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UFLP,UFLP,"Someone at planning has to balance the budget and convenience: decide which neighborhood libraries to open and make sure every regular reader is linked to one of the opened branches. For any setup, the city’s outlay equals the sum of the opening fees for the selected branches plus the travel cost for each reader to their single assigned branch; the setups with lower combined totals are preferable. Readers can only go to branches that are actually opened, no one is left unassigned, and libraries can serve any number of people. The detailed data are shown below.
There are 7 librarys and 14 readers in this instance.
**Librarys**
| library_id | opening_fee |
|---|---|
| F1 | 1956 |
| F2 | 1996 |
| F3 | 1058 |
| F4 | 1035 |
| F5 | 1123 |
| F6 | 1444 |
| F7 | 1690 |
**Readers**
| reader_id |
|---|
| A |
| B |
| C |
| D |
| E |
| F |
| G |
| H |
| I |
| J |
| K |
| L |
| M |
| N |
**Travel Cost**
| library_id | reader_id | travel_cost |
|---|---|---|
| F1 | A | 814 |
| F1 | B | 370 |
| F1 | C | 913 |
| F1 | D | 485 |
| F1 | E | 352 |
| F1 | F | 509 |
| F1 | G | 62 |
| F1 | H | 353 |
| F1 | I | 527 |
| F1 | J | 148 |
| F1 | K | 295 |
| F1 | L | 202 |
| F1 | M | 461 |
| F1 | N | 865 |
| F2 | A | 106 |
| F2 | B | 678 |
| F2 | C | 312 |
| F2 | D | 561 |
| F2 | E | 872 |
| F2 | F | 39 |
| F2 | G | 296 |
| F2 | H | 478 |
| F2 | I | 273 |
| F2 | J | 690 |
| F2 | K | 181 |
| F2 | L | 959 |
| F2 | M | 491 |
| F2 | N | 799 |
| F3 | A | 406 |
| F3 | B | 116 |
| F3 | C | 933 |
| F3 | D | 44 |
| F3 | E | 219 |
| F3 | F | 349 |
| F3 | G | 707 |
| F3 | H | 544 |
| F3 | I | 184 |
| F3 | J | 298 |
| F3 | K | 595 |
| F3 | L | 923 |
| F3 | M | 873 |
| F3 | N | 273 |
| F4 | A | 65 |
| F4 | B | 853 |
| F4 | C | 973 |
| F4 | D | 314 |
| F4 | E | 129 |
| F4 | F | 97 |
| F4 | G | 100 |
| F4 | H | 921 |
| F4 | I | 655 |
| F4 | J | 745 |
| F4 | K | 594 |
| F4 | L | 387 |
| F4 | M | 805 |
| F4 | N | 115 |
| F5 | A | 980 |
| F5 | B | 534 |
| F5 | C | 410 |
| F5 | D | 332 |
| F5 | E | 868 |
| F5 | F | 841 |
| F5 | G | 238 |
| F5 | H | 769 |
| F5 | I | 919 |
| F5 | J | 603 |
| F5 | K | 964 |
| F5 | L | 818 |
| F5 | M | 804 |
| F5 | N | 906 |
| F6 | A | 650 |
| F6 | B | 925 |
| F6 | C | 443 |
| F6 | D | 55 |
| F6 | E | 166 |
| F6 | F | 372 |
| F6 | G | 152 |
| F6 | H | 527 |
| F6 | I | 614 |
| F6 | J | 478 |
| F6 | K | 358 |
| F6 | L | 792 |
| F6 | M | 879 |
| F6 | N | 235 |
| F7 | A | 96 |
| F7 | B | 467 |
| F7 | C | 692 |
| F7 | D | 676 |
| F7 | E | 205 |
| F7 | F | 315 |
| F7 | G | 656 |
| F7 | H | 635 |
| F7 | I | 978 |
| F7 | J | 598 |
| F7 | K | 272 |
| F7 | L | 227 |
| F7 | M | 522 |
| F7 | N | 494 |
If you want to send back a candidate setup, just use this simple JSON layout so I can read it reliably.
{
""solution"": {
""selected"": [<library_to_open>, <library_to_open>, ...],
""assignments"": [<chosen_open_library>, <chosen_open_library>, ...]
}
}
Here, ""selected"" is the list of library locations you plan to open, and ""assignments"" is a list giving, for each reader in the input order, which opened library they would go to. Think of it like filling out a short form: pick the branches you open, then for every reader say which branch they use.
This JSON is only a sketch of the expected shape — not the final answer. Please make sure to use the exact identifiers from the instance input, with no renaming and no extra labels:
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”"".","{'opening_costs': [1956, 1996, 1058, 1035, 1123, 1444, 1690], 'connection_costs': [[814, 370, 913, 485, 352, 509, 62, 353, 527, 148, 295, 202, 461, 865], [106, 678, 312, 561, 872, 39, 296, 478, 273, 690, 181, 959, 491, 799], [406, 116, 933, 44, 219, 349, 707, 544, 184, 298, 595, 923, 873, 273], [65, 853, 973, 314, 129, 97, 100, 921, 655, 745, 594, 387, 805, 115], [980, 534, 410, 332, 868, 841, 238, 769, 919, 603, 964, 818, 804, 906], [650, 925, 443, 55, 166, 372, 152, 527, 614, 478, 358, 792, 879, 235], [96, 467, 692, 676, 205, 315, 656, 635, 978, 598, 272, 227, 522, 494]], 'objective': 6504.0}","{'open_facilities': [2, 3], 'assignments': [3, 2, 2, 2, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3]}",6504.0,"{'problem_type': 'UFLP', 'num_facilities': 7, 'num_customers': 14, 'facilities': [{'id': 'F1', 'opening_cost': 1956}, {'id': 'F2', 'opening_cost': 1996}, {'id': 'F3', 'opening_cost': 1058}, {'id': 'F4', 'opening_cost': 1035}, {'id': 'F5', 'opening_cost': 1123}, {'id': 'F6', 'opening_cost': 1444}, {'id': 'F7', 'opening_cost': 1690}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}, {'id': 'L'}, {'id': 'M'}, {'id': 'N'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 814}, {'facility': 'F1', 'customer': 'B', 'cost': 370}, {'facility': 'F1', 'customer': 'C', 'cost': 913}, {'facility': 'F1', 'customer': 'D', 'cost': 485}, {'facility': 'F1', 'customer': 'E', 'cost': 352}, {'facility': 'F1', 'customer': 'F', 'cost': 509}, {'facility': 'F1', 'customer': 'G', 'cost': 62}, {'facility': 'F1', 'customer': 'H', 'cost': 353}, {'facility': 'F1', 'customer': 'I', 'cost': 527}, {'facility': 'F1', 'customer': 'J', 'cost': 148}, {'facility': 'F1', 'customer': 'K', 'cost': 295}, {'facility': 'F1', 'customer': 'L', 'cost': 202}, {'facility': 'F1', 'customer': 'M', 'cost': 461}, {'facility': 'F1', 'customer': 'N', 'cost': 865}, {'facility': 'F2', 'customer': 'A', 'cost': 106}, {'facility': 'F2', 'customer': 'B', 'cost': 678}, {'facility': 'F2', 'customer': 'C', 'cost': 312}, {'facility': 'F2', 'customer': 'D', 'cost': 561}, {'facility': 'F2', 'customer': 'E', 'cost': 872}, {'facility': 'F2', 'customer': 'F', 'cost': 39}, {'facility': 'F2', 'customer': 'G', 'cost': 296}, {'facility': 'F2', 'customer': 'H', 'cost': 478}, {'facility': 'F2', 'customer': 'I', 'cost': 273}, {'facility': 'F2', 'customer': 'J', 'cost': 690}, {'facility': 'F2', 'customer': 'K', 'cost': 181}, {'facility': 'F2', 'customer': 'L', 'cost': 959}, {'facility': 'F2', 'customer': 'M', 'cost': 491}, {'facility': 'F2', 'customer': 'N', 'cost': 799}, {'facility': 'F3', 'customer': 'A', 'cost': 406}, {'facility': 'F3', 'customer': 'B', 'cost': 116}, {'facility': 'F3', 'customer': 'C', 'cost': 933}, {'facility': 'F3', 'customer': 'D', 'cost': 44}, {'facility': 'F3', 'customer': 'E', 'cost': 219}, {'facility': 'F3', 'customer': 'F', 'cost': 349}, {'facility': 'F3', 'customer': 'G', 'cost': 707}, {'facility': 'F3', 'customer': 'H', 'cost': 544}, {'facility': 'F3', 'customer': 'I', 'cost': 184}, {'facility': 'F3', 'customer': 'J', 'cost': 298}, {'facility': 'F3', 'customer': 'K', 'cost': 595}, {'facility': 'F3', 'customer': 'L', 'cost': 923}, {'facility': 'F3', 'customer': 'M', 'cost': 873}, {'facility': 'F3', 'customer': 'N', 'cost': 273}, {'facility': 'F4', 'customer': 'A', 'cost': 65}, {'facility': 'F4', 'customer': 'B', 'cost': 853}, {'facility': 'F4', 'customer': 'C', 'cost': 973}, {'facility': 'F4', 'customer': 'D', 'cost': 314}, {'facility': 'F4', 'customer': 'E', 'cost': 129}, {'facility': 'F4', 'customer': 'F', 'cost': 97}, {'facility': 'F4', 'customer': 'G', 'cost': 100}, {'facility': 'F4', 'customer': 'H', 'cost': 921}, {'facility': 'F4', 'customer': 'I', 'cost': 655}, {'facility': 'F4', 'customer': 'J', 'cost': 745}, {'facility': 'F4', 'customer': 'K', 'cost': 594}, {'facility': 'F4', 'customer': 'L', 'cost': 387}, {'facility': 'F4', 'customer': 'M', 'cost': 805}, {'facility': 'F4', 'customer': 'N', 'cost': 115}, {'facility': 'F5', 'customer': 'A', 'cost': 980}, {'facility': 'F5', 'customer': 'B', 'cost': 534}, {'facility': 'F5', 'customer': 'C', 'cost': 410}, {'facility': 'F5', 'customer': 'D', 'cost': 332}, {'facility': 'F5', 'customer': 'E', 'cost': 868}, {'facility': 'F5', 'customer': 'F', 'cost': 841}, {'facility': 'F5', 'customer': 'G', 'cost': 238}, {'facility': 'F5', 'customer': 'H', 'cost': 769}, {'facility': 'F5', 'customer': 'I', 'cost': 919}, {'facility': 'F5', 'customer': 'J', 'cost': 603}, {'facility': 'F5', 'customer': 'K', 'cost': 964}, {'facility': 'F5', 'customer': 'L', 'cost': 818}, {'facility': 'F5', 'customer': 'M', 'cost': 804}, {'facility': 'F5', 'customer': 'N', 'cost': 906}, {'facility': 'F6', 'customer': 'A', 'cost': 650}, {'facility': 'F6', 'customer': 'B', 'cost': 925}, {'facility': 'F6', 'customer': 'C', 'cost': 443}, {'facility': 'F6', 'customer': 'D', 'cost': 55}, {'facility': 'F6', 'customer': 'E', 'cost': 166}, {'facility': 'F6', 'customer': 'F', 'cost': 372}, {'facility': 'F6', 'customer': 'G', 'cost': 152}, {'facility': 'F6', 'customer': 'H', 'cost': 527}, {'facility': 'F6', 'customer': 'I', 'cost': 614}, {'facility': 'F6', 'customer': 'J', 'cost': 478}, {'facility': 'F6', 'customer': 'K', 'cost': 358}, {'facility': 'F6', 'customer': 'L', 'cost': 792}, {'facility': 'F6', 'customer': 'M', 'cost': 879}, {'facility': 'F6', 'customer': 'N', 'cost': 235}, {'facility': 'F7', 'customer': 'A', 'cost': 96}, {'facility': 'F7', 'customer': 'B', 'cost': 467}, {'facility': 'F7', 'customer': 'C', 'cost': 692}, {'facility': 'F7', 'customer': 'D', 'cost': 676}, {'facility': 'F7', 'customer': 'E', 'cost': 205}, {'facility': 'F7', 'customer': 'F', 'cost': 315}, {'facility': 'F7', 'customer': 'G', 'cost': 656}, {'facility': 'F7', 'customer': 'H', 'cost': 635}, {'facility': 'F7', 'customer': 'I', 'cost': 978}, {'facility': 'F7', 'customer': 'J', 'cost': 598}, {'facility': 'F7', 'customer': 'K', 'cost': 272}, {'facility': 'F7', 'customer': 'L', 'cost': 227}, {'facility': 'F7', 'customer': 'M', 'cost': 522}, {'facility': 'F7', 'customer': 'N', 'cost': 494}], 'objective': 6504.0}","{'selected': ['F3', 'F4'], 'assignments': ['F4', 'F3', 'F3', 'F3', 'F4', 'F4', 'F4', 'F3', 'F3', 'F3', 'F4', 'F4', 'F4', 'F4']}",1,markdown_table,names
UFLP,UFLP,"At the festival the logistical brief was: decide which kitchens to switch on and which switched-on kitchen will take care of each order. Each kitchen has an activation charge, and assigning an order to a kitchen brings a delivery-distance cost; the overall cost of any choice equals the sum of the activation charges for the kitchens used plus the delivery distances for every order. All orders must be assigned to one active kitchen only, and active kitchens can serve any number of orders, so the aim is to end up with the combination that produces the smallest total cost. The specific kitchens, their fees and the list of orders are shown below.
There are 6 kitchens and 13 orders in this instance.
**Kitchens**
| kitchen_id | activation_fee |
|---|---|
| F1 | 1000 |
| F2 | 1000 |
| F3 | 1000 |
| F4 | 1000 |
| F5 | 1000 |
| F6 | 1000 |
**Orders**
| order_id |
|---|
| A |
| B |
| C |
| D |
| E |
| F |
| G |
| H |
| I |
| J |
| K |
| L |
| M |
**Delivery Distance**
| kitchen_id | order_id | delivery_distance |
|---|---|---|
| F1 | A | 222 |
| F1 | B | 354 |
| F1 | C | 70 |
| F1 | D | 378 |
| F1 | E | 77 |
| F1 | F | 202 |
| F1 | G | 109 |
| F1 | H | 788 |
| F1 | I | 254 |
| F1 | J | 52 |
| F1 | K | 389 |
| F1 | L | 915 |
| F1 | M | 123 |
| F2 | A | 52 |
| F2 | B | 392 |
| F2 | C | 568 |
| F2 | D | 293 |
| F2 | E | 423 |
| F2 | F | 234 |
| F2 | G | 803 |
| F2 | H | 188 |
| F2 | I | 279 |
| F2 | J | 603 |
| F2 | K | 705 |
| F2 | L | 631 |
| F2 | M | 300 |
| F3 | A | 914 |
| F3 | B | 443 |
| F3 | C | 343 |
| F3 | D | 208 |
| F3 | E | 85 |
| F3 | F | 73 |
| F3 | G | 259 |
| F3 | H | 162 |
| F3 | I | 581 |
| F3 | J | 341 |
| F3 | K | 679 |
| F3 | L | 664 |
| F3 | M | 704 |
| F4 | A | 121 |
| F4 | B | 168 |
| F4 | C | 648 |
| F4 | D | 346 |
| F4 | E | 648 |
| F4 | F | 174 |
| F4 | G | 748 |
| F4 | H | 314 |
| F4 | I | 961 |
| F4 | J | 530 |
| F4 | K | 514 |
| F4 | L | 119 |
| F4 | M | 616 |
| F5 | A | 486 |
| F5 | B | 926 |
| F5 | C | 909 |
| F5 | D | 664 |
| F5 | E | 656 |
| F5 | F | 352 |
| F5 | G | 36 |
| F5 | H | 462 |
| F5 | I | 137 |
| F5 | J | 84 |
| F5 | K | 709 |
| F5 | L | 704 |
| F5 | M | 773 |
| F6 | A | 415 |
| F6 | B | 458 |
| F6 | C | 910 |
| F6 | D | 890 |
| F6 | E | 384 |
| F6 | F | 729 |
| F6 | G | 639 |
| F6 | H | 259 |
| F6 | I | 54 |
| F6 | J | 341 |
| F6 | K | 228 |
| F6 | L | 171 |
| F6 | M | 602 |
If you want to hand the plan back to me in a tidy form, a simple JSON sketch like this is perfect — nothing fancy, just the shape I expect:
{
""solution"": {
""selected"": [<kitchen_to_switch_on>, <kitchen_to_switch_on>, ...],
""assignments"": [<chosen_switched_on_kitchen>, <chosen_switched_on_kitchen>, ...]
