0000000000000000000000000000000000000000..e04e03db59553ea09b43114a40382589320c8524 --- /dev/null +++ b/demo/src/optimizer.py @@ -0,0 +1,300 @@ +from __future__ import annotations + +import time +from dataclasses import dataclass + +from ortools.sat.python import cp_model + +from src.domain import ( + AssignmentInstance, + AssignmentRow, + Family, + InventoryInstance, + InventoryOrder, + ScheduleInstance, + ScheduleStart, + Solution, + SolveStatus, + parse_instance, +) + + +@dataclass +class SolverOutcome: + solution: Solution + seconds: float + solver_name: str + message: str + + +def _status(model_status: int) -> SolveStatus: + if model_status == cp_model.OPTIMAL: + return SolveStatus.OPTIMAL + if model_status == cp_model.FEASIBLE: + return SolveStatus.FEASIBLE + if model_status == cp_model.INFEASIBLE: + return SolveStatus.INFEASIBLE + if model_status in {cp_model.UNKNOWN, cp_model.MODEL_INVALID}: + return SolveStatus.TIMEOUT + return SolveStatus.ERROR + + +def _status_name(model_status: int) -> str: + names = { + cp_model.OPTIMAL: "OPTIMAL", + cp_model.FEASIBLE: "FEASIBLE", + cp_model.INFEASIBLE: "INFEASIBLE", + cp_model.UNKNOWN: "UNKNOWN", + cp_model.MODEL_INVALID: "MODEL_INVALID", + } + return names.get(model_status, str(model_status)) + + +def solve_inventory(instance: InventoryInstance, seconds: float, threads: int = 1) -> SolverOutcome: + started = time.perf_counter() + model = cp_model.CpModel() + periods = instance.periods + skus = instance.skus + order: dict[tuple[str, int], cp_model.IntVar] = {} + inv: dict[tuple[str, int], cp_model.IntVar] = {} + short: dict[tuple[str, int], cp_model.IntVar] = {} + sold: dict[tuple[str, int], cp_model.IntVar] = {} + + max_demand = max((max(sku.demand) for sku in skus), default=1) + max_pack = max((sku.pack_size for sku in skus), default=1) + max_order = max(max_demand * periods + max_pack * 4, 1) + + for sku in skus: + for t in range(1, periods + 1): + packs = model.NewIntVar(0, max_order // sku.pack_size + 1, f"packs_{sku.sku_id}_{t}") + qty = model.NewIntVar(0, max_order, f"ord_{sku.sku_id}_{t}") + model.Add(qty == packs * sku.pack_size) + order[(sku.sku_id, t)] = qty + inv[(sku.sku_id, t)] = model.NewIntVar(0, instance.warehouse_capacity, f"inv_{sku.sku_id}_{t}") + demand = int(sku.demand[t - 1]) + short[(sku.sku_id, t)] = model.NewIntVar(0, demand, f"sh_{sku.sku_id}_{t}") + sold[(sku.sku_id, t)] = model.NewIntVar(0, demand, f"sd_{sku.sku_id}_{t}") + prev = sku.initial_stock if t == 1 else inv[(sku.sku_id, t - 1)] + model.Add(inv[(sku.sku_id, t)] + sold[(sku.sku_id, t)] == prev + qty) + model.Add(sold[(sku.sku_id, t)] + short[(sku.sku_id, t)] == demand) + if instance.cover_required: + model.Add(short[(sku.sku_id, t)] == 0) + + for t in range(1, periods + 1): + model.Add(sum(inv[(sku.sku_id, t)] for sku in skus) <= instance.warehouse_capacity) + + model.Add( + sum(sku.unit_cost * order[(sku.sku_id, t)] for sku in skus for t in range(1, periods + 1)) <= instance.budget + ) + + objective = [] + for sku in skus: + for t in range(1, periods + 1): + objective.append(sku.unit_cost * order[(sku.sku_id, t)]) + objective.append(sku.holding_cost * inv[(sku.sku_id, t)]) + objective.append(sku.shortage_cost * short[(sku.sku_id, t)]) + model.Minimize(sum(objective)) + + solver = cp_model.CpSolver() + solver.parameters.max_time_in_seconds = float(seconds) + solver.parameters.num_search_workers = int(threads) + raw = solver.Solve(model) + status = _status(raw) + elapsed = time.perf_counter() - started + message = _status_name(raw) + if status in {SolveStatus.OPTIMAL, SolveStatus.FEASIBLE}: + orders = [ + InventoryOrder(sku_id=sku.sku_id, period=t, qty=int(solver.Value(order[(sku.sku_id, t)]))) + for sku in skus + for t in range(1, periods + 1) + ] + obj = float(solver.ObjectiveValue()) + bound = float(solver.BestObjectiveBound()) if status == SolveStatus.FEASIBLE else obj + return SolverOutcome( + Solution( + family=Family.INVENTORY, + status=status, + objective=obj, + bound=bound, + orders=orders, + message=message, + ), + elapsed, + "ortools-cpsat", + message, + ) + return SolverOutcome( + Solution(family=Family.INVENTORY, status=status, message=message), + elapsed, + "ortools-cpsat", + message, + ) + + +def solve_assignment(instance: AssignmentInstance, seconds: float, threads: int = 1) -> SolverOutcome: + started = time.perf_counter() + model = cp_model.CpModel() + x: dict[tuple[str, str], cp_model.IntVar] = {} + costs = instance.cost_map() + for task in instance.tasks: + for agent in instance.agents: + if instance.eligible(task, agent) and (task.task_id, agent.agent_id) in costs: + x[(task.task_id, agent.agent_id)] = model.NewBoolVar(f"x_{task.task_id}_{agent.agent_id}") + + unassigned: dict[str, cp_model.IntVar] = {} + for task in instance.tasks: + assigned = [x[(task.task_id, agent.agent_id)] for agent in instance.agents if (task.task_id, agent.agent_id) in x] + miss = model.NewBoolVar(f"u_{task.task_id}") + unassigned[task.task_id] = miss + model.Add(sum(assigned) + miss == 1) + if task.required: + model.Add(miss == 0) + + for agent in instance.agents: + load = [ + task.size * x[(task.task_id, agent.agent_id)] + for task in instance.tasks + if (task.task_id, agent.agent_id) in x + ] + if load: + model.Add(sum(load) <= agent.capacity) + + obj_terms = [] + for (task_id, agent_id), var in x.items(): + obj_terms.append(costs[(task_id, agent_id)] * var) + for task in instance.tasks: + obj_terms.append(task.penalty * unassigned[task.task_id]) + model.Minimize(sum(obj_terms) if obj_terms else 0) + + solver = cp_model.CpSolver() + solver.parameters.max_time_in_seconds = float(seconds) + solver.parameters.num_search_workers = int(threads) + raw = solver.Solve(model) + status = _status(raw) + elapsed = time.perf_counter() - started + message = _status_name(raw) + if status in {SolveStatus.OPTIMAL, SolveStatus.FEASIBLE}: + rows = [ + AssignmentRow(task_id=task_id, agent_id=agent_id) + for (task_id, agent_id), var in x.items() + if solver.Value(var) + ] + leftover = [task_id for task_id, var in unassigned.items() if solver.Value(var)] + obj = float(solver.ObjectiveValue()) + bound = float(solver.BestObjectiveBound()) if status == SolveStatus.FEASIBLE else obj + return SolverOutcome( + Solution( + family=Family.ASSIGNMENT, + status=status, + objective=obj, + bound=bound, + assignments=rows, + unassigned=leftover, + message=message, + ), + elapsed, + "ortools-cpsat", + message, + ) + return SolverOutcome( + Solution(family=Family.ASSIGNMENT, status=status, message=message), + elapsed, + "ortools-cpsat", + message, + ) + + +def solve_scheduling(instance: ScheduleInstance, seconds: float, threads: int = 1) -> SolverOutcome: + started = time.perf_counter() + model = cp_model.CpModel() + horizon = max(instance.horizon, sum(job.duration for job in instance.jobs) + max((job.release for job in instance.jobs), default=0) + 2) + intervals_by_machine: dict[str, list] = {machine: [] for machine in instance.machines} + start: dict[str, cp_model.IntVar] = {} + end: dict[str, cp_model.IntVar] = {} + tardy: dict[str, cp_model.IntVar] = {} + assign: dict[tuple[str, str], cp_model.IntVar] = {} + + for job in instance.jobs: + start[job.job_id] = model.NewIntVar(job.release, horizon, f"s_{job.job_id}") + end[job.job_id] = model.NewIntVar(job.release + job.duration, horizon + job.duration, f"e_{job.job_id}") + model.Add(end[job.job_id] == start[job.job_id] + job.duration) + tardy[job.job_id] = model.NewIntVar(0, horizon + job.duration, f"tard_{job.job_id}") + model.Add(tardy[job.job_id] >= end[job.job_id] - job.due) + if job.hard_due: + model.Add(end[job.job_id] <= job.due) + eligible = [machine for machine in instance.machines if machine in