}
}
Think of ""selected"" as the list of kitchens you flip on (just put their exact IDs in that list), and ""assignments"" as, for each order in the same sequence as the input, which switched-on kitchen will handle it. Super casual: it's just two lists — which kitchens are active, and who serves which order.
This JSON is only a sketch of the expected shape, not the final answer — fill in the real kitchen IDs and assignments when you submit.
Also: all identifiers must be used exactly as they appear in the instance input — no renaming and no new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1000, 1000, 1000, 1000, 1000, 1000], 'connection_costs': [[222, 354, 70, 378, 77, 202, 109, 788, 254, 52, 389, 915, 123], [52, 392, 568, 293, 423, 234, 803, 188, 279, 603, 705, 631, 300], [914, 443, 343, 208, 85, 73, 259, 162, 581, 341, 679, 664, 704], [121, 168, 648, 346, 648, 174, 748, 314, 961, 530, 514, 119, 616], [486, 926, 909, 664, 656, 352, 36, 462, 137, 84, 709, 704, 773], [415, 458, 910, 890, 384, 729, 639, 259, 54, 341, 228, 171, 602]], 'objective': 4299.0}","{'open_facilities': [0, 5], 'assignments': [0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 5, 5, 0]}",4299.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 13, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}, {'id': 'F5', 'opening_cost': 1000}, {'id': 'F6', 'opening_cost': 1000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}, {'id': 'L'}, {'id': 'M'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 222}, {'facility': 'F1', 'customer': 'B', 'cost': 354}, {'facility': 'F1', 'customer': 'C', 'cost': 70}, {'facility': 'F1', 'customer': 'D', 'cost': 378}, {'facility': 'F1', 'customer': 'E', 'cost': 77}, {'facility': 'F1', 'customer': 'F', 'cost': 202}, {'facility': 'F1', 'customer': 'G', 'cost': 109}, {'facility': 'F1', 'customer': 'H', 'cost': 788}, {'facility': 'F1', 'customer': 'I', 'cost': 254}, {'facility': 'F1', 'customer': 'J', 'cost': 52}, {'facility': 'F1', 'customer': 'K', 'cost': 389}, {'facility': 'F1', 'customer': 'L', 'cost': 915}, {'facility': 'F1', 'customer': 'M', 'cost': 123}, {'facility': 'F2', 'customer': 'A', 'cost': 52}, {'facility': 'F2', 'customer': 'B', 'cost': 392}, {'facility': 'F2', 'customer': 'C', 'cost': 568}, {'facility': 'F2', 'customer': 'D', 'cost': 293}, {'facility': 'F2', 'customer': 'E', 'cost': 423}, {'facility': 'F2', 'customer': 'F', 'cost': 234}, {'facility': 'F2', 'customer': 'G', 'cost': 803}, {'facility': 'F2', 'customer': 'H', 'cost': 188}, {'facility': 'F2', 'customer': 'I', 'cost': 279}, {'facility': 'F2', 'customer': 'J', 'cost': 603}, {'facility': 'F2', 'customer': 'K', 'cost': 705}, {'facility': 'F2', 'customer': 'L', 'cost': 631}, {'facility': 'F2', 'customer': 'M', 'cost': 300}, {'facility': 'F3', 'customer': 'A', 'cost': 914}, {'facility': 'F3', 'customer': 'B', 'cost': 443}, {'facility': 'F3', 'customer': 'C', 'cost': 343}, {'facility': 'F3', 'customer': 'D', 'cost': 208}, {'facility': 'F3', 'customer': 'E', 'cost': 85}, {'facility': 'F3', 'customer': 'F', 'cost': 73}, {'facility': 'F3', 'customer': 'G', 'cost': 259}, {'facility': 'F3', 'customer': 'H', 'cost': 162}, {'facility': 'F3', 'customer': 'I', 'cost': 581}, {'facility': 'F3', 'customer': 'J', 'cost': 341}, {'facility': 'F3', 'customer': 'K', 'cost': 679}, {'facility': 'F3', 'customer': 'L', 'cost': 664}, {'facility': 'F3', 'customer': 'M', 'cost': 704}, {'facility': 'F4', 'customer': 'A', 'cost': 121}, {'facility': 'F4', 'customer': 'B', 'cost': 168}, {'facility': 'F4', 'customer': 'C', 'cost': 648}, {'facility': 'F4', 'customer': 'D', 'cost': 346}, {'facility': 'F4', 'customer': 'E', 'cost': 648}, {'facility': 'F4', 'customer': 'F', 'cost': 174}, {'facility': 'F4', 'customer': 'G', 'cost': 748}, {'facility': 'F4', 'customer': 'H', 'cost': 314}, {'facility': 'F4', 'customer': 'I', 'cost': 961}, {'facility': 'F4', 'customer': 'J', 'cost': 530}, {'facility': 'F4', 'customer': 'K', 'cost': 514}, {'facility': 'F4', 'customer': 'L', 'cost': 119}, {'facility': 'F4', 'customer': 'M', 'cost': 616}, {'facility': 'F5', 'customer': 'A', 'cost': 486}, {'facility': 'F5', 'customer': 'B', 'cost': 926}, {'facility': 'F5', 'customer': 'C', 'cost': 909}, {'facility': 'F5', 'customer': 'D', 'cost': 664}, {'facility': 'F5', 'customer': 'E', 'cost': 656}, {'facility': 'F5', 'customer': 'F', 'cost': 352}, {'facility': 'F5', 'customer': 'G', 'cost': 36}, {'facility': 'F5', 'customer': 'H', 'cost': 462}, {'facility': 'F5', 'customer': 'I', 'cost': 137}, {'facility': 'F5', 'customer': 'J', 'cost': 84}, {'facility': 'F5', 'customer': 'K', 'cost': 709}, {'facility': 'F5', 'customer': 'L', 'cost': 704}, {'facility': 'F5', 'customer': 'M', 'cost': 773}, {'facility': 'F6', 'customer': 'A', 'cost': 415}, {'facility': 'F6', 'customer': 'B', 'cost': 458}, {'facility': 'F6', 'customer': 'C', 'cost': 910}, {'facility': 'F6', 'customer': 'D', 'cost': 890}, {'facility': 'F6', 'customer': 'E', 'cost': 384}, {'facility': 'F6', 'customer': 'F', 'cost': 729}, {'facility': 'F6', 'customer': 'G', 'cost': 639}, {'facility': 'F6', 'customer': 'H', 'cost': 259}, {'facility': 'F6', 'customer': 'I', 'cost': 54}, {'facility': 'F6', 'customer': 'J', 'cost': 341}, {'facility': 'F6', 'customer': 'K', 'cost': 228}, {'facility': 'F6', 'customer': 'L', 'cost': 171}, {'facility': 'F6', 'customer': 'M', 'cost': 602}], 'objective': 4299.0}","{'selected': ['F1', 'F6'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F6', 'F6', 'F1', 'F6', 'F6', 'F1']}",2,markdown_table,names
UFLP,UFLP,"I’m trying to sort out which EV chargers to put in our apartment complex and how to link each resident’s car to one of the chargers. The idea is to pick a set of chargers to install (each has an installation fee) and then sign each car up to exactly one of the chargers that actually gets installed. A plan is better when the overall bill is lower — just add up all the installation fees for the chargers chosen plus the walking distance for every resident from their parking spot to their assigned charger — and the goal is to make that total as small as possible. Chargers can serve more than one car, but no car can be left unassigned or signed up to more than one charger. Concrete details about candidate charger locations, installation costs, residents, and distances are listed below.
{
""num_candidate_chargers"": 4,
""num_resident_cars"": 9,
""chargers"": [
{
""charger_id"": ""F1"",
""installation_cost"": 2000
},
{
""charger_id"": ""F2"",
""installation_cost"": 2000
},
{
""charger_id"": ""F3"",
""installation_cost"": 2000
},
{
""charger_id"": ""F4"",
""installation_cost"": 2000
}
],
""resident_cars"": [
{
""resident_car_id"": 0
},
{
""resident_car_id"": 1
},
{
""resident_car_id"": 2
},
{
""resident_car_id"": 3
},
{
""resident_car_id"": 4
},
{
""resident_car_id"": 5
},
{
""resident_car_id"": 6
},
{
""resident_car_id"": 7
},
{
""resident_car_id"": 8
}
],
""walking_distances"": [
{
""charger_id"": ""F1"",
""resident_car_id"": 0,
""walking_distance"": 822
},
{
""charger_id"": ""F1"",
""resident_car_id"": 1,
""walking_distance"": 913
},
{
""charger_id"": ""F1"",
""resident_car_id"": 2,
""walking_distance"": 554
},
{
""charger_id"": ""F1"",
""resident_car_id"": 3,
""walking_distance"": 414
},
{
""charger_id"": ""F1"",
""resident_car_id"": 4,
""walking_distance"": 965
},
{
""charger_id"": ""F1"",
""resident_car_id"": 5,
""walking_distance"": 480
},
{
""charger_id"": ""F1"",
""resident_car_id"": 6,
""walking_distance"": 120
},
{
""charger_id"": ""F1"",
""resident_car_id"": 7,
""walking_distance"": 523
},
{
""charger_id"": ""F1"",
""resident_car_id"": 8,
""walking_distance"": 296
},
{
""charger_id"": ""F2"",
""resident_car_id"": 0,
""walking_distance"": 380
},
{
""charger_id"": ""F2"",
""resident_car_id"": 1,
""walking_distance"": 61
},
{
""charger_id"": ""F2"",
""resident_car_id"": 2,
""walking_distance"": 28
},
{
""charger_id"": ""F2"",
""resident_car_id"": 3,
""walking_distance"": 762
},
{
""charger_id"": ""F2"",
""resident_car_id"": 4,
""walking_distance"": 355
},
{
""charger_id"": ""F2"",
""resident_car_id"": 5,
""walking_distance"": 991
},
{
""charger_id"": ""F2"",
""resident_car_id"": 6,
""walking_distance"": 826
},
{
""charger_id"": ""F2"",
""resident_car_id"": 7,
""walking_distance"": 439
},
{
""charger_id"": ""F2"",
""resident_car_id"": 8,
""walking_distance"": 388
},
{
""charger_id"": ""F3"",
""resident_car_id"": 0,
""walking_distance"": 129
},
{
""charger_id"": ""F3"",
""resident_car_id"": 1,
""walking_distance"": 653
},
{
""charger_id"": ""F3"",
""resident_car_id"": 2,
""walking_distance"": 451
},
{
""charger_id"": ""F3"",
""resident_car_id"": 3,
""walking_distance"": 76
},
{
""charger_id"": ""F3"",
""resident_car_id"": 4,
""walking_distance"": 733
},
{
""charger_id"": ""F3"",
""resident_car_id"": 5,
""walking_distance"": 817
},
{
""charger_id"": ""F3"",
""resident_car_id"": 6,
""walking_distance"": 260
},
{
""charger_id"": ""F3"",
""resident_car_id"": 7,
""walking_distance"": 127
},
{
""charger_id"": ""F3"",
""resident_car_id"": 8,
""walking_distance"": 662
},
{
""charger_id"": ""F4"",
""resident_car_id"": 0,
""walking_distance"": 976
},
{
""charger_id"": ""F4"",
""resident_car_id"": 1,
""walking_distance"": 901
},
{
""charger_id"": ""F4"",
""resident_car_id"": 2,
""walking_distance"": 354
},
{
""charger_id"": ""F4"",
""resident_car_id"": 3,
""walking_distance"": 418
},
{
""charger_id"": ""F4"",
""resident_car_id"": 4,
""walking_distance"": 647
},
{
""charger_id"": ""F4"",
""resident_car_id"": 5,
""walking_distance"": 280
},
{
""charger_id"": ""F4"",
""resident_car_id"": 6,
""walking_distance"": 979
},
{
""charger_id"": ""F4"",
""resident_car_id"": 7,
""walking_distance"": 403
},
{
""charger_id"": ""F4"",
""resident_car_id"": 8,
""walking_distance"": 739
}
]
}
When you reply with a plan, please use this simple JSON layout so I can parse it easily:
{
""solution"": {
""selected"": [<charger_site_to_open>, <charger_site_to_open>, ...],
""assignments"": [<assigned_charger_site>, <assigned_charger_site>, ...]
}
}
""selected"" is where you list the charger locations you want to install. ""assignments"" is a list with one entry per resident showing which installed charger they’ll use. Think of it like filling out a form: which chargers are installed, and for each resident, which charger they get. This is just the shape I need — not the final answer.
Please use the exact identifiers from the instance input — don’t rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [2000, 2000, 2000, 2000], 'connection_costs': [[822, 913, 554, 414, 965, 480, 120, 523, 296], [380, 61, 28, 762, 355, 991, 826, 439, 388], [129, 653, 451, 76, 733, 817, 260, 127, 662], [976, 901, 354, 418, 647, 280, 979, 403, 739]], 'objective': 5908.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2, 2]}",5908.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 9, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 822}, {'facility': 'F1', 'customer': 1, 'cost': 913}, {'facility': 'F1', 'customer': 2, 'cost': 554}, {'facility': 'F1', 'customer': 3, 'cost': 414}, {'facility': 'F1', 'customer': 4, 'cost': 965}, {'facility': 'F1', 'customer': 5, 'cost': 480}, {'facility': 'F1', 'customer': 6, 'cost': 120}, {'facility': 'F1', 'customer': 7, 'cost': 523}, {'facility': 'F1', 'customer': 8, 'cost': 296}, {'facility': 'F2', 'customer': 0, 'cost': 380}, {'facility': 'F2', 'customer': 1, 'cost': 61}, {'facility': 'F2', 'customer': 2, 'cost': 28}, {'facility': 'F2', 'customer': 3, 'cost': 762}, {'facility': 'F2', 'customer': 4, 'cost': 355}, {'facility': 'F2', 'customer': 5, 'cost': 991}, {'facility': 'F2', 'customer': 6, 'cost': 826}, {'facility': 'F2', 'customer': 7, 'cost': 439}, {'facility': 'F2', 'customer': 8, 'cost': 388}, {'facility': 'F3', 'customer': 0, 'cost': 129}, {'facility': 'F3', 'customer': 1, 'cost': 653}, {'facility': 'F3', 'customer': 2, 'cost': 451}, {'facility': 'F3', 'customer': 3, 'cost': 76}, {'facility': 'F3', 'customer': 4, 'cost': 733}, {'facility': 'F3', 'customer': 5, 'cost': 817}, {'facility': 'F3', 'customer': 6, 'cost': 260}, {'facility': 'F3', 'customer': 7, 'cost': 127}, {'facility': 'F3', 'customer': 8, 'cost': 662}, {'facility': 'F4', 'customer': 0, 'cost': 976}, {'facility': 'F4', 'customer': 1, 'cost': 901}, {'facility': 'F4', 'customer': 2, 'cost': 354}, {'facility': 'F4', 'customer': 3, 'cost': 418}, {'facility': 'F4', 'customer': 4, 'cost': 647}, {'facility': 'F4', 'customer': 5, 'cost': 280}, {'facility': 'F4', 'customer': 6, 'cost': 979}, {'facility': 'F4', 'customer': 7, 'cost': 403}, {'facility': 'F4', 'customer': 8, 'cost': 739}], 'objective': 5908.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",3,json,0
UFLP,UFLP,"Many people browse the clothing tents at the market, and the organizer needs to pick which pop-up stalls to pay for and then route every shopper to one of the paid stalls. Each stall carries a rent, and each shopper’s walk to their stall carries a travel cost, so the best setup is the one with the lowest total: add the rents for all the stalls that are booked and the travel cost for every shopper to reach their single assigned stall. Each shopper must be matched to exactly one rented stall, and shoppers are only allowed to go to stalls that were actually rented. The concrete details about stalls, prices, and shoppers appear below.