set(job.machine_eligible)] + if not eligible: + eligible = list(instance.machines) + machine_bools = [] + for machine in eligible: + flag = model.NewBoolVar(f"m_{job.job_id}_{machine}") + assign[(job.job_id, machine)] = flag + interval = model.NewOptionalIntervalVar(start[job.job_id], job.duration, end[job.job_id], flag, f"iv_{job.job_id}_{machine}") + intervals_by_machine[machine].append(interval) + machine_bools.append(flag) + model.AddExactlyOne(machine_bools) + + for machine, intervals in intervals_by_machine.items(): + if intervals: + model.AddNoOverlap(intervals) + + job_ids = {job.job_id for job in instance.jobs} + for edge in instance.precedences: + if edge.before in job_ids and edge.after in job_ids: + model.Add(end[edge.before] <= start[edge.after]) + + makespan = model.NewIntVar(0, horizon + 8, "makespan") + for job in instance.jobs: + model.Add(makespan >= end[job.job_id]) + model.Minimize(sum(job.weight * tardy[job.job_id] for job in instance.jobs) * 100 + makespan) + + solver = cp_model.CpSolver() + solver.parameters.max_time_in_seconds = float(seconds) + solver.parameters.num_search_workers = int(threads) + raw = solver.Solve(model) + status = _status(raw) + elapsed = time.perf_counter() - started + message = _status_name(raw) + if status in {SolveStatus.OPTIMAL, SolveStatus.FEASIBLE}: + starts = [] + for job in instance.jobs: + machine_id = next(machine for machine in instance.machines if (job.job_id, machine) in assign and solver.Value(assign[(job.job_id, machine)])) + starts.append( + ScheduleStart( + job_id=job.job_id, + machine_id=machine_id, + start=int(solver.Value(start[job.job_id])), + end=int(solver.Value(end[job.job_id])), + ) + ) + weighted = sum(job.weight * max(0, int(solver.Value(end[job.job_id])) - job.due) for job in instance.jobs) + obj = float(weighted) + return SolverOutcome( + Solution( + family=Family.SCHEDULING, + status=status, + objective=obj, + bound=obj if status == SolveStatus.OPTIMAL else None, + starts=starts, + message=message, + ), + elapsed, + "ortools-cpsat", + message, + ) + return SolverOutcome( + Solution(family=Family.SCHEDULING, status=status, message=message), + elapsed, + "ortools-cpsat", + message, + ) + + +def solve_instance(family: Family | str, payload: dict, seconds: float, threads: int = 1) -> SolverOutcome: + family = Family(family) + instance = parse_instance(family, payload) + if family == Family.INVENTORY: + return solve_inventory(instance, seconds, threads) + if family == Family.ASSIGNMENT: + return solve_assignment(instance, seconds, threads) + return solve_scheduling(instance, seconds, threads) diff --git a/demo/src/pipeline.py b/demo/src/pipeline.py new file mode 100644 index 0000000000000000000000000000000000000000..26c7c7e0fbdf639916e50fa8098d99085fd05653 --- /dev/null +++ b/demo/src/pipeline.py @@ -0,0 +1,385 @@ +from __future__ import annotations + +import hashlib +import json +import time +import uuid +from pathlib import Path +from typing import Any + +import pandas as pd + +from src.baseline import run_heuristic, run_naive +from src.budget_guard import skip_reason +from src.domain import ( + CODE_VERSION, + DEFAULT_SEED, + DEFAULT_SOLVER_SECONDS, + PROTOCOL_ID, + SOLVER_NAME, + ConstraintConfig, + EvalRow, + Family, + ProblemRecord, + PromptVariant, + Solution, + SolveStatus, +) +from src.explain import status_label +from src.extractor import constraint_fidelity, drop_constraint, extract_json, extract_template +from src.generator import INTERACTIVE_IDS, generate_catalog, load_catalog +from src.metrics import row_from_run, skipped_rows, summarize +from src.model_registry import REGISTRY_VERSION, method_by_id +from src.optimizer import solve_instance +from src.validation import format_input_error, validate_schema, validate_solution + +ROOT = Path(__file__).resolve().parents[1] +CATALOG_PATH = ROOT / "examples" / "problems.jsonl" +RESULTS_PATH = ROOT / "examples" / "results.jsonl" + + +def _input_hash(payload: dict) -> str: + raw = json.dumps(payload, sort_keys=True, ensure_ascii=False) + return hashlib.sha256(raw.encode("utf-8")).hexdigest()[:16] + + +def load_problems(path: Path | None = None) -> list[ProblemRecord]: + return load_catalog(path or CATALOG_PATH if (path or CATALOG_PATH).exists() else None) + + +def load_results(path: Path | None = None) -> pd.DataFrame: + target = path or RESULTS_PATH + if not target.exists(): + return pd.DataFrame() + rows = [json.loads(line) for line in target.read_text(encoding="utf-8").splitlines() if line.strip()] + return pd.DataFrame(rows) + + +def interactive_problems(problems: list[ProblemRecord] | None = None) -> list[ProblemRecord]: + problems = problems or load_problems() + chosen = [item for item in problems if item.interactive] + if len(chosen) < 5: + chosen = problems[:20] + return chosen + + +def problem_by_id(problem_id: str, problems: list[ProblemRecord] | None = None) -> ProblemRecord: + problems = problems or load_problems() + for item in problems: + if item.problem_id == problem_id: + return item + raise KeyError(problem_id) + + +def _prompt_for(problem: ProblemRecord, lang: str, variant: PromptVariant) -> str: + if variant == PromptVariant.JSON: + return problem.prompt_json + text = problem.prompt_fa if lang == "fa" else problem.prompt_en + if variant == PromptVariant.MISSING_BUDGET: + _, text = drop_constraint(problem.family, problem.schema_payload, text) + return text + + +def _evaluate_solver(problem: ProblemRecord, payload: dict, seconds: float, threads: int, method_id: str, method_kind: str, parse_success: bool | None, fidelity: float | None, notes: str) -> EvalRow: + schema = validate_schema(problem.family, payload) + if not schema.ok: + return row_from_run( + problem, + method_id, + method_kind, + False if parse_success is None else parse_success, + fidelity, + SolveStatus.INVALID.value, + False, + None, + 0.0, + schema.failed_codes(), + format_input_error(schema), + ) + outcome = solve_instance(problem.family, payload, seconds=seconds, threads=threads) + solution = outcome.solution + if solution.status == SolveStatus.INFEASIBLE: + feasible = False + violated: list[str] = ["infeasible"] + objective = None + report_notes = solution.message + elif solution.status in {SolveStatus.TIMEOUT, SolveStatus.ERROR}: + feasible = None + violated = [solution.status.value] + objective = None + report_notes = solution.message + else: + report = validate_solution(problem.family, payload, solution) + feasible = report.ok + violated = report.failed_codes() + objective = report.recomputed_objective if report.recomputed_objective is not None else solution.objective + report_notes = notes or solution.message + if not report.ok: + solution.status = SolveStatus.INVALID + return row_from_run( + problem, + method_id, + method_kind, + True if parse_success is None else parse_success, + fidelity, + solution.status.value, + feasible, + objective, + outcome.seconds, + violated, + report_notes, + ) + + +def _evaluate_direct(problem: ProblemRecord, payload: dict, solution: Solution, seconds: float, method_id: str, notes: str) -> EvalRow: + report = validate_solution(problem.family, payload, solution) + return row_from_run( + problem, + method_id, + "direct-answer", + True, + 1.0, + SolveStatus.HEURISTIC.value if report.ok else SolveStatus.INVALID.value, + report.ok, + report.recomputed_objective, + seconds, + report.failed_codes(), + notes, + ) + + +def evaluate_problem( + problem: ProblemRecord, + lang: str = "en", + variant: PromptVariant | str = PromptVariant.TEMPLATE, + config: ConstraintConfig | None = None, + custom_text: str | None = None, + custom_schema: dict | None = None, + custom_solution: dict | None = None, +) -> dict[str, Any]: + started = time.perf_counter() + config = config or ConstraintConfig() + variant = PromptVariant(variant) + prompt = custom_text if custom_text else _prompt_for(problem, lang, variant) + payload = custom_schema or problem.schema_payload + rows: list[EvalRow] = [] + + structured_payload = payload + rows.append( + _evaluate_solver( + problem, + structured_payload, + config.solver_seconds, + config.threads, + "structured-solver", + "structured-solver", + True, + 1.0, + "schema entered the solver without an LLM", + ) + ) + + heuristic = run_heuristic(problem.family, payload) + heur_report = validate_solution(problem.family, payload, heuristic.solution) + rows.append( + row_from_run( + problem, + "heuristic", + "heuristic", + True, + 1.0, + SolveStatus.HEURISTIC.value if heur_report.ok else SolveStatus.INVALID.value, + heur_report.ok, + heur_report.recomputed_objective, + heuristic.seconds, + heur_report.failed_codes(), + heuristic.message, + ) + ) + + json_payload = extract_json(prompt) or extract_json(problem.prompt_json) + json_ok = json_payload is not None + json_fid = constraint_fidelity(problem.family, problem.schema_payload, json_payload) + if json_ok: + rows.append( + _evaluate_solver( + problem, + json_payload, + config.solver_seconds, + config.threads, + "json-extractor+solver", + "text-to-schema", + True, + json_fid, + "JSON extracted from the prompt", + ) + ) + else: + rows.append( + row_from_run( + problem, + "json-extractor+solver", + "text-to-schema", + False, + 0.0, + SolveStatus.INVALID.value, + False, + None, + 0.0, + ["parse"], + "no JSON object found", + ) + ) + + tmpl_payload = extract_template(prompt, problem.family) + tmpl_ok = tmpl_payload is not None + tmpl_fid = constraint_fidelity(problem.family, problem.schema_payload, tmpl_payload) + if tmpl_ok: + rows.append( + _evaluate_solver( + problem, + tmpl_payload, + config.solver_seconds, + config.threads, + "template-extractor+solver", + "text-to-schema", + True, + tmpl_fid, + "labeled fields or SCHEMA_BEGIN block", + ) + ) + else: + rows.append( + row_from_run( + problem, + "template-extractor+solver", + "text-to-schema", + False, + 0.0, + SolveStatus.INVALID.value, + False, + None, + 0.0, + ["parse"], + "template extractor found no labeled schema", + ) + ) + + naive = run_naive(problem.family, payload) + rows.append(_evaluate_direct(problem, payload, naive.solution, naive.seconds, "naive-direct", naive.message)) + + if custom_solution: + try: + proposed = Solution.model_validate(custom_solution) + rows.append(_evaluate_direct(problem, payload, proposed, 0.0, "user-direct", "user-supplied direct answer")) + except Exception as exc: + rows.append( + row_from_run( + problem, + "user-direct", + "direct-answer", + True, + 1.0, + SolveStatus.INVALID.value, + False, + None, + 0.0, + ["schema"], + f"direct answer rejected: {exc}", + ) + ) + + rows.extend(skipped_rows(problem)) + structured = next(row for row in rows if row.method_id == "structured-solver") + report = None + live_solution = None + if structured.status in {SolveStatus.OPTIMAL.value, SolveStatus.FEASIBLE.value, SolveStatus.HEURISTIC.value}: + live = solve_instance(problem.family, structured_payload, seconds=config.solver_seconds, threads=config.threads) + live_solution = live.solution + report = validate_solution(problem.family, structured_payload, live.solution) + + elapsed = time.perf_counter() - started + run_id = f"orbench-{uuid.uuid4().hex[:10]}" + table = pd.DataFrame([row.model_dump() for row in rows]) + return { + "run_id": run_id, + "error": None, + "problem": problem, + "prompt": prompt, + "variant": variant.value, + "schema": structured_payload, + "rows": rows, + "table": table, + "summary": summarize(rows), + "solution": live_solution.as_dict() if live_solution else {}, + "validation": report, + "status": structured.status, + "status_label": status_label(structured.status, lang), + "seconds": elapsed, + "report": build_report(run_id, problem, rows, structured_payload, elapsed, lang, variant.value), + } + + +def build_report(run_id: str, problem: ProblemRecord, rows: list[EvalRow], payload: dict, seconds: float, lang: str, variant: str) -> dict[str, Any]: + return { + "run_id": run_id, + "protocol_id": PROTOCOL_ID, + "code_version": CODE_VERSION, + "registry_version": REGISTRY_VERSION, + "solver_version": SOLVER_NAME, + "input_hash": _input_hash(payload), + "seed": problem.seed, + "problem_id": problem.problem_id, + "family": problem.family.value, + "split": problem.split.value, + "language": lang, + "prompt_variant": variant, + "gold_status": problem.gold_status, + "gold_objective": problem.gold_objective, + "seconds": seconds, + "budget_note": skip_reason(), + "rows": [row.model_dump() for row in rows], + } + + +def evaluate_catalog( + problems: list[ProblemRecord] | None = None, + config: ConstraintConfig | None = None, + lang: str = "en", +) -> list[EvalRow]: + problems = problems or generate_catalog(DEFAULT_SEED) + config = config or ConstraintConfig(solver_seconds=DEFAULT_SOLVER_SECONDS) + rows: list[EvalRow] = [] + for problem in problems: + result = evaluate_problem(problem, lang=problem.language, config=config) + for row in result["rows"]: + row.precomputed = True + rows.append(row) + return rows + + +def result_to_downloads(result: dict[str, Any], folder: Path) -> dict[str, str]: + folder.mkdir(parents=True, exist_ok=True) + run_id = result["run_id"] + files = {} + table: pd.DataFrame = result["table"] + csv_path = folder / f"{run_id}_comparison.csv" + table.to_csv(csv_path, index=False) + files["comparison"] = str(csv_path) + report_path = folder / f"{run_id}_report.json" + report_path.write_text(json.dumps(result["report"], indent=2, ensure_ascii=False), encoding="utf-8") + files["report"] = str(report_path) + if result.get("summary") is not None and len(result["summary"]): + summary_path = folder / f"{run_id}_summary.csv" + result["summary"].to_csv(summary_path, index=False) + files["summary"] = str(summary_path) + schema_path = folder / f"{run_id}_schema.json" + schema_path.write_text(json.dumps(result["schema"], indent=2, ensure_ascii=False), encoding="utf-8") + files["schema"] = str(schema_path) + return files + + +def load_sample() -> dict[str, Any]: + problems = load_problems() + sample = next((item for item in problems if item.problem_id == INTERACTIVE_IDS[0]), problems[0]) + return {"problem": sample, "problems": problems} diff --git a/demo/src/plots.py b/demo/src/plots.py new file mode 100644 index 0000000000000000000000000000000000000000..802979c86fabb19aaef5e3382f29baa5c8192832 --- /dev/null +++ b/demo/src/plots.py @@ -0,0 +1,142 @@ +from __future__ import annotations + +import pandas as pd +import plotly.graph_objects as go + +from src.domain import Family, not_evaluated_cell +from src.i18n import t + + +def empty_plot(title: str = "—") -> go.Figure: + fig = go.Figure() + fig.update_layout(template="plotly_white", height=380, title=title, margin=dict(l=40, r=20, t=50, b=40)) + return fig + + +def kpi_html(kpis: dict, lang: str = "en") -> str: + gap = kpis.get("heuristic_gap") + fidelity = kpis.get("template_fidelity") + cards = [ + (t(lang, "kpi_n"), f"{kpis.get('n_problems', 0):.0f}", t(lang, "kpi_n_sub")), + (t(lang, "kpi_feas"), f"{100 * float(kpis.get('structured_feasible') or 0):.0f}%", t(lang, "kpi_feas_sub")), + (t(lang, "kpi_gap"), "—" if gap is None else f"{100 * float(gap):.1f}%", t(lang, "kpi_gap_sub")), + (t(lang, "kpi_fid"), "—" if fidelity is None else f"{100 * float(fidelity):.0f}%", t(lang, "kpi_fid_sub")), + (t(lang, "kpi_eval"), f"{kpis.get('n_methods_evaluated', 0):.0f}/{kpis.get('n_methods_listed', 0):.0f}", t(lang, "kpi_eval_sub")), + ] + blocks = [] + for label, value, sub in cards: + blocks.append( + f"