# num_candidate_stalls=3
# num_shoppers=9
# STALLS
stall_id,stall_rent
F1,3813
F2,4989
F3,5364
# SHOPPERS
shopper_id
0
1
2
3
4
5
6
7
8
# SHOPPER_WALKS
stall_id,shopper_id,shopper_walk_cost
F1,0,299
F1,1,309
F1,2,543
F1,3,353
F1,4,808
F1,5,3
F1,6,458
F1,7,256
F1,8,946
F2,0,819
F2,1,615
F2,2,306
F2,3,628
F2,4,521
F2,5,202
F2,6,677
F2,7,70
F2,8,509
F3,0,792
F3,1,575
F3,2,709
F3,3,380
F3,4,584
F3,5,85
F3,6,259
F3,7,832
F3,8,976
Also, when you hand back the final plan, please use this JSON layout so it's easy to read and check:
{
""solution"": {
""selected"": [<stall_to_rent>, <stall_to_rent>, ...],
""assignments"": [<chosen_rented_stall>, <chosen_rented_stall>, ...]
}
}
Pretty simple: ""selected"" is the list of stalls you decide to rent, and ""assignments"" lists, in the same order as the shoppers appear in the instance, which rented stall each shopper goes to. Think of it as a short form: which stalls are paid for, and then one chosen stall per shopper.
This JSON is just a sketch of the shape I expect, not the actual solution. All identifiers you use must match the instance exactly — do not rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".""","{'opening_costs': [3813, 4989, 5364], 'connection_costs': [[299, 309, 543, 353, 808, 3, 458, 256, 946], [819, 615, 306, 628, 521, 202, 677, 70, 509], [792, 575, 709, 380, 584, 85, 259, 832, 976]], 'objective': 7788.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0, 0, 0]}",7788.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 9, 'facilities': [{'id': 'F1', 'opening_cost': 3813}, {'id': 'F2', 'opening_cost': 4989}, {'id': 'F3', 'opening_cost': 5364}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 299}, {'facility': 'F1', 'customer': 1, 'cost': 309}, {'facility': 'F1', 'customer': 2, 'cost': 543}, {'facility': 'F1', 'customer': 3, 'cost': 353}, {'facility': 'F1', 'customer': 4, 'cost': 808}, {'facility': 'F1', 'customer': 5, 'cost': 3}, {'facility': 'F1', 'customer': 6, 'cost': 458}, {'facility': 'F1', 'customer': 7, 'cost': 256}, {'facility': 'F1', 'customer': 8, 'cost': 946}, {'facility': 'F2', 'customer': 0, 'cost': 819}, {'facility': 'F2', 'customer': 1, 'cost': 615}, {'facility': 'F2', 'customer': 2, 'cost': 306}, {'facility': 'F2', 'customer': 3, 'cost': 628}, {'facility': 'F2', 'customer': 4, 'cost': 521}, {'facility': 'F2', 'customer': 5, 'cost': 202}, {'facility': 'F2', 'customer': 6, 'cost': 677}, {'facility': 'F2', 'customer': 7, 'cost': 70}, {'facility': 'F2', 'customer': 8, 'cost': 509}, {'facility': 'F3', 'customer': 0, 'cost': 792}, {'facility': 'F3', 'customer': 1, 'cost': 575}, {'facility': 'F3', 'customer': 2, 'cost': 709}, {'facility': 'F3', 'customer': 3, 'cost': 380}, {'facility': 'F3', 'customer': 4, 'cost': 584}, {'facility': 'F3', 'customer': 5, 'cost': 85}, {'facility': 'F3', 'customer': 6, 'cost': 259}, {'facility': 'F3', 'customer': 7, 'cost': 832}, {'facility': 'F3', 'customer': 8, 'cost': 976}], 'objective': 7788.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",4,csv,0
UFLP,UFLP,"Recently the neighborhood board brought up which community tool sheds to keep maintained and how to assign homes to them. The job is to choose some sheds to pay for and then register each household with a single kept shed — households can only access sheds on that maintained list. To pick the best arrangement, you add the maintenance costs for the kept sheds and the travel cost for each household to reach its assigned shed; the arrangement with the lowest total of those added costs is preferred. No home can be left out or listed twice. The detailed costs and household distances are provided below.
# total_candidate_sheds=6
# total_households=14
# SHEDS
shed_id,maintenance_cost
F1,2000
F2,2000
F3,2000
F4,2000
F5,2000
F6,2000
# HOUSEHOLDS
household_id
1
2
3
4
5
6
7
8
9
10
11
12
13
14
# HOUSEHOLD_TRAVELS
shed_id,household_id,household_travel_cost
F1,1,242
F1,2,954
F1,3,724
F1,4,467
F1,5,691
F1,6,774
F1,7,490
F1,8,475
F1,9,432
F1,10,714
F1,11,547
F1,12,661
F1,13,519
F1,14,237
F2,1,992
F2,2,959
F2,3,294
F2,4,323
F2,5,828
F2,6,449
F2,7,765
F2,8,883
F2,9,985
F2,10,704
F2,11,363
F2,12,965
F2,13,191
F2,14,218
F3,1,28
F3,2,406
F3,3,536
F3,4,572
F3,5,269
F3,6,107
F3,7,106
F3,8,191
F3,9,377
F3,10,307
F3,11,472
F3,12,133
F3,13,943
F3,14,457
F4,1,127
F4,2,532
F4,3,879
F4,4,699
F4,5,423
F4,6,743
F4,7,138
F4,8,596
F4,9,661
F4,10,492
F4,11,566
F4,12,248
F4,13,647
F4,14,445
F5,1,599
F5,2,179
F5,3,730
F5,4,445
F5,5,768
F5,6,958
F5,7,287
F5,8,996
F5,9,360
F5,10,465
F5,11,40
F5,12,73
F5,13,823
F5,14,857
F6,1,650
F6,2,575
F6,3,557
F6,4,574
F6,5,740
F6,6,389
F6,7,357
F6,8,766
F6,9,328
F6,10,460
F6,11,424
F6,12,424
F6,13,153
F6,14,470
Also, when you send the actual solution back, just stick to a small JSON shape so it's easy to check. Something casual like this will do:
{
""solution"": {
""selected"": [<shed_to_keep>, <shed_to_keep>, ...],
""assignments"": [<assigned_shed>, <assigned_shed>, ...]
}
}
Here ""selected"" is the list of shed locations you choose to keep (their IDs), and ""assignments"" lists, for each household in the same order as the input, which kept shed they're signed up to. Think of it like filling out a simple form — which sheds are kept and where each house is registered. This JSON is just the sketch of the shape I expect, not the filled-in answer.
Please use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [2000, 2000, 2000, 2000, 2000, 2000], 'connection_costs': [[242, 954, 724, 467, 691, 774, 490, 475, 432, 714, 547, 661, 519, 237], [992, 959, 294, 323, 828, 449, 765, 883, 985, 704, 363, 965, 191, 218], [28, 406, 536, 572, 269, 107, 106, 191, 377, 307, 472, 133, 943, 457], [127, 532, 879, 699, 423, 743, 138, 596, 661, 492, 566, 248, 647, 445], [599, 179, 730, 445, 768, 958, 287, 996, 360, 465, 40, 73, 823, 857], [650, 575, 557, 574, 740, 389, 357, 766, 328, 460, 424, 424, 153, 470]], 'objective': 6904.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}",6904.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 14, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}, {'id': 'F6', 'opening_cost': 2000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}, {'id': 12}, {'id': 13}, {'id': 14}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 242}, {'facility': 'F1', 'customer': 2, 'cost': 954}, {'facility': 'F1', 'customer': 3, 'cost': 724}, {'facility': 'F1', 'customer': 4, 'cost': 467}, {'facility': 'F1', 'customer': 5, 'cost': 691}, {'facility': 'F1', 'customer': 6, 'cost': 774}, {'facility': 'F1', 'customer': 7, 'cost': 490}, {'facility': 'F1', 'customer': 8, 'cost': 475}, {'facility': 'F1', 'customer': 9, 'cost': 432}, {'facility': 'F1', 'customer': 10, 'cost': 714}, {'facility': 'F1', 'customer': 11, 'cost': 547}, {'facility': 'F1', 'customer': 12, 'cost': 661}, {'facility': 'F1', 'customer': 13, 'cost': 519}, {'facility': 'F1', 'customer': 14, 'cost': 237}, {'facility': 'F2', 'customer': 1, 'cost': 992}, {'facility': 'F2', 'customer': 2, 'cost': 959}, {'facility': 'F2', 'customer': 3, 'cost': 294}, {'facility': 'F2', 'customer': 4, 'cost': 323}, {'facility': 'F2', 'customer': 5, 'cost': 828}, {'facility': 'F2', 'customer': 6, 'cost': 449}, {'facility': 'F2', 'customer': 7, 'cost': 765}, {'facility': 'F2', 'customer': 8, 'cost': 883}, {'facility': 'F2', 'customer': 9, 'cost': 985}, {'facility': 'F2', 'customer': 10, 'cost': 704}, {'facility': 'F2', 'customer': 11, 'cost': 363}, {'facility': 'F2', 'customer': 12, 'cost': 965}, {'facility': 'F2', 'customer': 13, 'cost': 191}, {'facility': 'F2', 'customer': 14, 'cost': 218}, {'facility': 'F3', 'customer': 1, 'cost': 28}, {'facility': 'F3', 'customer': 2, 'cost': 406}, {'facility': 'F3', 'customer': 3, 'cost': 536}, {'facility': 'F3', 'customer': 4, 'cost': 572}, {'facility': 'F3', 'customer': 5, 'cost': 269}, {'facility': 'F3', 'customer': 6, 'cost': 107}, {'facility': 'F3', 'customer': 7, 'cost': 106}, {'facility': 'F3', 'customer': 8, 'cost': 191}, {'facility': 'F3', 'customer': 9, 'cost': 377}, {'facility': 'F3', 'customer': 10, 'cost': 307}, {'facility': 'F3', 'customer': 11, 'cost': 472}, {'facility': 'F3', 'customer': 12, 'cost': 133}, {'facility': 'F3', 'customer': 13, 'cost': 943}, {'facility': 'F3', 'customer': 14, 'cost': 457}, {'facility': 'F4', 'customer': 1, 'cost': 127}, {'facility': 'F4', 'customer': 2, 'cost': 532}, {'facility': 'F4', 'customer': 3, 'cost': 879}, {'facility': 'F4', 'customer': 4, 'cost': 699}, {'facility': 'F4', 'customer': 5, 'cost': 423}, {'facility': 'F4', 'customer': 6, 'cost': 743}, {'facility': 'F4', 'customer': 7, 'cost': 138}, {'facility': 'F4', 'customer': 8, 'cost': 596}, {'facility': 'F4', 'customer': 9, 'cost': 661}, {'facility': 'F4', 'customer': 10, 'cost': 492}, {'facility': 'F4', 'customer': 11, 'cost': 566}, {'facility': 'F4', 'customer': 12, 'cost': 248}, {'facility': 'F4', 'customer': 13, 'cost': 647}, {'facility': 'F4', 'customer': 14, 'cost': 445}, {'facility': 'F5', 'customer': 1, 'cost': 599}, {'facility': 'F5', 'customer': 2, 'cost': 179}, {'facility': 'F5', 'customer': 3, 'cost': 730}, {'facility': 'F5', 'customer': 4, 'cost': 445}, {'facility': 'F5', 'customer': 5, 'cost': 768}, {'facility': 'F5', 'customer': 6, 'cost': 958}, {'facility': 'F5', 'customer': 7, 'cost': 287}, {'facility': 'F5', 'customer': 8, 'cost': 996}, {'facility': 'F5', 'customer': 9, 'cost': 360}, {'facility': 'F5', 'customer': 10, 'cost': 465}, {'facility': 'F5', 'customer': 11, 'cost': 40}, {'facility': 'F5', 'customer': 12, 'cost': 73}, {'facility': 'F5', 'customer': 13, 'cost': 823}, {'facility': 'F5', 'customer': 14, 'cost': 857}, {'facility': 'F6', 'customer': 1, 'cost': 650}, {'facility': 'F6', 'customer': 2, 'cost': 575}, {'facility': 'F6', 'customer': 3, 'cost': 557}, {'facility': 'F6', 'customer': 4, 'cost': 574}, {'facility': 'F6', 'customer': 5, 'cost': 740}, {'facility': 'F6', 'customer': 6, 'cost': 389}, {'facility': 'F6', 'customer': 7, 'cost': 357}, {'facility': 'F6', 'customer': 8, 'cost': 766}, {'facility': 'F6', 'customer': 9, 'cost': 328}, {'facility': 'F6', 'customer': 10, 'cost': 460}, {'facility': 'F6', 'customer': 11, 'cost': 424}, {'facility': 'F6', 'customer': 12, 'cost': 424}, {'facility': 'F6', 'customer': 13, 'cost': 153}, {'facility': 'F6', 'customer': 14, 'cost': 470}], 'objective': 6904.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",5,csv,1
UFLP,UFLP,"Back when the shop was deciding routes for the month, the owner had to choose which mobile grooming vans to deploy and who would service each client. The constraint was clear: each appointment must be covered by exactly one van that was actually sent out — no appointment left out, no appointment served twice, and no assigning to vans that weren’t deployed. A smarter schedule is simply the cheaper one overall: add together the deployment charges for the vans chosen and the travel costs for every appointment, and keep that combined amount as low as possible. The detailed van information and appointments are shown below.
There were 5 candidate vans, 13 appointments, and deployment costs 1000, 1000, 1000, 1000, 1000.
Van F1 had a deployment cost of 1000.
Van F2 had a deployment cost of 1000.
Van F3 had a deployment cost of 1000.
Van F4 had a deployment cost of 1000.
Van F5 had a deployment cost of 1000.
Van F1 serving appointment 1 had travel cost 296.
Van F1 serving appointment 2 had travel cost 926.
Van F1 serving appointment 3 had travel cost 877.
Van F1 serving appointment 4 had travel cost 848.
Van F1 serving appointment 5 had travel cost 706.
Van F1 serving appointment 6 had travel cost 666.
Van F1 serving appointment 7 had travel cost 807.
Van F1 serving appointment 8 had travel cost 946.
Van F1 serving appointment 9 had travel cost 603.
Van F1 serving appointment 10 had travel cost 802.
Van F1 serving appointment 11 had travel cost 608.
Van F1 serving appointment 12 had travel cost 341.
Van F1 serving appointment 13 had travel cost 133.
Van F2 serving appointment 1 had travel cost 780.
Van F2 serving appointment 2 had travel cost 390.
Van F2 serving appointment 3 had travel cost 637.
Van F2 serving appointment 4 had travel cost 421.
Van F2 serving appointment 5 had travel cost 773.
Van F2 serving appointment 6 had travel cost 995.
Van F2 serving appointment 7 had travel cost 850.
Van F2 serving appointment 8 had travel cost 212.
Van F2 serving appointment 9 had travel cost 727.
Van F2 serving appointment 10 had travel cost 320.
Van F2 serving appointment 11 had travel cost 182.
Van F2 serving appointment 12 had travel cost 746.
Van F2 serving appointment 13 had travel cost 18.
Van F3 serving appointment 1 had travel cost 921.
Van F3 serving appointment 2 had travel cost 650.
Van F3 serving appointment 3 had travel cost 22.
Van F3 serving appointment 4 had travel cost 324.
Van F3 serving appointment 5 had travel cost 252.
Van F3 serving appointment 6 had travel cost 812.
Van F3 serving appointment 7 had travel cost 964.
Van F3 serving appointment 8 had travel cost 214.
Van F3 serving appointment 9 had travel cost 71.
Van F3 serving appointment 10 had travel cost 587.
Van F3 serving appointment 11 had travel cost 474.
Van F3 serving appointment 12 had travel cost 118.
Van F3 serving appointment 13 had travel cost 858.
Van F4 serving appointment 1 had travel cost 56.
Van F4 serving appointment 2 had travel cost 407.
Van F4 serving appointment 3 had travel cost 220.
Van F4 serving appointment 4 had travel cost 672.
Van F4 serving appointment 5 had travel cost 948.
Van F4 serving appointment 6 had travel cost 130.
Van F4 serving appointment 7 had travel cost 240.
Van F4 serving appointment 8 had travel cost 606.
Van F4 serving appointment 9 had travel cost 501.
Van F4 serving appointment 10 had travel cost 101.
Van F4 serving appointment 11 had travel cost 975.
Van F4 serving appointment 12 had travel cost 198.
Van F4 serving appointment 13 had travel cost 174.
Van F5 serving appointment 1 had travel cost 279.
Van F5 serving appointment 2 had travel cost 866.
Van F5 serving appointment 3 had travel cost 126.
Van F5 serving appointment 4 had travel cost 881.
Van F5 serving appointment 5 had travel cost 959.
Van F5 serving appointment 6 had travel cost 468.
Van F5 serving appointment 7 had travel cost 684.
Van F5 serving appointment 8 had travel cost 41.
Van F5 serving appointment 9 had travel cost 335.
Van F5 serving appointment 10 had travel cost 125.
Van F5 serving appointment 11 had travel cost 410.
Van F5 serving appointment 12 had travel cost 708.
Van F5 serving appointment 13 had travel cost 654.
The owner then chose vans and assignments to minimize the combined deployment and travel cost.
If you want to tell me which vans you actually sent and who each client got, please use this simple JSON layout so it's easy to read and check:
{
""solution"": {
""selected"": [<van_to_deploy>, <van_to_deploy>, ...],
""assignments"": [<van_assigned_to_customer>, <van_assigned_to_customer>, ...]
}
}
Pretty straightforward: ""selected"" is the list of vans you decide to send out, and ""assignments"" lists, in the same order as the appointments in the instance, which van handles each appointment. Think of it like filling out a form — pick the vans you deploy, then next to each client write the van that will serve them.
This JSON is just the expected shape — a sketch — not the actual solution.
Important: all identifiers must be used exactly as they appear in the instance input — no renaming and no new labels.
For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1000, 1000, 1000, 1000, 1000], 'connection_costs': [[296, 926, 877, 848, 706, 666, 807, 946, 603, 802, 608, 341, 133], [780, 390, 637, 421, 773, 995, 850, 212, 727, 320, 182, 746, 18], [921, 650, 22, 324, 252, 812, 964, 214, 71, 587, 474, 118, 858], [56, 407, 220, 672, 948, 130, 240, 606, 501, 101, 975, 198, 174], [279, 866, 126, 881, 959, 468, 684, 41, 335, 125, 410, 708, 654]], 'objective': 4583.0}","{'open_facilities': [2, 3], 'assignments': [3, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 3]}",4583.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 13, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}, {'id': 'F5', 'opening_cost': 1000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}, {'id': 12}, {'id': 13}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 296}, {'facility': 'F1', 'customer': 2, 'cost': 926}, {'facility': 'F1', 'customer': 3, 'cost': 877}, {'facility': 'F1', 'customer': 4, 'cost': 848}, {'facility': 'F1', 'customer': 5, 'cost': 706}, {'facility': 'F1', 'customer': 6, 'cost': 666}, {'facility': 'F1', 'customer': 7, 'cost': 807}, {'facility': 'F1', 'customer': 8, 'cost': 946}, {'facility': 'F1', 'customer': 9, 'cost': 603}, {'facility': 'F1', 'customer': 10, 'cost': 802}, {'facility': 'F1', 'customer': 11, 'cost': 608}, {'facility': 'F1', 'customer': 12, 'cost': 341}, {'facility': 'F1', 'customer': 13, 'cost': 133}, {'facility': 'F2', 'customer': 1, 'cost': 780}, {'facility': 'F2', 'customer': 2, 'cost': 390}, {'facility': 'F2', 'customer': 3, 'cost': 637}, {'facility': 'F2', 'customer': 4, 'cost': 421}, {'facility': 'F2', 'customer': 5, 'cost': 773}, {'facility': 'F2', 'customer': 6, 'cost': 995}, {'facility': 'F2', 'customer': 7, 'cost': 850}, {'facility': 'F2', 'customer': 8, 'cost': 212}, {'facility': 'F2', 'customer': 9, 'cost': 727}, {'facility': 'F2', 'customer': 10, 'cost': 320}, {'facility': 'F2', 'customer': 11, 'cost': 182}, {'facility': 'F2', 'customer': 12, 'cost': 746}, {'facility': 'F2', 'customer': 13, 'cost': 18}, {'facility': 'F3', 'customer': 1, 'cost': 921}, {'facility': 'F3', 'customer': 2, 'cost': 650}, {'facility': 'F3', 'customer': 3, 'cost': 22}, {'facility': 'F3', 'customer': 4, 'cost': 324}, {'facility': 'F3', 'customer': 5, 'cost': 252}, {'facility': 'F3', 'customer': 6, 'cost': 812}, {'facility': 'F3', 'customer': 7, 'cost': 964}, {'facility': 'F3', 'customer': 8, 'cost': 214}, {'facility': 'F3', 'customer': 9, 'cost': 71}, {'facility': 'F3', 'customer': 10, 'cost': 587}, {'facility': 'F3', 'customer': 11, 'cost': 474}, {'facility': 'F3', 'customer': 12, 'cost': 118}, {'facility': 'F3', 'customer': 13, 'cost': 858}, {'facility': 'F4', 'customer': 1, 'cost': 56}, {'facility': 'F4', 'customer': 2, 'cost': 407}, {'facility': 'F4', 'customer': 3, 'cost': 220}, {'facility': 'F4', 'customer': 4, 'cost': 672}, {'facility': 'F4', 'customer': 5, 'cost': 948}, {'facility': 'F4', 'customer': 6, 'cost': 130}, {'facility': 'F4', 'customer': 7, 'cost': 240}, {'facility': 'F4', 'customer': 8, 'cost': 606}, {'facility': 'F4', 'customer': 9, 'cost': 501}, {'facility': 'F4', 'customer': 10, 'cost': 101}, {'facility': 'F4', 'customer': 11, 'cost': 975}, {'facility': 'F4', 'customer': 12, 'cost': 198}, {'facility': 'F4', 'customer': 13, 'cost': 174}, {'facility': 'F5', 'customer': 1, 'cost': 279}, {'facility': 'F5', 'customer': 2, 'cost': 866}, {'facility': 'F5', 'customer': 3, 'cost': 126}, {'facility': 'F5', 'customer': 4, 'cost': 881}, {'facility': 'F5', 'customer': 5, 'cost': 959}, {'facility': 'F5', 'customer': 6, 'cost': 468}, {'facility': 'F5', 'customer': 7, 'cost': 684}, {'facility': 'F5', 'customer': 8, 'cost': 41}, {'facility': 'F5', 'customer': 9, 'cost': 335}, {'facility': 'F5', 'customer': 10, 'cost': 125}, {'facility': 'F5', 'customer': 11, 'cost': 410}, {'facility': 'F5', 'customer': 12, 'cost': 708}, {'facility': 'F5', 'customer': 13, 'cost': 654}], 'objective': 4583.0}","{'selected': ['F3', 'F4'], 'assignments': ['F4', 'F4', 'F3', 'F3', 'F3', 'F4', 'F4', 'F3', 'F3', 'F4', 'F3', 'F3', 'F4']}",6,nl,1
UFLP,UFLP,"Many people on the planning team are working through a straightforward trade-off: open more pickup hubs (which costs money) or have customers travel farther (which raises travel bills). The task is to choose which hubs to open and register each customer to a single opened hub so that when you add together the hub opening charges and all customer travel costs the total is as small as it can be. Every customer must be assigned to exactly one hub that’s been opened, and customers can’t use hubs that remain closed. The specific options and numbers are shown below.
There are 6 hubs and 13 customers in this instance.
**Hubs**
| hub_id | hub_opening_fee |
|---|---|
| F1 | 6721 |
| F2 | 9459 |
| F3 | 9823 |
| F4 | 6765 |
| F5 | 1198 |
| F6 | 3977 |
**Customers**
| customer_id |
|---|
| A |
| B |
| C |
| D |
| E |
| F |
| G |
| H |
| I |
| J |
| K |
| L |
| M |
**Travel Cost To Hub**
| hub_id | customer_id | travel_cost_to_hub |
|---|---|---|
| F1 | A | 602 |
| F1 | B | 683 |
| F1 | C | 265 |
| F1 | D | 350 |
| F1 | E | 846 |
| F1 | F | 931 |
| F1 | G | 149 |
| F1 | H | 118 |
| F1 | I | 302 |
| F1 | J | 644 |
| F1 | K | 570 |
| F1 | L | 163 |
| F1 | M | 642 |
| F2 | A | 297 |
| F2 | B | 339 |
| F2 | C | 744 |
| F2 | D | 486 |
| F2 | E | 285 |
| F2 | F | 492 |
| F2 | G | 942 |
| F2 | H | 133 |
| F2 | I | 334 |
| F2 | J | 850 |
| F2 | K | 852 |
| F2 | L | 353 |
| F2 | M | 51 |
| F3 | A | 3 |
| F3 | B | 991 |
| F3 | C | 759 |
| F3 | D | 949 |
| F3 | E | 755 |
| F3 | F | 827 |
| F3 | G | 624 |
| F3 | H | 304 |
| F3 | I | 487 |
| F3 | J | 144 |
| F3 | K | 151 |
| F3 | L | 555 |
| F3 | M | 928 |
| F4 | A | 884 |
| F4 | B | 749 |
| F4 | C | 861 |
| F4 | D | 875 |
| F4 | E | 972 |
| F4 | F | 974 |
| F4 | G | 440 |
| F4 | H | 334 |
| F4 | I | 193 |
| F4 | J | 425 |
| F4 | K | 277 |
| F4 | L | 834 |
| F4 | M | 851 |
| F5 | A | 179 |
| F5 | B | 407 |
| F5 | C | 50 |
| F5 | D | 464 |
| F5 | E | 263 |
| F5 | F | 339 |
| F5 | G | 961 |
| F5 | H | 379 |
| F5 | I | 449 |
| F5 | J | 139 |
| F5 | K | 515 |
| F5 | L | 665 |
| F5 | M | 773 |
| F6 | A | 252 |
| F6 | B | 159 |
| F6 | C | 6 |
| F6 | D | 635 |
| F6 | E | 492 |
| F6 | F | 520 |
| F6 | G | 661 |
| F6 | H | 688 |
| F6 | I | 498 |
| F6 | J | 734 |
| F6 | K | 385 |
| F6 | L | 262 |
| F6 | M | 271 |
Just so we're on the same page about how I want the answer formatted, please use this simple JSON shape when you send the solution — it makes it easy to read and plug into the rest of the workflow.
{
""solution"": {
""selected"": [<hub_to_open>, <hub_to_open>, ...],
""assignments"": [<chosen_open_hub>, <chosen_open_hub>, ...]
}
}
Think of it like a little form: ""selected"" is the list of hubs you choose to open, and ""assignments"" is the list that says, for each customer (in the same order as the input), which opened hub they will use. This is just the shape I expect — fill in the actual identifiers from the instance when you produce the final answer.
Please use the exact identifiers from the instance input — don't rename them or invent new labels.