{label}

" + f"

{value}

{sub}

" + ) + return f"
{''.join(blocks)}
" + + +def method_bars(summary: pd.DataFrame, title: str) -> go.Figure: + if summary is None or summary.empty: + return empty_plot(title) + live = summary.loc[summary["evaluated"] == True] # noqa: E712 + if live.empty: + return empty_plot(title) + fig = go.Figure() + fig.add_bar(name="feasible", x=live["method_id"], y=live["feasible_rate"].fillna(0)) + fig.add_bar(name="parse", x=live["method_id"], y=live["parse_rate"].fillna(0)) + fig.update_layout( + template="plotly_white", + barmode="group", + height=400, + title=title, + yaxis=dict(range=[0, 1], title="rate"), + legend=dict(orientation="h"), + margin=dict(l=40, r=20, t=50, b=80), + ) + return fig + + +def family_bars(family_tbl: pd.DataFrame, title: str) -> go.Figure: + if family_tbl is None or family_tbl.empty: + return empty_plot(title) + fig = go.Figure() + for method_id, group in family_tbl.groupby("method_id"): + fig.add_bar(name=str(method_id), x=group["family"], y=group["feasible_rate"].fillna(0)) + fig.update_layout( + template="plotly_white", + barmode="group", + height=400, + title=title, + yaxis=dict(range=[0, 1], title="feasible rate"), + legend=dict(orientation="h"), + margin=dict(l=40, r=20, t=50, b=40), + ) + return fig + + +def schedule_gantt(solution: dict, title: str) -> go.Figure: + starts = (solution or {}).get("starts") or [] + if not starts: + return empty_plot(title) + fig = go.Figure() + colors = ["#2563eb", "#0f766e", "#7c3aed", "#b45309", "#db2777", "#334155"] + for idx, row in enumerate(starts): + fig.add_bar( + x=[int(row["end"]) - int(row["start"])], + y=[row["machine_id"]], + base=[int(row["start"])], + orientation="h", + marker_color=colors[idx % len(colors)], + name=row["job_id"], + text=row["job_id"], + textposition="inside", + hovertemplate=f"{row['job_id']} {row['start']}-{row['end']}", + ) + fig.update_layout(template="plotly_white", height=360, title=title, barmode="stack", showlegend=False) + return fig + + +def inventory_orders(solution: dict, title: str) -> go.Figure: + orders = (solution or {}).get("orders") or [] + if not orders: + return empty_plot(title) + frame = pd.DataFrame(orders) + fig = go.Figure() + for sku_id, group in frame.groupby("sku_id"): + fig.add_bar(name=str(sku_id), x=group["period"].astype(str), y=group["qty"]) + fig.update_layout(template="plotly_white", barmode="group", height=360, title=title) + return fig + + +def assignment_table_plot(solution: dict, title: str) -> go.Figure: + rows = (solution or {}).get("assignments") or [] + if not rows: + return empty_plot(title) + fig = go.Figure( + data=[ + go.Table( + header=dict(values=["task_id", "agent_id"], fill_color="#e0e7ff"), + cells=dict(values=[[row["task_id"] for row in rows], [row["agent_id"] for row in rows]]), + ) + ] + ) + fig.update_layout(template="plotly_white", height=320, title=title) + return fig + + +def solution_plot(family: str, solution: dict, title: str) -> go.Figure: + if family == Family.SCHEDULING.value: + return schedule_gantt(solution, title) + if family == Family.INVENTORY.value: + return inventory_orders(solution, title) + return assignment_table_plot(solution, title) + + +def format_leaderboard(frame: pd.DataFrame) -> pd.DataFrame: + if frame is None or frame.empty: + return pd.DataFrame() + show = frame.copy() + for col in ("parse_success", "feasible", "constraint_fidelity", "optimality_gap", "objective", "cost_usd"): + if col in show.columns: + show[col] = show[col].apply(lambda value: not_evaluated_cell() if pd.isna(value) else value) + uneval = show["evaluated"] == False # noqa: E712 + if "status" in show.columns: + show.loc[uneval, "status"] = not_evaluated_cell() + return show diff --git a/demo/src/ui.py b/demo/src/ui.py new file mode 100644 index 0000000000000000000000000000000000000000..57f9194090dec0758eb09c4d753d661ebc13c00b --- /dev/null +++ b/demo/src/ui.py @@ -0,0 +1,470 @@ +from __future__ import annotations + +import json +import tempfile +from pathlib import Path +from zipfile import ZipFile + +import gradio as gr +import pandas as pd +import plotly.graph_objects as go + +from src.domain import DEFAULT_SOLVER_SECONDS, ConstraintConfig, PromptVariant +from src.explain import numeric_reasons, status_label +from src.i18n import TEXTS, t +from src.metrics import family_summary, kpi_snapshot, summarize +from src.model_registry import all_methods +from src.pipeline import ( + evaluate_problem, + interactive_problems, + load_problems, + load_results, + load_sample, + problem_by_id, + result_to_downloads, +) +from src.plots import empty_plot, family_bars, format_leaderboard, kpi_html, method_bars, solution_plot +from src.validation import ValidationReport + +ROOT = Path(__file__).resolve().parents[1] +SAMPLE_PREVIEW = ROOT / "examples" / "sample_preview.json" +CSS = """ +.gradio-container {max-width: 1280px !important; margin: 0 auto;} +.dark .gradio-container {color: var(--body-text-color);} +.aria-header h1 {margin-bottom: 0.2rem;} +.aria-header p {opacity: 0.85;} +.kpi-grid {display:grid; grid-template-columns: repeat(auto-fit, minmax(170px, 1fr)); gap: 12px;} +.kpi-card {background: linear-gradient(180deg, #eef2ff, #ffffff); border: 1px solid #c7d2fe; border-radius: 16px; padding: 14px 16px;} +.kpi-label {font-size: 0.8rem; color: #3730a3; margin: 0;} +.kpi-value {font-size: 1.55rem; font-weight: 700; color: #312e81; margin: 4px 0;} +.kpi-sub {margin: 0; font-size: 0.78rem; color: #334155;} +.rtl-mode {direction: rtl; text-align: right;} +""" + + +def _preview_payload() -> dict: + if SAMPLE_PREVIEW.exists(): + return json.loads(SAMPLE_PREVIEW.read_text(encoding="utf-8")) + return {} + + +def _empty_plot() -> go.Figure: + return empty_plot("—") + + +def _variant_choices(lang: str) -> list[str]: + return [t(lang, "template"), t(lang, "json"), t(lang, "missing")] + + +def _parse_variant(value: str) -> PromptVariant: + if value in {PromptVariant.JSON.value, t("en", "json"), t("fa", "json")}: + return PromptVariant.JSON + if value in {PromptVariant.MISSING_BUDGET.value, t("en", "missing"), t("fa", "missing")}: + return PromptVariant.MISSING_BUDGET + return PromptVariant.TEMPLATE + + +def _problem_choices() -> list[str]: + return [item.problem_id for item in interactive_problems()] + + +def apply_language(lang: str): + rtl = lang == "fa" + preview = _preview_payload() + header = ( + f"
" + f"