- for example: Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [6721, 9459, 9823, 6765, 1198, 3977], 'connection_costs': [[602, 683, 265, 350, 846, 931, 149, 118, 302, 644, 570, 163, 642], [297, 339, 744, 486, 285, 492, 942, 133, 334, 850, 852, 353, 51], [3, 991, 759, 949, 755, 827, 624, 304, 487, 144, 151, 555, 928], [884, 749, 861, 875, 972, 974, 440, 334, 193, 425, 277, 834, 851], [179, 407, 50, 464, 263, 339, 961, 379, 449, 139, 515, 665, 773], [252, 159, 6, 635, 492, 520, 661, 688, 498, 734, 385, 262, 271]], 'objective': 6781.0}","{'open_facilities': [4], 'assignments': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]}",6781.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 13, 'facilities': [{'id': 'F1', 'opening_cost': 6721}, {'id': 'F2', 'opening_cost': 9459}, {'id': 'F3', 'opening_cost': 9823}, {'id': 'F4', 'opening_cost': 6765}, {'id': 'F5', 'opening_cost': 1198}, {'id': 'F6', 'opening_cost': 3977}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}, {'id': 'L'}, {'id': 'M'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 602}, {'facility': 'F1', 'customer': 'B', 'cost': 683}, {'facility': 'F1', 'customer': 'C', 'cost': 265}, {'facility': 'F1', 'customer': 'D', 'cost': 350}, {'facility': 'F1', 'customer': 'E', 'cost': 846}, {'facility': 'F1', 'customer': 'F', 'cost': 931}, {'facility': 'F1', 'customer': 'G', 'cost': 149}, {'facility': 'F1', 'customer': 'H', 'cost': 118}, {'facility': 'F1', 'customer': 'I', 'cost': 302}, {'facility': 'F1', 'customer': 'J', 'cost': 644}, {'facility': 'F1', 'customer': 'K', 'cost': 570}, {'facility': 'F1', 'customer': 'L', 'cost': 163}, {'facility': 'F1', 'customer': 'M', 'cost': 642}, {'facility': 'F2', 'customer': 'A', 'cost': 297}, {'facility': 'F2', 'customer': 'B', 'cost': 339}, {'facility': 'F2', 'customer': 'C', 'cost': 744}, {'facility': 'F2', 'customer': 'D', 'cost': 486}, {'facility': 'F2', 'customer': 'E', 'cost': 285}, {'facility': 'F2', 'customer': 'F', 'cost': 492}, {'facility': 'F2', 'customer': 'G', 'cost': 942}, {'facility': 'F2', 'customer': 'H', 'cost': 133}, {'facility': 'F2', 'customer': 'I', 'cost': 334}, {'facility': 'F2', 'customer': 'J', 'cost': 850}, {'facility': 'F2', 'customer': 'K', 'cost': 852}, {'facility': 'F2', 'customer': 'L', 'cost': 353}, {'facility': 'F2', 'customer': 'M', 'cost': 51}, {'facility': 'F3', 'customer': 'A', 'cost': 3}, {'facility': 'F3', 'customer': 'B', 'cost': 991}, {'facility': 'F3', 'customer': 'C', 'cost': 759}, {'facility': 'F3', 'customer': 'D', 'cost': 949}, {'facility': 'F3', 'customer': 'E', 'cost': 755}, {'facility': 'F3', 'customer': 'F', 'cost': 827}, {'facility': 'F3', 'customer': 'G', 'cost': 624}, {'facility': 'F3', 'customer': 'H', 'cost': 304}, {'facility': 'F3', 'customer': 'I', 'cost': 487}, {'facility': 'F3', 'customer': 'J', 'cost': 144}, {'facility': 'F3', 'customer': 'K', 'cost': 151}, {'facility': 'F3', 'customer': 'L', 'cost': 555}, {'facility': 'F3', 'customer': 'M', 'cost': 928}, {'facility': 'F4', 'customer': 'A', 'cost': 884}, {'facility': 'F4', 'customer': 'B', 'cost': 749}, {'facility': 'F4', 'customer': 'C', 'cost': 861}, {'facility': 'F4', 'customer': 'D', 'cost': 875}, {'facility': 'F4', 'customer': 'E', 'cost': 972}, {'facility': 'F4', 'customer': 'F', 'cost': 974}, {'facility': 'F4', 'customer': 'G', 'cost': 440}, {'facility': 'F4', 'customer': 'H', 'cost': 334}, {'facility': 'F4', 'customer': 'I', 'cost': 193}, {'facility': 'F4', 'customer': 'J', 'cost': 425}, {'facility': 'F4', 'customer': 'K', 'cost': 277}, {'facility': 'F4', 'customer': 'L', 'cost': 834}, {'facility': 'F4', 'customer': 'M', 'cost': 851}, {'facility': 'F5', 'customer': 'A', 'cost': 179}, {'facility': 'F5', 'customer': 'B', 'cost': 407}, {'facility': 'F5', 'customer': 'C', 'cost': 50}, {'facility': 'F5', 'customer': 'D', 'cost': 464}, {'facility': 'F5', 'customer': 'E', 'cost': 263}, {'facility': 'F5', 'customer': 'F', 'cost': 339}, {'facility': 'F5', 'customer': 'G', 'cost': 961}, {'facility': 'F5', 'customer': 'H', 'cost': 379}, {'facility': 'F5', 'customer': 'I', 'cost': 449}, {'facility': 'F5', 'customer': 'J', 'cost': 139}, {'facility': 'F5', 'customer': 'K', 'cost': 515}, {'facility': 'F5', 'customer': 'L', 'cost': 665}, {'facility': 'F5', 'customer': 'M', 'cost': 773}, {'facility': 'F6', 'customer': 'A', 'cost': 252}, {'facility': 'F6', 'customer': 'B', 'cost': 159}, {'facility': 'F6', 'customer': 'C', 'cost': 6}, {'facility': 'F6', 'customer': 'D', 'cost': 635}, {'facility': 'F6', 'customer': 'E', 'cost': 492}, {'facility': 'F6', 'customer': 'F', 'cost': 520}, {'facility': 'F6', 'customer': 'G', 'cost': 661}, {'facility': 'F6', 'customer': 'H', 'cost': 688}, {'facility': 'F6', 'customer': 'I', 'cost': 498}, {'facility': 'F6', 'customer': 'J', 'cost': 734}, {'facility': 'F6', 'customer': 'K', 'cost': 385}, {'facility': 'F6', 'customer': 'L', 'cost': 262}, {'facility': 'F6', 'customer': 'M', 'cost': 271}], 'objective': 6781.0}","{'selected': ['F5'], 'assignments': ['F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5']}",7,markdown_table,names
UFLP,UFLP,"I’m the one putting together the community garden plan this season: pick which plots to get ready and then place every interested family into exactly one of those prepared plots. Only plots that are prepared can take families, and a plot can host any number of families. The goal is to keep the total bill down — add up the setup cost for each plot that’s prepared plus the travel cost for every family to their assigned plot — and choose the combination that yields the smallest total. The exact plots, their setup costs, and the family travel numbers are listed below.
{
""num_plots"": 4,
""num_families"": 11,
""plots"": [
{
""plot_id"": ""F1"",
""plot_setup_cost"": 1000
},
{
""plot_id"": ""F2"",
""plot_setup_cost"": 1000
},
{
""plot_id"": ""F3"",
""plot_setup_cost"": 1000
},
{
""plot_id"": ""F4"",
""plot_setup_cost"": 1000
}
],
""familys"": [
{
""family_id"": 0
},
{
""family_id"": 1
},
{
""family_id"": 2
},
{
""family_id"": 3
},
{
""family_id"": 4
},
{
""family_id"": 5
},
{
""family_id"": 6
},
{
""family_id"": 7
},
{
""family_id"": 8
},
{
""family_id"": 9
},
{
""family_id"": 10
}
],
""travels"": [
{
""plot_id"": ""F1"",
""family_id"": 0,
""travel_cost"": 370
},
{
""plot_id"": ""F1"",
""family_id"": 1,
""travel_cost"": 10
},
{
""plot_id"": ""F1"",
""family_id"": 2,
""travel_cost"": 680
},
{
""plot_id"": ""F1"",
""family_id"": 3,
""travel_cost"": 775
},
{
""plot_id"": ""F1"",
""family_id"": 4,
""travel_cost"": 919
},
{
""plot_id"": ""F1"",
""family_id"": 5,
""travel_cost"": 366
},
{
""plot_id"": ""F1"",
""family_id"": 6,
""travel_cost"": 476
},
{
""plot_id"": ""F1"",
""family_id"": 7,
""travel_cost"": 472
},
{
""plot_id"": ""F1"",
""family_id"": 8,
""travel_cost"": 931
},
{
""plot_id"": ""F1"",
""family_id"": 9,
""travel_cost"": 138
},
{
""plot_id"": ""F1"",
""family_id"": 10,
""travel_cost"": 132
},
{
""plot_id"": ""F2"",
""family_id"": 0,
""travel_cost"": 542
},
{
""plot_id"": ""F2"",
""family_id"": 1,
""travel_cost"": 65
},
{
""plot_id"": ""F2"",
""family_id"": 2,
""travel_cost"": 378
},
{
""plot_id"": ""F2"",
""family_id"": 3,
""travel_cost"": 373
},
{
""plot_id"": ""F2"",
""family_id"": 4,
""travel_cost"": 640
},
{
""plot_id"": ""F2"",
""family_id"": 5,
""travel_cost"": 739
},
{
""plot_id"": ""F2"",
""family_id"": 6,
""travel_cost"": 711
},
{
""plot_id"": ""F2"",
""family_id"": 7,
""travel_cost"": 318
},
{
""plot_id"": ""F2"",
""family_id"": 8,
""travel_cost"": 607
},
{
""plot_id"": ""F2"",
""family_id"": 9,
""travel_cost"": 582
},
{
""plot_id"": ""F2"",
""family_id"": 10,
""travel_cost"": 574
},
{
""plot_id"": ""F3"",
""family_id"": 0,
""travel_cost"": 832
},
{
""plot_id"": ""F3"",
""family_id"": 1,
""travel_cost"": 251
},
{
""plot_id"": ""F3"",
""family_id"": 2,
""travel_cost"": 742
},
{
""plot_id"": ""F3"",
""family_id"": 3,
""travel_cost"": 229
},
{
""plot_id"": ""F3"",
""family_id"": 4,
""travel_cost"": 830
},
{
""plot_id"": ""F3"",
""family_id"": 5,
""travel_cost"": 240
},
{
""plot_id"": ""F3"",
""family_id"": 6,
""travel_cost"": 640
},
{
""plot_id"": ""F3"",
""family_id"": 7,
""travel_cost"": 574
},
{
""plot_id"": ""F3"",
""family_id"": 8,
""travel_cost"": 143
},
{
""plot_id"": ""F3"",
""family_id"": 9,
""travel_cost"": 444
},
{
""plot_id"": ""F3"",
""family_id"": 10,
""travel_cost"": 817
},
{
""plot_id"": ""F4"",
""family_id"": 0,
""travel_cost"": 488
},
{
""plot_id"": ""F4"",
""family_id"": 1,
""travel_cost"": 516
},
{
""plot_id"": ""F4"",
""family_id"": 2,
""travel_cost"": 878
},
{
""plot_id"": ""F4"",
""family_id"": 3,
""travel_cost"": 775
},
{
""plot_id"": ""F4"",
""family_id"": 4,
""travel_cost"": 313
},
{
""plot_id"": ""F4"",
""family_id"": 5,
""travel_cost"": 283
},
{
""plot_id"": ""F4"",
""family_id"": 6,
""travel_cost"": 216
},
{
""plot_id"": ""F4"",
""family_id"": 7,
""travel_cost"": 199
},
{
""plot_id"": ""F4"",
""family_id"": 8,
""travel_cost"": 613
},
{
""plot_id"": ""F4"",
""family_id"": 9,
""travel_cost"": 780
},
{
""plot_id"": ""F4"",
""family_id"": 10,
""travel_cost"": 401
}
]
}
You can send back the final plan in a little JSON snippet like this — just helps me parse it easily. Something in this shape will do:
{
""solution"": {
""selected"": [<plot_to_prepare>, <plot_to_prepare>, ...],
""assignments"": [<assigned_plot>, <assigned_plot>, ...]
}
}
Quick, friendly guide: ""selected"" is the list of plots you decide to get ready (those incur setup costs). ""assignments"" lists, in order, which prepared plot each family will use (so the first entry is the plot for the first family, the second for the second family, and so on). Think of this JSON as a simple form — a sketch of the shape I need, not the final numbers.
Please make sure all plot and family identifiers you put in there match the instance exactly — don’t rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1000, 1000, 1000, 1000], 'connection_costs': [[370, 10, 680, 775, 919, 366, 476, 472, 931, 138, 132], [542, 65, 378, 373, 640, 739, 711, 318, 607, 582, 574], [832, 251, 742, 229, 830, 240, 640, 574, 143, 444, 817], [488, 516, 878, 775, 313, 283, 216, 199, 613, 780, 401]], 'objective': 5666.0}","{'open_facilities': [2, 3], 'assignments': [3, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3]}",5666.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 370}, {'facility': 'F1', 'customer': 1, 'cost': 10}, {'facility': 'F1', 'customer': 2, 'cost': 680}, {'facility': 'F1', 'customer': 3, 'cost': 775}, {'facility': 'F1', 'customer': 4, 'cost': 919}, {'facility': 'F1', 'customer': 5, 'cost': 366}, {'facility': 'F1', 'customer': 6, 'cost': 476}, {'facility': 'F1', 'customer': 7, 'cost': 472}, {'facility': 'F1', 'customer': 8, 'cost': 931}, {'facility': 'F1', 'customer': 9, 'cost': 138}, {'facility': 'F1', 'customer': 10, 'cost': 132}, {'facility': 'F2', 'customer': 0, 'cost': 542}, {'facility': 'F2', 'customer': 1, 'cost': 65}, {'facility': 'F2', 'customer': 2, 'cost': 378}, {'facility': 'F2', 'customer': 3, 'cost': 373}, {'facility': 'F2', 'customer': 4, 'cost': 640}, {'facility': 'F2', 'customer': 5, 'cost': 739}, {'facility': 'F2', 'customer': 6, 'cost': 711}, {'facility': 'F2', 'customer': 7, 'cost': 318}, {'facility': 'F2', 'customer': 8, 'cost': 607}, {'facility': 'F2', 'customer': 9, 'cost': 582}, {'facility': 'F2', 'customer': 10, 'cost': 574}, {'facility': 'F3', 'customer': 0, 'cost': 832}, {'facility': 'F3', 'customer': 1, 'cost': 251}, {'facility': 'F3', 'customer': 2, 'cost': 742}, {'facility': 'F3', 'customer': 3, 'cost': 229}, {'facility': 'F3', 'customer': 4, 'cost': 830}, {'facility': 'F3', 'customer': 5, 'cost': 240}, {'facility': 'F3', 'customer': 6, 'cost': 640}, {'facility': 'F3', 'customer': 7, 'cost': 574}, {'facility': 'F3', 'customer': 8, 'cost': 143}, {'facility': 'F3', 'customer': 9, 'cost': 444}, {'facility': 'F3', 'customer': 10, 'cost': 817}, {'facility': 'F4', 'customer': 0, 'cost': 488}, {'facility': 'F4', 'customer': 1, 'cost': 516}, {'facility': 'F4', 'customer': 2, 'cost': 878}, {'facility': 'F4', 'customer': 3, 'cost': 775}, {'facility': 'F4', 'customer': 4, 'cost': 313}, {'facility': 'F4', 'customer': 5, 'cost': 283}, {'facility': 'F4', 'customer': 6, 'cost': 216}, {'facility': 'F4', 'customer': 7, 'cost': 199}, {'facility': 'F4', 'customer': 8, 'cost': 613}, {'facility': 'F4', 'customer': 9, 'cost': 780}, {'facility': 'F4', 'customer': 10, 'cost': 401}], 'objective': 5666.0}","{'selected': ['F3', 'F4'], 'assignments': ['F4', 'F3', 'F3', 'F3', 'F4', 'F3', 'F4', 'F4', 'F3', 'F3', 'F4']}",8,json,0
UFLP,UFLP,"Someone on the team needs to decide which weekend sites to launch so all students have a weekend tutoring spot. Each candidate site carries a launch price, and every student will have some commute cost depending on which site they use. The choice is twofold: pick which sites to open, then put each student at exactly one of those opened sites — no skipping students and no splitting them between centers. To compare choices, add up the costs to open the chosen sites plus the commuting costs for all students to their assigned sites; the plan with the smallest total bill is preferable. Sites aren’t capacity-limited, but students may only be assigned to sites that are actually launched. The concrete details are shown below.
There are 4 centers and 11 students in this instance.
**Centers**
| center_id | launch_cost |
|---|---|
| F1 | 2000 |
| F2 | 2000 |
| F3 | 2000 |
| F4 | 2000 |
**Students**
| student_id |
|---|
| A |
| B |
| C |
| D |
| E |
| F |
| G |
| H |
| I |
| J |
| K |
**Commute Cost**
| center_id | student_id | commute_cost |
|---|---|---|
| F1 | A | 281 |
| F1 | B | 496 |
| F1 | C | 966 |
| F1 | D | 913 |
| F1 | E | 299 |
| F1 | F | 234 |
| F1 | G | 670 |
| F1 | H | 80 |
| F1 | I | 675 |
| F1 | J | 281 |
| F1 | K | 834 |
| F2 | A | 847 |
| F2 | B | 391 |
| F2 | C | 620 |
| F2 | D | 874 |
| F2 | E | 341 |
| F2 | F | 753 |
| F2 | G | 88 |
| F2 | H | 600 |
| F2 | I | 292 |
| F2 | J | 442 |
| F2 | K | 998 |
| F3 | A | 44 |
| F3 | B | 166 |
| F3 | C | 346 |
| F3 | D | 862 |
| F3 | E | 27 |
| F3 | F | 116 |
| F3 | G | 579 |
| F3 | H | 745 |
| F3 | I | 267 |
| F3 | J | 499 |
| F3 | K | 295 |
| F4 | A | 999 |
| F4 | B | 601 |
| F4 | C | 476 |
| F4 | D | 26 |
| F4 | E | 90 |
| F4 | F | 176 |
| F4 | G | 828 |
| F4 | H | 280 |
| F4 | I | 664 |
| F4 | J | 211 |
| F4 | K | 877 |
Also, when you hand back the plan, it helps if you use a simple JSON shape like this so we can read it automatically — nothing fancy, just the bits we need:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
Think of ""selected"" as the list of weekend sites you decide to launch, and ""assignments"" as, for each student (in the same order as the input), which launched site they’ll go to. This block is just a sketch of the shape I expect, not the actual answer.
Please make sure every identifier you use matches the instance input exactly — don’t rename IDs or invent new ones. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [2000, 2000, 2000, 2000], 'connection_costs': [[281, 496, 966, 913, 299, 234, 670, 80, 675, 281, 834], [847, 391, 620, 874, 341, 753, 88, 600, 292, 442, 998], [44, 166, 346, 862, 27, 116, 579, 745, 267, 499, 295], [999, 601, 476, 26, 90, 176, 828, 280, 664, 211, 877]], 'objective': 5946.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}",5946.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 281}, {'facility': 'F1', 'customer': 'B', 'cost': 496}, {'facility': 'F1', 'customer': 'C', 'cost': 966}, {'facility': 'F1', 'customer': 'D', 'cost': 913}, {'facility': 'F1', 'customer': 'E', 'cost': 299}, {'facility': 'F1', 'customer': 'F', 'cost': 234}, {'facility': 'F1', 'customer': 'G', 'cost': 670}, {'facility': 'F1', 'customer': 'H', 'cost': 80}, {'facility': 'F1', 'customer': 'I', 'cost': 675}, {'facility': 'F1', 'customer': 'J', 'cost': 281}, {'facility': 'F1', 'customer': 'K', 'cost': 834}, {'facility': 'F2', 'customer': 'A', 'cost': 847}, {'facility': 'F2', 'customer': 'B', 'cost': 391}, {'facility': 'F2', 'customer': 'C', 'cost': 620}, {'facility': 'F2', 'customer': 'D', 'cost': 874}, {'facility': 'F2', 'customer': 'E', 'cost': 341}, {'facility': 'F2', 'customer': 'F', 'cost': 753}, {'facility': 'F2', 'customer': 'G', 'cost': 88}, {'facility': 'F2', 'customer': 'H', 'cost': 600}, {'facility': 'F2', 'customer': 'I', 'cost': 292}, {'facility': 'F2', 'customer': 'J', 'cost': 442}, {'facility': 'F2', 'customer': 'K', 'cost': 998}, {'facility': 'F3', 'customer': 'A', 'cost': 44}, {'facility': 'F3', 'customer': 'B', 'cost': 166}, {'facility': 'F3', 'customer': 'C', 'cost': 346}, {'facility': 'F3', 'customer': 'D', 'cost': 862}, {'facility': 'F3', 'customer': 'E', 'cost': 27}, {'facility': 'F3', 'customer': 'F', 'cost': 116}, {'facility': 'F3', 'customer': 'G', 'cost': 579}, {'facility': 'F3', 'customer': 'H', 'cost': 745}, {'facility': 'F3', 'customer': 'I', 'cost': 267}, {'facility': 'F3', 'customer': 'J', 'cost': 499}, {'facility': 'F3', 'customer': 'K', 'cost': 295}, {'facility': 'F4', 'customer': 'A', 'cost': 999}, {'facility': 'F4', 'customer': 'B', 'cost': 601}, {'facility': 'F4', 'customer': 'C', 'cost': 476}, {'facility': 'F4', 'customer': 'D', 'cost': 26}, {'facility': 'F4', 'customer': 'E', 'cost': 90}, {'facility': 'F4', 'customer': 'F', 'cost': 176}, {'facility': 'F4', 'customer': 'G', 'cost': 828}, {'facility': 'F4', 'customer': 'H', 'cost': 280}, {'facility': 'F4', 'customer': 'I', 'cost': 664}, {'facility': 'F4', 'customer': 'J', 'cost': 211}, {'facility': 'F4', 'customer': 'K', 'cost': 877}], 'objective': 5946.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",9,markdown_table,names
UFLP,UFLP,"Our team is sketching out where to place repair kiosks along the loop: there are candidate locations and a list of riders who might stop by. The job is to pick which locations to actually install and then assign every single rider to one of those installed kiosks. A good layout minimizes the overall cost — sum up the installation costs for the kiosks that are built plus the extra miles (or cost) riders take to reach their assigned kiosk, and prefer the plan with the smallest total. Kiosks not built are off-limits, and built kiosks can serve unlimited riders. The detailed instance information is below.
# num_kiosk_locations=4
# num_riders=9
# KIOSKS
kiosk_id,installation_cost
F1,1009
F2,2688
F3,1290
F4,5752
# RIDERS
rider_id
A
B
C
D
E
F
G
H
I
# DETOUR_DISTANCE_ORS
kiosk_id,rider_id,detour_distance_or_cost
F1,A,507
F1,B,833
F1,C,596
F1,D,869
F1,E,606
F1,F,430
F1,G,418
F1,H,461
F1,I,908
F2,A,970
F2,B,886
F2,C,401
F2,D,957
F2,E,799
F2,F,799
F2,G,640
F2,H,71
F2,I,499
F3,A,228
F3,B,783
F3,C,108
F3,D,855
F3,E,41
F3,F,474
F3,G,621
F3,H,579
F3,I,448
F4,A,75
F4,B,989
F4,C,659
F4,D,53
F4,E,323
F4,F,746
F4,G,101
F4,H,872
F4,I,45
You can just send the plan back in a small JSON file like this so it's easy to check and parse.
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<assigned_site>, <assigned_site>, ...]
}
}
Think of it like a simple form: ""selected"" is the list of kiosk locations you choose to build, and ""assignments"" tells, for each rider (in the same order they were listed in the input), which opened kiosk they will use. This is just the expected shape — not the actual answer — so fill in the real IDs from the instance when you submit.
Please make sure to use the exact identifiers from the input — do not rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1009, 2688, 1290, 5752], 'connection_costs': [[507, 833, 596, 869, 606, 430, 418, 461, 908], [970, 886, 401, 957, 799, 799, 640, 71, 499], [228, 783, 108, 855, 41, 474, 621, 579, 448], [75, 989, 659, 53, 323, 746, 101, 872, 45]], 'objective': 5427.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2, 2]}",5427.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 9, 'facilities': [{'id': 'F1', 'opening_cost': 1009}, {'id': 'F2', 'opening_cost': 2688}, {'id': 'F3', 'opening_cost': 1290}, {'id': 'F4', 'opening_cost': 5752}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 507}, {'facility': 'F1', 'customer': 'B', 'cost': 833}, {'facility': 'F1', 'customer': 'C', 'cost': 596}, {'facility': 'F1', 'customer': 'D', 'cost': 869}, {'facility': 'F1', 'customer': 'E', 'cost': 606}, {'facility': 'F1', 'customer': 'F', 'cost': 430}, {'facility': 'F1', 'customer': 'G', 'cost': 418}, {'facility': 'F1', 'customer': 'H', 'cost': 461}, {'facility': 'F1', 'customer': 'I', 'cost': 908}, {'facility': 'F2', 'customer': 'A', 'cost': 970}, {'facility': 'F2', 'customer': 'B', 'cost': 886}, {'facility': 'F2', 'customer': 'C', 'cost': 401}, {'facility': 'F2', 'customer': 'D', 'cost': 957}, {'facility': 'F2', 'customer': 'E', 'cost': 799}, {'facility': 'F2', 'customer': 'F', 'cost': 799}, {'facility': 'F2', 'customer': 'G', 'cost': 640}, {'facility': 'F2', 'customer': 'H', 'cost': 71}, {'facility': 'F2', 'customer': 'I', 'cost': 499}, {'facility': 'F3', 'customer': 'A', 'cost': 228}, {'facility': 'F3', 'customer': 'B', 'cost': 783}, {'facility': 'F3', 'customer': 'C', 'cost': 108}, {'facility': 'F3', 'customer': 'D', 'cost': 855}, {'facility': 'F3', 'customer': 'E', 'cost': 41}, {'facility': 'F3', 'customer': 'F', 'cost': 474}, {'facility': 'F3', 'customer': 'G', 'cost': 621}, {'facility': 'F3', 'customer': 'H', 'cost': 579}, {'facility': 'F3', 'customer': 'I', 'cost': 448}, {'facility': 'F4', 'customer': 'A', 'cost': 75}, {'facility': 'F4', 'customer': 'B', 'cost': 989}, {'facility': 'F4', 'customer': 'C', 'cost': 659}, {'facility': 'F4', 'customer': 'D', 'cost': 53}, {'facility': 'F4', 'customer': 'E', 'cost': 323}, {'facility': 'F4', 'customer': 'F', 'cost': 746}, {'facility': 'F4', 'customer': 'G', 'cost': 101}, {'facility': 'F4', 'customer': 'H', 'cost': 872}, {'facility': 'F4', 'customer': 'I', 'cost': 45}], 'objective': 5427.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",10,csv,names
UFLP,UFLP,"Someone on the relief team has to decide which supply caches to put resources into and which stocked cache each household should use. The rule is simple: each household must be assigned to one stocked cache only, and they can’t go to caches we didn’t stock. What we’re trying to do, practically, is keep the total expense down — that total is just the stocking bills for the caches we pick plus the retrieval distance or travel cost for every household, all added together. The candidate locations, costs, and household distances are shown below.
We have 4 candidate caches, 10 households, and stocking costs 1246, 1777, 1385, 1078.
Cache F1 costs 1246 to stock.
Cache F2 costs 1777 to stock.
Cache F3 costs 1385 to stock.
Cache F4 costs 1078 to stock.
If we serve household 0 from cache F1, the travel cost is 573.
If we serve household 1 from cache F1, the travel cost is 878.
If we serve household 2 from cache F1, the travel cost is 303.
If we serve household 3 from cache F1, the travel cost is 931.
If we serve household 4 from cache F1, the travel cost is 504.
If we serve household 5 from cache F1, the travel cost is 990.
If we serve household 6 from cache F1, the travel cost is 725.
If we serve household 7 from cache F1, the travel cost is 110.
If we serve household 8 from cache F1, the travel cost is 233.
If we serve household 9 from cache F1, the travel cost is 115.
If we serve household 0 from cache F2, the travel cost is 933.
If we serve household 1 from cache F2, the travel cost is 73.
If we serve household 2 from cache F2, the travel cost is 282.
If we serve household 3 from cache F2, the travel cost is 947.
If we serve household 4 from cache F2, the travel cost is 786.
If we serve household 5 from cache F2, the travel cost is 776.
If we serve household 6 from cache F2, the travel cost is 644.
If we serve household 7 from cache F2, the travel cost is 104.
If we serve household 8 from cache F2, the travel cost is 212.
If we serve household 9 from cache F2, the travel cost is 301.
If we serve household 0 from cache F3, the travel cost is 33.
If we serve household 1 from cache F3, the travel cost is 679.
If we serve household 2 from cache F3, the travel cost is 519.
If we serve household 3 from cache F3, the travel cost is 523.
If we serve household 4 from cache F3, the travel cost is 824.
If we serve household 5 from cache F3, the travel cost is 924.
If we serve household 6 from cache F3, the travel cost is 337.
If we serve household 7 from cache F3, the travel cost is 29.
If we serve household 8 from cache F3, the travel cost is 621.
If we serve household 9 from cache F3, the travel cost is 667.
If we serve household 0 from cache F4, the travel cost is 179.
If we serve household 1 from cache F4, the travel cost is 462.
If we serve household 2 from cache F4, the travel cost is 736.
If we serve household 3 from cache F4, the travel cost is 834.
If we serve household 4 from cache F4, the travel cost is 936.
If we serve household 5 from cache F4, the travel cost is 395.
If we serve household 6 from cache F4, the travel cost is 275.
If we serve household 7 from cache F4, the travel cost is 925.
If we serve household 8 from cache F4, the travel cost is 903.
If we serve household 9 from cache F4, the travel cost is 3.
We’ll use these entries to choose which caches to stock and which stocked cache each household should use.
If you want to hand me the plan, just follow this simple JSON shape so I can read it automatically — nothing fancy, just a small form to fill in.
{
""solution"": {
""selected"": [<cache_to_stock>, <cache_to_stock>, ...],
""assignments"": [<chosen_stocked_cache>, <chosen_stocked_cache>, ...]
}
}
Think of ""selected"" as the list of caches we decide to stock, and ""assignments"" as, for each household in the same order as the input, which stocked cache they will use. Super casual: ""selected"" = which caches we put supplies into; ""assignments"" = which stocked cache each household goes to.
This JSON is just a sketch of the shape I expect in the answer — not the actual plan itself.
Please use the exact identifiers from the instance input when you fill this in — no renaming and no new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1246, 1777, 1385, 1078], 'connection_costs': [[573, 878, 303, 931, 504, 990, 725, 110, 233, 115], [933, 73, 282, 947, 786, 776, 644, 104, 212, 301], [33, 679, 519, 523, 824, 924, 337, 29, 621, 667], [179, 462, 736, 834, 936, 395, 275, 925, 903, 3]], 'objective': 5622.0}","{'open_facilities': [0, 3], 'assignments': [3, 3, 0, 3, 0, 3, 3, 0, 0, 3]}",5622.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 10, 'facilities': [{'id': 'F1', 'opening_cost': 1246}, {'id': 'F2', 'opening_cost': 1777}, {'id': 'F3', 'opening_cost': 1385}, {'id': 'F4', 'opening_cost': 1078}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 573}, {'facility': 'F1', 'customer': 1, 'cost': 878}, {'facility': 'F1', 'customer': 2, 'cost': 303}, {'facility': 'F1', 'customer': 3, 'cost': 931}, {'facility': 'F1', 'customer': 4, 'cost': 504}, {'facility': 'F1', 'customer': 5, 'cost': 990}, {'facility': 'F1', 'customer': 6, 'cost': 725}, {'facility': 'F1', 'customer': 7, 'cost': 110}, {'facility': 'F1', 'customer': 8, 'cost': 233}, {'facility': 'F1', 'customer': 9, 'cost': 115}, {'facility': 'F2', 'customer': 0, 'cost': 933}, {'facility': 'F2', 'customer': 1, 'cost': 73}, {'facility': 'F2', 'customer': 2, 'cost': 282}, {'facility': 'F2', 'customer': 3, 'cost': 947}, {'facility': 'F2', 'customer': 4, 'cost': 786}, {'facility': 'F2', 'customer': 5, 'cost': 776}, {'facility': 'F2', 'customer': 6, 'cost': 644}, {'facility': 'F2', 'customer': 7, 'cost': 104}, {'facility': 'F2', 'customer': 8, 'cost': 212}, {'facility': 'F2', 'customer': 9, 'cost': 301}, {'facility': 'F3', 'customer': 0, 'cost': 33}, {'facility': 'F3', 'customer': 1, 'cost': 679}, {'facility': 'F3', 'customer': 2, 'cost': 519}, {'facility': 'F3', 'customer': 3, 'cost': 523}, {'facility': 'F3', 'customer': 4, 'cost': 824}, {'facility': 'F3', 'customer': 5, 'cost': 924}, {'facility': 'F3', 'customer': 6, 'cost': 337}, {'facility': 'F3', 'customer': 7, 'cost': 29}, {'facility': 'F3', 'customer': 8, 'cost': 621}, {'facility': 'F3', 'customer': 9, 'cost': 667}, {'facility': 'F4', 'customer': 0, 'cost': 179}, {'facility': 'F4', 'customer': 1, 'cost': 462}, {'facility': 'F4', 'customer': 2, 'cost': 736}, {'facility': 'F4', 'customer': 3, 'cost': 834}, {'facility': 'F4', 'customer': 4, 'cost': 936}, {'facility': 'F4', 'customer': 5, 'cost': 395}, {'facility': 'F4', 'customer': 6, 'cost': 275}, {'facility': 'F4', 'customer': 7, 'cost': 925}, {'facility': 'F4', 'customer': 8, 'cost': 903}, {'facility': 'F4', 'customer': 9, 'cost': 3}], 'objective': 5622.0}","{'selected': ['F1', 'F4'], 'assignments': ['F4', 'F4', 'F1', 'F4', 'F1', 'F4', 'F4', 'F1', 'F1', 'F4']}",11,nl,0
UFLP,UFLP,"At the festival gates the problem is practical: decide which vendor stalls to lease and assign every artisan to one leased stall. Leasing a stall costs money, only leased stalls can be used, and each artisan needs a single stall (no doubles, no omissions). Festival-goers will head to a single vendor, and the final tally is the rent paid for the leased stalls plus the total walking distance of all attendees to their vendor — the task is to make that tally as small as it can be. Concrete data follows below.