{t(lang, 'title')}

{t(lang, 'subtitle')}

{t(lang, 'kind')}

" + ) + return ( + gr.update(value=header), + gr.update(value=t(lang, "run_sample")), + gr.update(value=t(lang, "cancel")), + gr.update(value=t(lang, "reset")), + gr.update(value=t(lang, "load_sample")), + gr.update(label=t(lang, "problem")), + gr.update(label=t(lang, "variant"), choices=_variant_choices(lang), value=_variant_choices(lang)[0]), + gr.update(label=t(lang, "time_limit")), + gr.update(value=t(lang, "sample_note")), + gr.update(value=preview.get("kpi_html", "")), + gr.update(open=False, label=t(lang, "advanced")), + gr.update(value=t(lang, "method_body"), rtl=rtl), + gr.update(value=t(lang, "upload_hint")), + gr.update(label=t(lang, "custom_text")), + gr.update(label=t(lang, "custom_schema")), + gr.update(label=t(lang, "direct_json")), + ) + + +def _load_problem_fields(problem_id: str): + problem = problem_by_id(problem_id) + return ( + problem.prompt_en, + problem.prompt_fa, + problem.prompt_json, + json.dumps(problem.schema_payload, indent=2, ensure_ascii=False), + problem.gold_status, + problem.gold_objective, + problem.family.value, + problem.split.value, + problem.difficulty.value, + problem.language, + problem.template_id, + ) + + +def load_sample_ui(): + ids = _problem_choices() + fields = _load_problem_fields(ids[0]) + return (ids[0], *fields) + + +def run_live(lang, problem_id, variant, time_limit, custom_text, schema_text, direct_text): + problem = problem_by_id(problem_id) + schema = None + if schema_text and str(schema_text).strip(): + try: + schema = json.loads(schema_text) + except json.JSONDecodeError as exc: + raise gr.Error(f"schema JSON: {exc}") from exc + direct = None + if direct_text and str(direct_text).strip(): + try: + direct = json.loads(direct_text) + except json.JSONDecodeError as exc: + raise gr.Error(f"direct-answer JSON: {exc}") from exc + result = evaluate_problem( + problem, + lang=lang, + variant=_parse_variant(variant), + config=ConstraintConfig(solver_seconds=float(time_limit)), + custom_text=custom_text or None, + custom_schema=schema, + custom_solution=direct, + ) + if result.get("error"): + raise gr.Error(result["error"]) + validation: ValidationReport | None = result["validation"] + reasons = "\n".join(f"- {line}" for line in numeric_reasons(problem, result["rows"], validation, lang)) + kpis = kpi_snapshot(result["table"]) + status = ( + f"**{t(lang, 'status')}:** {result['status_label']}\n\n" + f"{t(lang, 'live_note')}\n\n" + f"Gold `{problem.gold_status}` / {problem.gold_objective}. Validator " + f"{'ok' if validation is None or validation.ok else 'failed'}." + ) + tmp = Path(tempfile.mkdtemp(prefix="orbench-")) + files = result_to_downloads(result, tmp) + zip_path = tmp / f"{result['run_id']}_tables.zip" + with ZipFile(zip_path, "w") as zipped: + for key, path in files.items(): + zipped.write(path, arcname=Path(path).name) + live_table = format_leaderboard(result["table"]) + summary = result["summary"] + fam = family_summary(result["table"]) + plot = solution_plot(problem.family.value, result.get("solution") or {}, t(lang, "sol_plot")) + method_fig = method_bars(summary, t(lang, "method_plot")) + family_fig = family_bars(fam, t(lang, "family_plot")) + violated = pd.DataFrame( + [{"method_id": row.method_id, "status": row.status, "violated": ", ".join(row.violated), "notes": row.notes} for row in result["rows"]] + ) + facts = pd.DataFrame( + [ + {"field": "family", "value": problem.family.value}, + {"field": "split", "value": problem.split.value}, + {"field": "difficulty", "value": problem.difficulty.value}, + {"field": "template_id", "value": problem.template_id}, + {"field": "gold_status", "value": problem.gold_status}, + {"field": "gold_objective", "value": problem.gold_objective}, + {"field": "cover_or_hard", "value": str(problem.schema_payload.get("cover_required") or "")}, + ] + ) + return ( + kpi_html(kpis, lang), + status, + reasons, + live_table, + summary, + violated, + facts, + plot, + method_fig, + family_fig, + str(zip_path), + files["report"], + result["prompt"], + json.dumps(result["schema"], indent=2, ensure_ascii=False), + ) + + +def filter_catalog(family, split, language, difficulty, evaluated_only): + frame = load_results() + if frame.empty: + return pd.DataFrame(), pd.DataFrame(), _empty_plot(), _empty_plot() + view = frame.copy() + if family and family != "all": + view = view.loc[view["family"] == family] + if split and split != "all": + view = view.loc[view["split"] == split] + if language and language != "all": + view = view.loc[view["language"] == language] + if difficulty and difficulty != "all": + view = view.loc[view["difficulty"] == difficulty] + if evaluated_only: + view = view.loc[view["evaluated"] == True] # noqa: E712 + summary = summarize(view) + fam = family_summary(view) + return format_leaderboard(view), summary, method_bars(summary, "Filtered methods"), family_bars(fam, "Filtered families") + + +def compare_interactive(lang, time_limit): + rows = [] + for problem in interactive_problems(): + result = evaluate_problem(problem, lang=lang, config=ConstraintConfig(solver_seconds=min(6.0, float(time_limit)))) + for row in result["rows"]: + if row.method_id in {"structured-solver", "heuristic", "template-extractor+solver"}: + rows.append(row.model_dump()) + frame = pd.DataFrame(rows) + return format_leaderboard(frame), summarize(frame) + + +def registry_table() -> pd.DataFrame: + return pd.DataFrame( + [ + { + "method_id": item.method_id, + "kind": item.kind.value, + "evaluated": item.evaluated, + "version": item.version, + "notes": item.notes or item.reason_if_skipped, + } + for item in all_methods() + ] + ) + + +def solve_sample_api(): + pack = load_sample() + result = evaluate_problem(pack["problem"], lang="en", config=ConstraintConfig(solver_seconds=6)) + structured = result["table"].loc[result["table"]["method_id"] == "structured-solver"].iloc[0] + return result["status"], float(structured.get("feasible") or 0), float(structured.get("objective") or 0), float(result["seconds"]) + + +def build_demo() -> gr.Blocks: + pack = load_sample() + preview = _preview_payload() + ids = _problem_choices() + recorded = load_results() + preview_kpis = preview.get("kpis") or kpi_snapshot(recorded) if not recorded.empty else { + "n_problems": 100, + "structured_feasible": 0.0, + "heuristic_gap": None, + "template_fidelity": None, + "n_methods_evaluated": 5, + "n_methods_listed": 10, + } + + with gr.Blocks(theme=gr.themes.Soft(primary_hue="indigo", secondary_hue="purple"), css=CSS) as demo: + lang = gr.Radio(["en", "fa"], value="en", label=TEXTS["en"]["language"]) + header = gr.HTML() + with gr.Row(): + run_btn = gr.Button(t("en", "run_sample"), variant="primary") + cancel_btn = gr.Button(t("en", "cancel"), variant="stop") + reset_btn = gr.Button(t("en", "reset")) + load_btn = gr.Button(t("en", "load_sample")) + note = gr.Markdown(t("en", "sample_note")) + kpis = gr.HTML(preview.get("kpi_html") or kpi_html(preview_kpis, "en")) + status = gr.Markdown(t("en", "empty")) + + with gr.Tabs(): + with gr.Tab("Data"): + hint = gr.Markdown(t("en", "upload_hint")) + problem = gr.Dropdown(choices=ids, value=ids[0] if ids else None, label=t("en", "problem")) + with gr.Row(): + prompt_en = gr.Textbox(value=pack["problem"].prompt_en, label="prompt_en", lines=8) + prompt_fa = gr.Textbox(value=pack["problem"].prompt_fa, label="prompt_fa", lines=8) + prompt_json = gr.Code(value=pack["problem"].prompt_json, language="json", label="prompt_json") + custom_text = gr.Textbox(label=t("en", "custom_text"), lines=4) + schema_text = gr.Code( + value=json.dumps(pack["problem"].schema_payload, indent=2, ensure_ascii=False), + language="json", + label=t("en", "custom_schema"), + ) + direct_text = gr.Textbox(label=t("en", "direct_json"), lines=4, placeholder='{"orders":[],"assignments":[],"starts":[]}') + + with gr.Tab("Constraints"): + variant = gr.Radio(choices=_variant_choices("en"), value=_variant_choices("en")[0], label=t("en", "variant")) + with gr.Accordion(t("en", "advanced"), open=False) as advanced: + time_limit = gr.Slider(3, 20, value=DEFAULT_SOLVER_SECONDS, step=1, label=t("en", "time_limit")) + facts = gr.Dataframe( + value=pd.DataFrame( + [ + {"field": "family", "value": pack["problem"].family.value}, + {"field": "gold_status", "value": pack["problem"].gold_status}, + {"field": "gold_objective", "value": pack["problem"].gold_objective}, + ] + ), + label="Instance facts", + ) + meta = gr.Markdown( + f"family `{pack['problem'].family.value}` · split `{pack['problem'].split.value}` · " + f"difficulty `{pack['problem'].difficulty.value}` · template `{pack['problem'].template_id}`" + ) + + with gr.Tab("Results"): + reasons = gr.Markdown() + live_table = gr.Dataframe(label="Per-method cells (not_evaluated is not a score)") + violated = gr.Dataframe(label="Violated constraints / skip reasons") + sol_plot = gr.Plot(value=_empty_plot()) + method_plot = gr.Plot(value=_empty_plot()) + live_summary = gr.Dataframe(label="Evaluated-method summary") + with gr.Row(): + zip_out = gr.File(label="CSV / JSON bundle") + json_out = gr.File(label="JSON report") + + with gr.Tab("Scenario comparison"): + with gr.Row(): + family_f = gr.Dropdown(["all", "inventory", "assignment", "scheduling"], value="all", label="family") + split_f = gr.Dropdown(["all", "development", "test"], value="all", label="split") + lang_f = gr.Dropdown(["all", "en", "fa"], value="all", label="prompt language") + diff_f = gr.Dropdown(["all", "easy", "medium", "hard", "infeasible"], value="all", label="difficulty") + eval_only = gr.Checkbox(value=False, label="hide not_evaluated rows") + filter_btn = gr.Button("Filter recorded catalog") + compare_btn = gr.Button("Re-run 20 interactive problems") + board = gr.Dataframe(label="Recorded leaderboard", value=format_leaderboard(recorded) if not recorded.empty else None) + board_summary = gr.Dataframe(label="Catalog summary") + family_plot = gr.Plot(value=_empty_plot()) + catalog_plot = gr.Plot(value=_empty_plot()) + interactive_tbl = gr.Dataframe(label="Interactive re-run") + interactive_sum = gr.Dataframe(label="Interactive summary") + + with gr.Tab("Method and limits"): + method = gr.Markdown(t("en", "method_body")) + registry = gr.Dataframe(value=registry_table(), label="Versioned method registry") + gr.Markdown( + "Organization: [AriaAICompany](https://huggingface.co/AriaAICompany) · " + "Dataset: [or-bench-problems](https://huggingface.co/datasets/AriaAICompany/or-bench-problems) · " + "Site: [aria-ai.ir](https://aria-ai.ir/)" + ) + + hidden_gold_status = gr.Textbox(visible=False, value=pack["problem"].gold_status) + hidden_gold_obj = gr.Number(visible=False, value=pack["problem"].gold_objective or 0) + hidden_family = gr.Textbox(visible=False, value=pack["problem"].family.value) + hidden_split = gr.Textbox(visible=False, value=pack["problem"].split.value) + hidden_diff = gr.Textbox(visible=False, value=pack["problem"].difficulty.value) + hidden_plang = gr.Textbox(visible=False, value=pack["problem"].language) + hidden_tmpl = gr.Textbox(visible=False, value=pack["problem"].template_id) + + outputs_lang = [ + header, + run_btn, + cancel_btn, + reset_btn, + load_btn, + problem, + variant, + time_limit, + note, + kpis, + advanced, + method, + hint, + custom_text, + schema_text, + direct_text, + ] + lang.change(apply_language, inputs=[lang], outputs=outputs_lang) + demo.load(apply_language, inputs=[lang], outputs=outputs_lang) + + problem.change( + _load_problem_fields, + inputs=[problem], + outputs=[ + prompt_en, + prompt_fa, + prompt_json, + schema_text, + hidden_gold_status, + hidden_gold_obj, + hidden_family, + hidden_split, + hidden_diff, + hidden_plang, + hidden_tmpl, + ], + ) + load_btn.click( + load_sample_ui, + outputs=[ + problem, + prompt_en, + prompt_fa, + prompt_json, + schema_text, + hidden_gold_status, + hidden_gold_obj, + hidden_family, + hidden_split, + hidden_diff, + hidden_plang, + hidden_tmpl, + ], + ) + reset_btn.click( + load_sample_ui, + outputs=[ + problem, + prompt_en, + prompt_fa, + prompt_json, + schema_text, + hidden_gold_status, + hidden_gold_obj, + hidden_family, + hidden_split, + hidden_diff, + hidden_plang, + hidden_tmpl, + ], + ) + + run_event = run_live + event = run_btn.click( + run_live, + inputs=[lang, problem, variant, time_limit, custom_text, schema_text, direct_text], + outputs=[ + kpis, + status, + reasons, + live_table, + live_summary, + violated, + facts, + sol_plot, + method_plot, + family_plot, + zip_out, + json_out, + custom_text, + schema_text, + ], + ) + cancel_btn.click(lambda: None, cancels=[event]) + filter_btn.click( + filter_catalog, + inputs=[family_f, split_f, lang_f, diff_f, eval_only], + outputs=[board, board_summary, catalog_plot, family_plot], + ) + compare_btn.click(compare_interactive, inputs=[lang, time_limit], outputs=[interactive_tbl, interactive_sum]) + + api_status = gr.Textbox(visible=False) + api_feas = gr.Number(visible=False) + api_obj = gr.Number(visible=False) + api_sec = gr.Number(visible=False) + api_btn = gr.Button("solve_sample_api", visible=False) + api_btn.click(solve_sample_api, outputs=[api_status, api_feas, api_obj, api_sec], api_name="solve_sample") + + _ = run_event + _ = meta + + demo.queue(default_concurrency_limit=1) + return demo diff --git a/demo/src/validation.py b/demo/src/validation.py new file mode 100644 index 0000000000000000000000000000000000000000..aa975fda279c8997e631b89ff181cb73e3fb1e72 --- /dev/null +++ b/demo/src/validation.py @@ -0,0 +1,235 @@ +from __future__ import annotations + +from collections import defaultdict + +from src.domain import ( + AssignmentInstance, + Family, + InventoryInstance, + ScheduleInstance, + Solution, + ValidationIssue, + ValidationReport, + parse_instance, +) + + +def _issue(code: str, message: str, entity_id: str | None = None, passed: bool = False) -> ValidationIssue: + return ValidationIssue(code=code, message=message, entity_id=entity_id, passed=passed) + + +def validate_schema(family: Family | str, payload: dict) -> ValidationReport: + issues: list[ValidationIssue] = [] + checked = ["schema", "ids", "values"] + try: + instance = parse_instance(family, payload) + except Exception as exc: + return ValidationReport(ok=False, issues=[_issue("schema", f"schema rejected: {exc}")], checked=checked) + + if isinstance(instance, InventoryInstance): + ids = [sku.sku_id for sku in instance.skus] + if len(ids) != len(set(ids)): + issues.append(_issue("ids", "duplicate SKU ids")) + if not instance.skus: + issues.append(_issue("schema", "inventory needs at least one SKU")) + for sku in instance.skus: + if len(sku.demand) != instance.periods: + issues.append(_issue("values", f"{sku.sku_id} demand length must equal periods", sku.sku_id)) + if any(value < 0 for value in sku.demand): + issues.append(_issue("values", f"{sku.sku_id} demand must be non-negative", sku.sku_id)) + elif isinstance(instance, AssignmentInstance): + if not instance.tasks or not instance.agents: + issues.append(_issue("schema", "assignment needs tasks and agents")) + task_ids = [task.task_id for task in instance.tasks] + agent_ids = [agent.agent_id for agent in instance.agents] + if len(task_ids) != len(set(task_ids)) or len(agent_ids) != len(set(agent_ids)): + issues.append(_issue("ids", "duplicate task or agent ids")) + known = {(task.task_id, agent.agent_id) for task in instance.tasks for agent in instance.agents} + for row in instance.costs: + if (row.task_id, row.agent_id) not in known: + issues.append(_issue("references", f"cost for unknown pair {row.task_id}/{row.agent_id}")) + else: + job_ids = [job.job_id for job in instance.jobs] + if len(job_ids) != len(set(job_ids)): + issues.append(_issue("ids", "duplicate job ids")) + if not instance.machines or not instance.jobs: + issues.append(_issue("schema", "scheduling needs jobs and machines")) + seen = set() + for edge in instance.precedences: + if edge.before not in job_ids or edge.after not in job_ids: + issues.append(_issue("references", f"precedence {edge.before}->{edge.after} is unknown")) + if edge.before == edge.after: + issues.append(_issue("values", f"self precedence on {edge.before}", edge.before)) + pair = (edge.before, edge.after) + if pair in seen: + continue + seen.add(pair) + if _has_cycle(instance.precedences): + issues.append(_issue("values", "precedence graph has a cycle")) + return ValidationReport(ok=not issues, issues=issues, checked=checked) + + +def _has_cycle(edges) -> bool: + graph: dict[str, list[str]] = defaultdict(list) + nodes: set[str] = set() + for edge in edges: + graph[edge.before].append(edge.after) + nodes.add(edge.before) + nodes.add(edge.after) + state: dict[str, int] = {} + + def visit(node: str) -> bool: + state[node] = 1 + for nxt in graph.get(node, []): + if state.get(nxt) == 1: + return True + if state.get(nxt, 0) == 0 and visit(nxt): + return True + state[node] = 2 + return False + + return any(state.get(node, 0) == 0 and visit(node) for node in nodes) + + +def validate_solution(family: Family | str, payload: dict, solution: Solution | dict) -> ValidationReport: + family = Family(family) + schema_report = validate_schema(family, payload) + if not schema_report.ok: + return schema_report + instance = parse_instance(family, payload) + if not isinstance(solution, Solution): + solution = Solution.model_validate(solution) + if family == Family.INVENTORY: + return _validate_inventory(instance, solution) + if family == Family.ASSIGNMENT: + return _validate_assignment(instance, solution) + return _validate_schedule(instance, solution) + + +def _validate_inventory(instance: InventoryInstance, solution: Solution) -> ValidationReport: + issues: list[ValidationIssue] = [] + checked = ["pack", "budget", "balance", "capacity", "cover", "objective"] + qty = {(row.sku_id, int(row.period)): int(row.qty) for row in solution.orders} + spend = 0 + hold_cost = 0 + short_cost = 0 + stock = {sku.sku_id: sku.initial_stock for sku in instance.skus} + for t in range(1, instance.periods + 1): + ending = 0 + for sku in instance.skus: + order = int(qty.get((sku.sku_id, t), 0)) + if order < 0: + issues.append(_issue("values", f"negative order {sku.sku_id}@{t}", sku.sku_id)) + if sku.pack_size and order % sku.pack_size != 0: + issues.append(_issue("pack", f"{sku.sku_id}@{t} qty {order} is not a multiple of pack {sku.pack_size}", sku.sku_id)) + spend += order * sku.unit_cost + demand = int(sku.demand[t - 1]) + available = stock[sku.sku_id] + order + sold = min(available, demand) + short = demand - sold + stock[sku.sku_id] = available - sold + if stock[sku.sku_id] < 0: + issues.append(_issue("balance", f"negative inventory {sku.sku_id}@{t}", sku.sku_id)) + if instance.cover_required and short: + issues.append(_issue("cover", f"{sku.sku_id}@{t} shortage {short} while cover is required", sku.sku_id)) + ending += stock[sku.sku_id] + hold_cost += stock[sku.sku_id] * sku.holding_cost + short_cost += short * sku.shortage_cost + if ending > instance.warehouse_capacity: + issues.append(_issue("capacity", f"period {t} inventory {ending} exceeds capacity {instance.warehouse_capacity}")) + if spend > instance.budget: + issues.append(_issue("budget", f"purchase {spend} exceeds budget {instance.budget}")) + objective = float(spend + hold_cost + short_cost) + return ValidationReport(ok=not issues, issues=issues, checked=checked, recomputed_objective=objective) + + +def _validate_assignment(instance: AssignmentInstance, solution: Solution) -> ValidationReport: + issues: list[ValidationIssue] = [] + checked = ["unique", "eligible", "capacity", "required", "objective"] + seen_tasks: set[str] = set() + load: dict[str, int] = defaultdict(int) + cost_map = instance.cost_map() + agents = {agent.agent_id: agent for agent in instance.agents} + tasks = {task.task_id: task for task in instance.tasks} + spend = 0 + for row in solution.assignments: + if row.task_id in seen_tasks: + issues.append(_issue("unique", f"task {row.task_id} assigned more than once", row.task_id)) + seen_tasks.add(row.task_id) + task = tasks.get(row.task_id) + agent = agents.get(row.agent_id) + if task is None or agent is None: + issues.append(_issue("references", f"unknown pair {row.task_id}/{row.agent_id}", row.task_id)) + continue + if not instance.eligible(task, agent): + issues.append(_issue("eligible", f"{row.task_id} is not eligible for {row.agent_id}", row.task_id)) + if (row.task_id, row.agent_id) not in cost_map: + issues.append(_issue("references", f"no cost for {row.task_id}/{row.agent_id}", row.task_id)) + else: + spend += cost_map[(row.task_id, row.agent_id)] + load[row.agent_id] += task.size + for agent in instance.agents: + if load[agent.agent_id] > agent.capacity: + issues.append(_issue("capacity", f"{agent.agent_id} load {load[agent.agent_id]} exceeds {agent.capacity}", agent.agent_id)) + leftover = set(solution.unassigned) + for task in instance.tasks: + assigned = task.task_id in seen_tasks + if task.required and not assigned: + issues.append(_issue("required", f"required task {task.task_id} is unassigned", task.task_id)) + if not assigned: + leftover.add(task.task_id) + spend += task.penalty + if assigned and task.task_id in leftover: + leftover.discard(task.task_id) + return ValidationReport(ok=not issues, issues=issues, checked=checked, recomputed_objective=float(spend)) + + +def _validate_schedule(instance: ScheduleInstance, solution: Solution) -> ValidationReport: + issues: list[ValidationIssue] = [] + checked = ["unique", "eligible", "release", "overlap", "precedence", "hard_due", "duration", "objective"] + jobs = {job.job_id: job for job in instance.jobs} + seen: set[str] = set() + by_machine: dict[str, list[tuple[int, int, str]]] = defaultdict(list) + ends: dict[str, int] = {} + starts: dict[str, int] = {} + tardy = 0 + for row in solution.starts: + if row.job_id in seen: + issues.append(_issue("unique", f"job {row.job_id} starts more than once", row.job_id)) + seen.add(row.job_id) + job = jobs.get(row.job_id) + if job is None: + issues.append(_issue("references", f"unknown job {row.job_id}", row.job_id)) + continue + if row.machine_id not in instance.machines: + issues.append(_issue("references", f"unknown machine {row.machine_id}", row.job_id)) + if job.machine_eligible and row.machine_id not in set(job.machine_eligible): + issues.append(_issue("eligible", f"{row.job_id} cannot use {row.machine_id}", row.job_id)) + if row.start < job.release: + issues.append(_issue("release", f"{row.job_id} starts at {row.start} before release {job.release}", row.job_id)) + if row.end - row.start != job.duration: + issues.append(_issue("duration", f"{row.job_id} duration {row.end - row.start} != {job.duration}", row.job_id)) + if job.hard_due and row.end > job.due: + issues.append(_issue("hard_due", f"{row.job_id} ends at {row.end} after hard due {job.due}", row.job_id)) + by_machine[row.machine_id].append((row.start, row.end, row.job_id)) + ends[row.job_id] = row.end + starts[row.job_id] = row.start + tardy += job.weight * max(0, row.end - job.due) + for job in instance.jobs: + if job.job_id not in seen: + issues.append(_issue("cover", f"job {job.job_id} has no start", job.job_id)) + for machine, blocks in by_machine.items(): + ordered = sorted(blocks) + for prev, cur in zip(ordered, ordered[1:]): + if prev[1] > cur[0]: + issues.append(_issue("overlap", f"{machine} overlap {prev[2]} and {cur[2]}", machine)) + for edge in instance.precedences: + if edge.before in ends and edge.after in starts and ends[edge.before] > starts[edge.after]: + issues.append(_issue("precedence", f"{edge.before} must finish before {edge.after}", edge.after)) + return ValidationReport(ok=not issues, issues=issues, checked=checked, recomputed_objective=float(tardy)) + + +def format_input_error(report: ValidationReport) -> str: + if report.ok: + return "" + return " | ".join(f"{item.code}: {item.message}" for item in report.issues[:8]) diff --git a/demo/tests/__pycache__/conftest.cpython-312-pytest-8.3.4.pyc b/demo/tests/__pycache__/conftest.cpython-312-pytest-8.3.4.pyc new file mode 100644 index 0000000000000000000000000000000000000000..1e8e551f92655f80d5e8b9be9d3ab9d6af87af0a Binary files /dev/null and b/demo/tests/__pycache__/conftest.cpython-312-pytest-8.3.4.pyc differ diff --git a/demo/tests/__pycache__/test_pipeline.cpython-312-pytest-8.3.4.pyc b/demo/tests/__pycache__/test_pipeline.cpython-312-pytest-8.3.4.pyc new file mode 100644 index 0000000000000000000000000000000000000000..904eb235f80d33216ff482ba55e3126f9a149415 Binary files /dev/null and b/demo/tests/__pycache__/test_pipeline.cpython-312-pytest-8.3.4.pyc differ diff --git a/demo/tests/conftest.py b/demo/tests/conftest.py new file mode 100644 index 0000000000000000000000000000000000000000..2a855d9fdb8debae0b082088580a4c41e499e33c --- /dev/null +++ b/demo/tests/conftest.py @@ -0,0 +1,6 @@ +import sys +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +if str(ROOT) not in sys.path: + sys.path.insert(0, str(ROOT)) diff --git a/demo/tests/test_pipeline.py b/demo/tests/test_pipeline.py new file mode 100644 index 0000000000000000000000000000000000000000..ef870e18a332a4d84c9a32921834702a901ca6c4 --- /dev/null +++ b/demo/tests/test_pipeline.py @@ -0,0 +1,190 @@ +from __future__ import annotations + +import json + +import pandas as pd +import pytest + +from src.baseline import naive_direct, run_heuristic +from src.domain import DEFAULT_SEED, N_INTERACTIVE, N_PROBLEMS, ConstraintConfig, Family, SolveStatus +from src.extractor import constraint_fidelity, extract_json, extract_template +from pathlib import Path + +from src.domain import EvalRow +from src.generator import INTERACTIVE_IDS, generate_catalog, load_catalog +from src.metrics import summarize +from src.model_registry import UNEVALUATED_MODELS, evaluated_ids +from src.optimizer import solve_instance +from src.pipeline import evaluate_catalog, evaluate_problem +from src.validation import validate_schema, validate_solution + +ROOT = Path(__file__).resolve().parents[1] + + +@pytest.fixture(scope="session") +def catalog(): + path = ROOT / "examples" / "problems.jsonl" + return load_catalog(path if path.exists() else None) + + +@pytest.fixture(scope="session") +def recorded(catalog): + path = ROOT / "examples" / "results.jsonl" + if path.exists(): + return [EvalRow.model_validate_json(line) for line in path.read_text(encoding="utf-8").splitlines() if line.strip()] + return evaluate_catalog(catalog, config=ConstraintConfig(solver_seconds=5)) + + +def test_catalog_size_and_ids(catalog): + assert len(catalog) == N_PROBLEMS + ids = [item.problem_id for item in catalog] + assert len(ids) == len(set(ids)) + assert sum(item.family == Family.INVENTORY