There are 4 stalls and 9 attendees in this instance.
**Stalls**
| stall_id | stall_rent |
|---|---|
| F1 | 1251 |
| F2 | 1780 |
| F3 | 1764 |
| F4 | 1638 |
**Attendees**
| attendee_id |
|---|
| 0 |
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| 7 |
| 8 |
**Walking Distance Cost**
| stall_id | attendee_id | walking_distance_cost |
|---|---|---|
| F1 | 0 | 243 |
| F1 | 1 | 988 |
| F1 | 2 | 980 |
| F1 | 3 | 364 |
| F1 | 4 | 735 |
| F1 | 5 | 359 |
| F1 | 6 | 241 |
| F1 | 7 | 798 |
| F1 | 8 | 474 |
| F2 | 0 | 546 |
| F2 | 1 | 92 |
| F2 | 2 | 676 |
| F2 | 3 | 866 |
| F2 | 4 | 426 |
| F2 | 5 | 693 |
| F2 | 6 | 100 |
| F2 | 7 | 455 |
| F2 | 8 | 721 |
| F3 | 0 | 760 |
| F3 | 1 | 389 |
| F3 | 2 | 428 |
| F3 | 3 | 645 |
| F3 | 4 | 896 |
| F3 | 5 | 423 |
| F3 | 6 | 967 |
| F3 | 7 | 322 |
| F3 | 8 | 512 |
| F4 | 0 | 37 |
| F4 | 1 | 718 |
| F4 | 2 | 875 |
| F4 | 3 | 933 |
| F4 | 4 | 328 |
| F4 | 5 | 17 |
| F4 | 6 | 894 |
| F4 | 7 | 693 |
| F4 | 8 | 312 |
Also, just so we're on the same page, please return your choice in this little JSON layout — keeps things tidy and machine-friendly:
{
""solution"": {
""selected"": [<stall_to_lease>, <stall_to_lease>, ...],
""assignments"": [<leased_stall_for_artisan>, <leased_stall_for_artisan>, ...]
}
}
""selected"" is the list of stalls you decide to lease. ""assignments"" is a list with one entry per artisan saying which leased stall they will use. Think of it like filling out a simple form: pick the stalls, then point each artisan to one of the picked stalls.
This JSON is just the outline of the shape I expect — not the actual answer. Please make sure every identifier you put in here matches exactly the identifiers in the instance input — don't rename them and don't invent new ones.
- for example: Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [1251, 1780, 1764, 1638], 'connection_costs': [[243, 988, 980, 364, 735, 359, 241, 798, 474], [546, 92, 676, 866, 426, 693, 100, 455, 721], [760, 389, 428, 645, 896, 423, 967, 322, 512], [37, 718, 875, 933, 328, 17, 894, 693, 312]], 'objective': 6220.0}","{'open_facilities': [0, 1], 'assignments': [0, 1, 1, 0, 1, 0, 1, 1, 0]}",6220.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 9, 'facilities': [{'id': 'F1', 'opening_cost': 1251}, {'id': 'F2', 'opening_cost': 1780}, {'id': 'F3', 'opening_cost': 1764}, {'id': 'F4', 'opening_cost': 1638}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 243}, {'facility': 'F1', 'customer': 1, 'cost': 988}, {'facility': 'F1', 'customer': 2, 'cost': 980}, {'facility': 'F1', 'customer': 3, 'cost': 364}, {'facility': 'F1', 'customer': 4, 'cost': 735}, {'facility': 'F1', 'customer': 5, 'cost': 359}, {'facility': 'F1', 'customer': 6, 'cost': 241}, {'facility': 'F1', 'customer': 7, 'cost': 798}, {'facility': 'F1', 'customer': 8, 'cost': 474}, {'facility': 'F2', 'customer': 0, 'cost': 546}, {'facility': 'F2', 'customer': 1, 'cost': 92}, {'facility': 'F2', 'customer': 2, 'cost': 676}, {'facility': 'F2', 'customer': 3, 'cost': 866}, {'facility': 'F2', 'customer': 4, 'cost': 426}, {'facility': 'F2', 'customer': 5, 'cost': 693}, {'facility': 'F2', 'customer': 6, 'cost': 100}, {'facility': 'F2', 'customer': 7, 'cost': 455}, {'facility': 'F2', 'customer': 8, 'cost': 721}, {'facility': 'F3', 'customer': 0, 'cost': 760}, {'facility': 'F3', 'customer': 1, 'cost': 389}, {'facility': 'F3', 'customer': 2, 'cost': 428}, {'facility': 'F3', 'customer': 3, 'cost': 645}, {'facility': 'F3', 'customer': 4, 'cost': 896}, {'facility': 'F3', 'customer': 5, 'cost': 423}, {'facility': 'F3', 'customer': 6, 'cost': 967}, {'facility': 'F3', 'customer': 7, 'cost': 322}, {'facility': 'F3', 'customer': 8, 'cost': 512}, {'facility': 'F4', 'customer': 0, 'cost': 37}, {'facility': 'F4', 'customer': 1, 'cost': 718}, {'facility': 'F4', 'customer': 2, 'cost': 875}, {'facility': 'F4', 'customer': 3, 'cost': 933}, {'facility': 'F4', 'customer': 4, 'cost': 328}, {'facility': 'F4', 'customer': 5, 'cost': 17}, {'facility': 'F4', 'customer': 6, 'cost': 894}, {'facility': 'F4', 'customer': 7, 'cost': 693}, {'facility': 'F4', 'customer': 8, 'cost': 312}], 'objective': 6220.0}","{'selected': ['F1', 'F2'], 'assignments': ['F1', 'F2', 'F2', 'F1', 'F2', 'F1', 'F2', 'F2', 'F1']}",12,markdown_table,0
UFLP,UFLP,"Someone in charge needs to figure out which remote work pods to put up on campus and how to seat the freelancers. The rule is every freelancer gets assigned to one and only one of the pods that were actually installed — no double-assignments and no sending anyone to a non-existent pod. The best setup is the one that keeps the total cost down, where that total is the sum of all pod installation charges plus all freelancers’ commuting inconvenience to their assigned pod. The specific instance details follow below.
# num_candidate_pods=5
# num_freelancers=10
# PODS
pod_id,pod_setup_cost
F1,2000
F2,2000
F3,2000
F4,2000
F5,2000
# FREELANCERS
freelancer_id
0
1
2
3
4
5
6
7
8
9
# COMMUTE_INCONVENIENCES
pod_id,freelancer_id,commute_inconvenience_cost
F1,0,910
F1,1,848
F1,2,172
F1,3,809
F1,4,405
F1,5,118
F1,6,633
F1,7,439
F1,8,315
F1,9,92
F2,0,435
F2,1,729
F2,2,443
F2,3,146
F2,4,839
F2,5,152
F2,6,248
F2,7,936
F2,8,861
F2,9,12
F3,0,897
F3,1,754
F3,2,204
F3,3,576
F3,4,449
F3,5,455
F3,6,49
F3,7,310
F3,8,914
F3,9,954
F4,0,822
F4,1,835
F4,2,495
F4,3,862
F4,4,880
F4,5,699
F4,6,855
F4,7,415
F4,8,203
F4,9,49
F5,0,720
F5,1,123
F5,2,58
F5,3,76
F5,4,909
F5,5,517
F5,6,851
F5,7,719
F5,8,490
F5,9,422
So, when you send the answer back, a little JSON sketch like this is perfect — just showing which pods you actually install and which pod each freelancer is sent to:
{
""solution"": {
""selected"": [<pod_to_install>, <pod_to_install>, ...],
""assignments"": [<assigned_pod>, <assigned_pod>, ...]
}
}
""selected"" is where you list the pods you put up (one entry per pod). ""assignments"" lists, in order, the pod each freelancer uses — one entry per freelancer. Super informal: think of ""selected"" as the installations box and ""assignments"" as the seating map. This is only the shape I expect, not the final choices.
Please use the exact identifiers from the instance input — do not rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000, 2000], 'connection_costs': [[910, 848, 172, 809, 405, 118, 633, 439, 315, 92], [435, 729, 443, 146, 839, 152, 248, 936, 861, 12], [897, 754, 204, 576, 449, 455, 49, 310, 914, 954], [822, 835, 495, 862, 880, 699, 855, 415, 203, 49], [720, 123, 58, 76, 909, 517, 851, 719, 490, 422]], 'objective': 6741.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}",6741.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 10, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 910}, {'facility': 'F1', 'customer': 1, 'cost': 848}, {'facility': 'F1', 'customer': 2, 'cost': 172}, {'facility': 'F1', 'customer': 3, 'cost': 809}, {'facility': 'F1', 'customer': 4, 'cost': 405}, {'facility': 'F1', 'customer': 5, 'cost': 118}, {'facility': 'F1', 'customer': 6, 'cost': 633}, {'facility': 'F1', 'customer': 7, 'cost': 439}, {'facility': 'F1', 'customer': 8, 'cost': 315}, {'facility': 'F1', 'customer': 9, 'cost': 92}, {'facility': 'F2', 'customer': 0, 'cost': 435}, {'facility': 'F2', 'customer': 1, 'cost': 729}, {'facility': 'F2', 'customer': 2, 'cost': 443}, {'facility': 'F2', 'customer': 3, 'cost': 146}, {'facility': 'F2', 'customer': 4, 'cost': 839}, {'facility': 'F2', 'customer': 5, 'cost': 152}, {'facility': 'F2', 'customer': 6, 'cost': 248}, {'facility': 'F2', 'customer': 7, 'cost': 936}, {'facility': 'F2', 'customer': 8, 'cost': 861}, {'facility': 'F2', 'customer': 9, 'cost': 12}, {'facility': 'F3', 'customer': 0, 'cost': 897}, {'facility': 'F3', 'customer': 1, 'cost': 754}, {'facility': 'F3', 'customer': 2, 'cost': 204}, {'facility': 'F3', 'customer': 3, 'cost': 576}, {'facility': 'F3', 'customer': 4, 'cost': 449}, {'facility': 'F3', 'customer': 5, 'cost': 455}, {'facility': 'F3', 'customer': 6, 'cost': 49}, {'facility': 'F3', 'customer': 7, 'cost': 310}, {'facility': 'F3', 'customer': 8, 'cost': 914}, {'facility': 'F3', 'customer': 9, 'cost': 954}, {'facility': 'F4', 'customer': 0, 'cost': 822}, {'facility': 'F4', 'customer': 1, 'cost': 835}, {'facility': 'F4', 'customer': 2, 'cost': 495}, {'facility': 'F4', 'customer': 3, 'cost': 862}, {'facility': 'F4', 'customer': 4, 'cost': 880}, {'facility': 'F4', 'customer': 5, 'cost': 699}, {'facility': 'F4', 'customer': 6, 'cost': 855}, {'facility': 'F4', 'customer': 7, 'cost': 415}, {'facility': 'F4', 'customer': 8, 'cost': 203}, {'facility': 'F4', 'customer': 9, 'cost': 49}, {'facility': 'F5', 'customer': 0, 'cost': 720}, {'facility': 'F5', 'customer': 1, 'cost': 123}, {'facility': 'F5', 'customer': 2, 'cost': 58}, {'facility': 'F5', 'customer': 3, 'cost': 76}, {'facility': 'F5', 'customer': 4, 'cost': 909}, {'facility': 'F5', 'customer': 5, 'cost': 517}, {'facility': 'F5', 'customer': 6, 'cost': 851}, {'facility': 'F5', 'customer': 7, 'cost': 719}, {'facility': 'F5', 'customer': 8, 'cost': 490}, {'facility': 'F5', 'customer': 9, 'cost': 422}], 'objective': 6741.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",13,csv,0
UFLP,UFLP,"In our district the administrator must choose which temporary classroom trailers to bring in and then put every after-school student into one of the trailers that arrived. The decision is to select which trailers to bring and then assign each student to exactly one of those brought trailers (students can’t go to trailers that weren’t brought, and nobody gets left without an assignment). What makes one plan preferable is the total cost you end up with — add together the cost to bring the chosen trailers plus the travel-time cost for every student getting to their assigned trailer; the plan with the lowest combined total is best. Trailers can hold any number of students, and the concrete details will be shown below.