for item in catalog) == 34 + assert sum(item.family == Family.ASSIGNMENT for item in catalog) == 33 + assert sum(item.family == Family.SCHEDULING for item in catalog) == 33 + assert sum(item.interactive for item in catalog) == N_INTERACTIVE + assert set(INTERACTIVE_IDS).issubset(set(ids)) + + +def test_split_and_template_separation(catalog): + dev = [item for item in catalog if item.split.value == "development"] + test = [item for item in catalog if item.split.value == "test"] + assert len(dev) == 60 + assert len(test) == 40 + dev_templates = {(item.family.value, item.template_id) for item in dev} + test_templates = {(item.family.value, item.template_id) for item in test} + assert not (dev_templates & test_templates) + hashes = [item.structural_key for item in catalog] + assert len(hashes) == len(set(hashes)) + + +def test_no_duplicate_payloads(catalog): + payloads = [json.dumps(item.schema_payload, sort_keys=True) for item in catalog] + assert len(payloads) == len(set(payloads)) + + +def test_only_designed_infeasible_are_infeasible(catalog): + unexpected = [item.problem_id for item in catalog if item.gold_status == "infeasible" and item.difficulty.value != "infeasible"] + assert unexpected == [] + assert sum(item.difficulty.value == "infeasible" for item in catalog) == 8 + assert sum(item.gold_status == "infeasible" for item in catalog) == 8 + + +def test_gold_solutions_validate(catalog): + feasible_rows = [item for item in catalog if item.gold_status in {"optimal", "feasible"}] + assert feasible_rows + for item in feasible_rows: + report = validate_solution(item.family, item.schema_payload, item.gold_solution) + assert report.ok, (item.problem_id, report.issues) + if item.gold_objective is not None and report.recomputed_objective is not None: + assert abs(report.recomputed_objective - item.gold_objective) <= 1e-6 or item.family == Family.SCHEDULING + + +def test_bad_schema_is_rejected(catalog): + problem = catalog[0] + payload = dict(problem.schema_payload) + if problem.family == Family.INVENTORY: + payload["skus"] = [] + elif problem.family == Family.ASSIGNMENT: + payload["tasks"] = [] + else: + payload["jobs"] = [] + report = validate_schema(problem.family, payload) + assert not report.ok + + +def test_validator_catches_violations(catalog): + inv = next(item for item in catalog if item.family == Family.INVENTORY and item.gold_status == "optimal") + bad = json.loads(json.dumps(inv.gold_solution)) + if bad.get("orders"): + bad["orders"][0]["qty"] = int(bad["orders"][0]["qty"]) + 1 + report = validate_solution(inv.family, inv.schema_payload, bad) + assert (not report.ok) or bad["orders"][0]["qty"] % inv.schema_payload["skus"][0]["pack_size"] == 0 + + asn = next(item for item in catalog if item.family == Family.ASSIGNMENT and item.gold_solution.get("assignments")) + clash = json.loads(json.dumps(asn.gold_solution)) + first = clash["assignments"][0] + clash["assignments"].append(dict(first)) + clash["assignments"][-1]["agent_id"] = asn.schema_payload["agents"][-1]["agent_id"] + report = validate_solution(asn.family, asn.schema_payload, clash) + assert not report.ok + assert "unique" in report.failed_codes() + + sch = next(item for item in catalog if item.family == Family.SCHEDULING and item.gold_solution.get("starts")) + overlap = json.loads(json.dumps(sch.gold_solution)) + if len(overlap["starts"]) >= 2: + overlap["starts"][0]["machine_id"] = overlap["starts"][1]["machine_id"] + overlap["starts"][0]["start"] = overlap["starts"][1]["start"] + overlap["starts"][0]["end"] = overlap["starts"][1]["end"] + report = validate_solution(sch.family, sch.schema_payload, overlap) + assert not report.ok + assert any(code in {"overlap", "duration", "unique"} for code in report.failed_codes()) + + +def test_cycle_is_rejected(catalog): + sch = next(item for item in catalog if item.family == Family.SCHEDULING) + payload = json.loads(json.dumps(sch.schema_payload)) + if len(payload["jobs"]) >= 2: + a, b = payload["jobs"][0]["job_id"], payload["jobs"][1]["job_id"] + payload["precedences"] = [{"before": a, "after": b}, {"before": b, "after": a}] + report = validate_schema(Family.SCHEDULING, payload) + assert not report.ok + + +def test_heuristic_is_never_labeled_optimal(catalog): + problem = next(item for item in catalog if item.gold_status == "optimal") + outcome = run_heuristic(problem.family, problem.schema_payload) + assert outcome.solution.status != SolveStatus.OPTIMAL + + +def test_json_extractor_recovers_gold(catalog): + problem = next(item for item in catalog if item.template_id.startswith("D-")) + extracted = extract_json(problem.prompt_en) or extract_json(problem.prompt_json) + assert extracted is not None + assert constraint_fidelity(problem.family, problem.schema_payload, extracted) == 1.0 + + +def test_template_extractor_on_development_inventory(catalog): + problem = next(item for item in catalog if item.family == Family.INVENTORY and item.template_id.startswith("D-")) + extracted = extract_template(problem.prompt_en, problem.family) + assert extracted is not None + assert constraint_fidelity(problem.family, problem.schema_payload, extracted) >= 0.9 + + +def test_unevaluated_models_are_not_zero(recorded): + frame = pd.DataFrame([row.model_dump() for row in recorded]) + skipped = frame.loc[frame["method_id"].isin([item.method_id for item in UNEVALUATED_MODELS])] + assert not skipped.empty + assert skipped["evaluated"].eq(False).all() + assert skipped["status"].eq("not_evaluated").all() + assert skipped["feasible"].isna().all() + assert skipped["optimality_gap"].isna().all() + summary = summarize(recorded) + qwen = summary.loc[summary["method_id"] == "Qwen/Qwen3-4B-Instruct-2507"].iloc[0] + assert qwen["evaluated"] == False # noqa: E712 + assert qwen["feasible_rate"] == "not_evaluated" + assert qwen["mean_gap"] == "not_evaluated" + + +def test_evaluate_problem_has_all_local_methods(catalog): + problem = next(item for item in catalog if item.interactive) + result = evaluate_problem(problem, lang="en", config=ConstraintConfig(solver_seconds=5)) + ids = {row.method_id for row in result["rows"]} + assert set(evaluated_ids()).issubset(ids) + assert "Qwen/Qwen3.8-27B" in ids + structured = next(row for row in result["rows"] if row.method_id == "structured-solver") + assert structured.status in {"optimal", "feasible", "infeasible", "timeout"} + + +def test_naive_direct_is_often_invalid(catalog): + problem = next(item for item in catalog if item.family == Family.ASSIGNMENT and item.gold_status == "optimal") + naive = naive_direct(problem.family, problem.schema_payload) + report = validate_solution(problem.family, problem.schema_payload, naive) + assert report.ok is False or report.recomputed_objective is not None + + +def test_solver_agrees_with_gold_on_sample(catalog): + problem = next(item for item in catalog if item.gold_status == "optimal" and item.family == Family.ASSIGNMENT) + outcome = solve_instance(problem.family, problem.schema_payload, seconds=5) + assert outcome.solution.status == SolveStatus.OPTIMAL + assert outcome.solution.objective == pytest.approx(problem.gold_objective) diff --git a/showcase/README.md b/showcase/README.md new file mode 100644 index 0000000000000000000000000000000000000000..e8e9f964684af176d0efc9509e13ec25fa4270f7 --- /dev/null +++ b/showcase/README.md @@ -0,0 +1,19 @@ +--- +title: ORBench +emoji: 🧪 +colorFrom: indigo +colorTo: purple +sdk: static +pinned: true +short_description: Aria AI OR solver and agent benchmark card +license: apache-2.0 +tags: + - model-benchmarking + - operations-research + - structured-generation + - evaluation +datasets: + - AriaAICompany/or-bench-problems +--- + +Static project page for ORBench on the Aria AI organization. diff --git a/showcase/index.html b/showcase/index.html new file mode 100644 index 0000000000000000000000000000000000000000..77fd98a84a6808de619bb8655f7ae7ebdd8b2520 --- /dev/null +++ b/showcase/index.html @@ -0,0 +1,64 @@ + + + + + + ORBench — Aria AI + + + +
+

Aria AI · Project 25 / 25

+

ORBench — Solver and Agent Benchmark

+

+ Compare structured CP-SAT, fixed heuristics, and text-to-schema agents on + 100 small inventory, assignment, and scheduling tasks. The numeric + validator is the judge. Unevaluated models stay not_evaluated. +

+
+ Open live demo + Dataset + Organization + Project 22 Dock +
+
+
+
+
100 tasksInventory, assignment, scheduling
+
60 / 40Development / test, 20 interactive
+
ValidatorFeasibility and gap, not an LLM judge
+
CPUOR-Tools · no paid API
+
+

+ Organization Gradio hosting needs Team/Enterprise. This page is the AriaAICompany project card; + the iframe is the live benchmark on the personal PRO account when org compute is unavailable. +

+
+

اوربنچ

+

روش‌های ساخت تصمیم را روی مسئله‌های کوچک موجودی، تخصیص و زمان‌بندی مقایسه می‌کند. داور validator عددی است. خانه مدل اجرا‌نشده «ارزیابی نشده» است، نه صفر.

+
+ +
+ + +