{
""num_candidate_trailers"": 5,
""num_students"": 11,
""trailers"": [
{
""trailer_id"": ""F1"",
""trailer_bring_cost"": 1000
},
{
""trailer_id"": ""F2"",
""trailer_bring_cost"": 1000
},
{
""trailer_id"": ""F3"",
""trailer_bring_cost"": 1000
},
{
""trailer_id"": ""F4"",
""trailer_bring_cost"": 1000
},
{
""trailer_id"": ""F5"",
""trailer_bring_cost"": 1000
}
],
""students"": [
{
""student_id"": 0
},
{
""student_id"": 1
},
{
""student_id"": 2
},
{
""student_id"": 3
},
{
""student_id"": 4
},
{
""student_id"": 5
},
{
""student_id"": 6
},
{
""student_id"": 7
},
{
""student_id"": 8
},
{
""student_id"": 9
},
{
""student_id"": 10
}
],
""student_travel_times"": [
{
""trailer_id"": ""F1"",
""student_id"": 0,
""student_travel_time_cost"": 513
},
{
""trailer_id"": ""F1"",
""student_id"": 1,
""student_travel_time_cost"": 435
},
{
""trailer_id"": ""F1"",
""student_id"": 2,
""student_travel_time_cost"": 467
},
{
""trailer_id"": ""F1"",
""student_id"": 3,
""student_travel_time_cost"": 605
},
{
""trailer_id"": ""F1"",
""student_id"": 4,
""student_travel_time_cost"": 305
},
{
""trailer_id"": ""F1"",
""student_id"": 5,
""student_travel_time_cost"": 376
},
{
""trailer_id"": ""F1"",
""student_id"": 6,
""student_travel_time_cost"": 152
},
{
""trailer_id"": ""F1"",
""student_id"": 7,
""student_travel_time_cost"": 427
},
{
""trailer_id"": ""F1"",
""student_id"": 8,
""student_travel_time_cost"": 470
},
{
""trailer_id"": ""F1"",
""student_id"": 9,
""student_travel_time_cost"": 851
},
{
""trailer_id"": ""F1"",
""student_id"": 10,
""student_travel_time_cost"": 185
},
{
""trailer_id"": ""F2"",
""student_id"": 0,
""student_travel_time_cost"": 226
},
{
""trailer_id"": ""F2"",
""student_id"": 1,
""student_travel_time_cost"": 639
},
{
""trailer_id"": ""F2"",
""student_id"": 2,
""student_travel_time_cost"": 346
},
{
""trailer_id"": ""F2"",
""student_id"": 3,
""student_travel_time_cost"": 719
},
{
""trailer_id"": ""F2"",
""student_id"": 4,
""student_travel_time_cost"": 86
},
{
""trailer_id"": ""F2"",
""student_id"": 5,
""student_travel_time_cost"": 580
},
{
""trailer_id"": ""F2"",
""student_id"": 6,
""student_travel_time_cost"": 589
},
{
""trailer_id"": ""F2"",
""student_id"": 7,
""student_travel_time_cost"": 852
},
{
""trailer_id"": ""F2"",
""student_id"": 8,
""student_travel_time_cost"": 671
},
{
""trailer_id"": ""F2"",
""student_id"": 9,
""student_travel_time_cost"": 786
},
{
""trailer_id"": ""F2"",
""student_id"": 10,
""student_travel_time_cost"": 873
},
{
""trailer_id"": ""F3"",
""student_id"": 0,
""student_travel_time_cost"": 257
},
{
""trailer_id"": ""F3"",
""student_id"": 1,
""student_travel_time_cost"": 381
},
{
""trailer_id"": ""F3"",
""student_id"": 2,
""student_travel_time_cost"": 431
},
{
""trailer_id"": ""F3"",
""student_id"": 3,
""student_travel_time_cost"": 667
},
{
""trailer_id"": ""F3"",
""student_id"": 4,
""student_travel_time_cost"": 732
},
{
""trailer_id"": ""F3"",
""student_id"": 5,
""student_travel_time_cost"": 867
},
{
""trailer_id"": ""F3"",
""student_id"": 6,
""student_travel_time_cost"": 964
},
{
""trailer_id"": ""F3"",
""student_id"": 7,
""student_travel_time_cost"": 563
},
{
""trailer_id"": ""F3"",
""student_id"": 8,
""student_travel_time_cost"": 702
},
{
""trailer_id"": ""F3"",
""student_id"": 9,
""student_travel_time_cost"": 495
},
{
""trailer_id"": ""F3"",
""student_id"": 10,
""student_travel_time_cost"": 525
},
{
""trailer_id"": ""F4"",
""student_id"": 0,
""student_travel_time_cost"": 121
},
{
""trailer_id"": ""F4"",
""student_id"": 1,
""student_travel_time_cost"": 448
},
{
""trailer_id"": ""F4"",
""student_id"": 2,
""student_travel_time_cost"": 114
},
{
""trailer_id"": ""F4"",
""student_id"": 3,
""student_travel_time_cost"": 623
},
{
""trailer_id"": ""F4"",
""student_id"": 4,
""student_travel_time_cost"": 325
},
{
""trailer_id"": ""F4"",
""student_id"": 5,
""student_travel_time_cost"": 583
},
{
""trailer_id"": ""F4"",
""student_id"": 6,
""student_travel_time_cost"": 307
},
{
""trailer_id"": ""F4"",
""student_id"": 7,
""student_travel_time_cost"": 910
},
{
""trailer_id"": ""F4"",
""student_id"": 8,
""student_travel_time_cost"": 860
},
{
""trailer_id"": ""F4"",
""student_id"": 9,
""student_travel_time_cost"": 691
},
{
""trailer_id"": ""F4"",
""student_id"": 10,
""student_travel_time_cost"": 522
},
{
""trailer_id"": ""F5"",
""student_id"": 0,
""student_travel_time_cost"": 764
},
{
""trailer_id"": ""F5"",
""student_id"": 1,
""student_travel_time_cost"": 746
},
{
""trailer_id"": ""F5"",
""student_id"": 2,
""student_travel_time_cost"": 284
},
{
""trailer_id"": ""F5"",
""student_id"": 3,
""student_travel_time_cost"": 853
},
{
""trailer_id"": ""F5"",
""student_id"": 4,
""student_travel_time_cost"": 44
},
{
""trailer_id"": ""F5"",
""student_id"": 5,
""student_travel_time_cost"": 40
},
{
""trailer_id"": ""F5"",
""student_id"": 6,
""student_travel_time_cost"": 443
},
{
""trailer_id"": ""F5"",
""student_id"": 7,
""student_travel_time_cost"": 140
},
{
""trailer_id"": ""F5"",
""student_id"": 8,
""student_travel_time_cost"": 447
},
{
""trailer_id"": ""F5"",
""student_id"": 9,
""student_travel_time_cost"": 304
},
{
""trailer_id"": ""F5"",
""student_id"": 10,
""student_travel_time_cost"": 279
}
]
}
If you want to send back a plan, just use this simple JSON shape so I can read it easily — nothing fancy, just a small form that says which trailers you brought and which trailer each student goes to.
{
""solution"": {
""selected"": [""<trailer_to_bring>"", ""<trailer_to_bring>"", ...],
""assignments"": [""<assigned_trailer>"", ""<assigned_trailer>"", ...]
}
}
Think of ""selected"" as the list of trailers you decided to bring in, and ""assignments"" as a student-by-student list saying which of the brought trailers each student will go to (in the same student order as the instance). Super casual — it's just a sketch of the shape I expect, not the actual answer.
Please make sure you use the exact identifiers from the instance input when you fill this in — don't rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [1000, 1000, 1000, 1000, 1000], 'connection_costs': [[513, 435, 467, 605, 305, 376, 152, 427, 470, 851, 185], [226, 639, 346, 719, 86, 580, 589, 852, 671, 786, 873], [257, 381, 431, 667, 732, 867, 964, 563, 702, 495, 525], [121, 448, 114, 623, 325, 583, 307, 910, 860, 691, 522], [764, 746, 284, 853, 44, 40, 443, 140, 447, 304, 279]], 'objective': 4867.0}","{'open_facilities': [3, 4], 'assignments': [3, 3, 3, 3, 4, 4, 3, 4, 4, 4, 4]}",4867.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}, {'id': 'F5', 'opening_cost': 1000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 513}, {'facility': 'F1', 'customer': 1, 'cost': 435}, {'facility': 'F1', 'customer': 2, 'cost': 467}, {'facility': 'F1', 'customer': 3, 'cost': 605}, {'facility': 'F1', 'customer': 4, 'cost': 305}, {'facility': 'F1', 'customer': 5, 'cost': 376}, {'facility': 'F1', 'customer': 6, 'cost': 152}, {'facility': 'F1', 'customer': 7, 'cost': 427}, {'facility': 'F1', 'customer': 8, 'cost': 470}, {'facility': 'F1', 'customer': 9, 'cost': 851}, {'facility': 'F1', 'customer': 10, 'cost': 185}, {'facility': 'F2', 'customer': 0, 'cost': 226}, {'facility': 'F2', 'customer': 1, 'cost': 639}, {'facility': 'F2', 'customer': 2, 'cost': 346}, {'facility': 'F2', 'customer': 3, 'cost': 719}, {'facility': 'F2', 'customer': 4, 'cost': 86}, {'facility': 'F2', 'customer': 5, 'cost': 580}, {'facility': 'F2', 'customer': 6, 'cost': 589}, {'facility': 'F2', 'customer': 7, 'cost': 852}, {'facility': 'F2', 'customer': 8, 'cost': 671}, {'facility': 'F2', 'customer': 9, 'cost': 786}, {'facility': 'F2', 'customer': 10, 'cost': 873}, {'facility': 'F3', 'customer': 0, 'cost': 257}, {'facility': 'F3', 'customer': 1, 'cost': 381}, {'facility': 'F3', 'customer': 2, 'cost': 431}, {'facility': 'F3', 'customer': 3, 'cost': 667}, {'facility': 'F3', 'customer': 4, 'cost': 732}, {'facility': 'F3', 'customer': 5, 'cost': 867}, {'facility': 'F3', 'customer': 6, 'cost': 964}, {'facility': 'F3', 'customer': 7, 'cost': 563}, {'facility': 'F3', 'customer': 8, 'cost': 702}, {'facility': 'F3', 'customer': 9, 'cost': 495}, {'facility': 'F3', 'customer': 10, 'cost': 525}, {'facility': 'F4', 'customer': 0, 'cost': 121}, {'facility': 'F4', 'customer': 1, 'cost': 448}, {'facility': 'F4', 'customer': 2, 'cost': 114}, {'facility': 'F4', 'customer': 3, 'cost': 623}, {'facility': 'F4', 'customer': 4, 'cost': 325}, {'facility': 'F4', 'customer': 5, 'cost': 583}, {'facility': 'F4', 'customer': 6, 'cost': 307}, {'facility': 'F4', 'customer': 7, 'cost': 910}, {'facility': 'F4', 'customer': 8, 'cost': 860}, {'facility': 'F4', 'customer': 9, 'cost': 691}, {'facility': 'F4', 'customer': 10, 'cost': 522}, {'facility': 'F5', 'customer': 0, 'cost': 764}, {'facility': 'F5', 'customer': 1, 'cost': 746}, {'facility': 'F5', 'customer': 2, 'cost': 284}, {'facility': 'F5', 'customer': 3, 'cost': 853}, {'facility': 'F5', 'customer': 4, 'cost': 44}, {'facility': 'F5', 'customer': 5, 'cost': 40}, {'facility': 'F5', 'customer': 6, 'cost': 443}, {'facility': 'F5', 'customer': 7, 'cost': 140}, {'facility': 'F5', 'customer': 8, 'cost': 447}, {'facility': 'F5', 'customer': 9, 'cost': 304}, {'facility': 'F5', 'customer': 10, 'cost': 279}], 'objective': 4867.0}","{'selected': ['F4', 'F5'], 'assignments': ['F4', 'F4', 'F4', 'F4', 'F5', 'F5', 'F4', 'F5', 'F5', 'F5', 'F5']}",14,json,0
UFLP,UFLP,"Around town the recycling squad is planning which drop-off sites to maintain and how to route every block to a single maintained site. Closed sites won’t be available, blocks can’t split their pickups, and maintained sites can serve unlimited blocks. What makes one plan better is the total sum: all the maintenance fees for the kept sites plus the distances people from each block must travel to their assigned site — the lower that combined sum, the better the plan. The specific instance details follow below.
{
""total_dropoff_sites"": 6,
""total_blocks"": 12,
""sites"": [
{
""site_id"": ""F1"",
""maintenance_fee"": 1000
},
{
""site_id"": ""F2"",
""maintenance_fee"": 1000
},
{
""site_id"": ""F3"",
""maintenance_fee"": 1000
},
{
""site_id"": ""F4"",
""maintenance_fee"": 1000
},
{
""site_id"": ""F5"",
""maintenance_fee"": 1000
},
{
""site_id"": ""F6"",
""maintenance_fee"": 1000
}
],
""blocks"": [
{
""block_id"": 0
},
{
""block_id"": 1
},
{
""block_id"": 2
},
{
""block_id"": 3
},
{
""block_id"": 4
},
{
""block_id"": 5
},
{
""block_id"": 6
},
{
""block_id"": 7
},
{
""block_id"": 8
},
{
""block_id"": 9
},
{
""block_id"": 10
},
{
""block_id"": 11
}
],
""walking_distances"": [
{
""site_id"": ""F1"",
""block_id"": 0,
""walking_distance"": 39
},
{
""site_id"": ""F1"",
""block_id"": 1,
""walking_distance"": 160
},
{
""site_id"": ""F1"",
""block_id"": 2,
""walking_distance"": 210
},
{
""site_id"": ""F1"",
""block_id"": 3,
""walking_distance"": 289
},
{
""site_id"": ""F1"",
""block_id"": 4,
""walking_distance"": 156
},
{
""site_id"": ""F1"",
""block_id"": 5,
""walking_distance"": 65
},
{
""site_id"": ""F1"",
""block_id"": 6,
""walking_distance"": 296
},
{
""site_id"": ""F1"",
""block_id"": 7,
""walking_distance"": 631
},
{
""site_id"": ""F1"",
""block_id"": 8,
""walking_distance"": 440
},
{
""site_id"": ""F1"",
""block_id"": 9,
""walking_distance"": 359
},
{
""site_id"": ""F1"",
""block_id"": 10,
""walking_distance"": 646
},
{
""site_id"": ""F1"",
""block_id"": 11,
""walking_distance"": 451
},
{
""site_id"": ""F2"",
""block_id"": 0,
""walking_distance"": 384
},
{
""site_id"": ""F2"",
""block_id"": 1,
""walking_distance"": 663
},
{
""site_id"": ""F2"",
""block_id"": 2,
""walking_distance"": 104
},
{
""site_id"": ""F2"",
""block_id"": 3,
""walking_distance"": 271
},
{
""site_id"": ""F2"",
""block_id"": 4,
""walking_distance"": 433
},
{
""site_id"": ""F2"",
""block_id"": 5,
""walking_distance"": 126
},
{
""site_id"": ""F2"",
""block_id"": 6,
""walking_distance"": 256
},
{
""site_id"": ""F2"",
""block_id"": 7,
""walking_distance"": 70
},
{
""site_id"": ""F2"",
""block_id"": 8,
""walking_distance"": 763
},
{
""site_id"": ""F2"",
""block_id"": 9,
""walking_distance"": 4
},
{
""site_id"": ""F2"",
""block_id"": 10,
""walking_distance"": 331
},
{
""site_id"": ""F2"",
""block_id"": 11,
""walking_distance"": 619
},
{
""site_id"": ""F3"",
""block_id"": 0,
""walking_distance"": 737
},
{
""site_id"": ""F3"",
""block_id"": 1,
""walking_distance"": 325
},
{
""site_id"": ""F3"",
""block_id"": 2,
""walking_distance"": 404
},
{
""site_id"": ""F3"",
""block_id"": 3,
""walking_distance"": 190
},
{
""site_id"": ""F3"",
""block_id"": 4,
""walking_distance"": 268
},
{
""site_id"": ""F3"",
""block_id"": 5,
""walking_distance"": 79
},
{
""site_id"": ""F3"",
""block_id"": 6,
""walking_distance"": 888
},
{
""site_id"": ""F3"",
""block_id"": 7,
""walking_distance"": 119
},
{
""site_id"": ""F3"",
""block_id"": 8,
""walking_distance"": 308
},
{
""site_id"": ""F3"",
""block_id"": 9,
""walking_distance"": 165
},
{
""site_id"": ""F3"",
""block_id"": 10,
""walking_distance"": 257
},
{
""site_id"": ""F3"",
""block_id"": 11,
""walking_distance"": 409
},
{
""site_id"": ""F4"",
""block_id"": 0,
""walking_distance"": 688
},
{
""site_id"": ""F4"",
""block_id"": 1,
""walking_distance"": 502
},
{
""site_id"": ""F4"",
""block_id"": 2,
""walking_distance"": 674
},
{
""site_id"": ""F4"",
""block_id"": 3,
""walking_distance"": 208
},
{
""site_id"": ""F4"",
""block_id"": 4,
""walking_distance"": 314
},
{
""site_id"": ""F4"",
""block_id"": 5,
""walking_distance"": 714
},
{
""site_id"": ""F4"",
""block_id"": 6,
""walking_distance"": 661
},
{
""site_id"": ""F4"",
""block_id"": 7,
""walking_distance"": 365
},
{
""site_id"": ""F4"",
""block_id"": 8,
""walking_distance"": 427
},
{
""site_id"": ""F4"",
""block_id"": 9,
""walking_distance"": 1
},
{
""site_id"": ""F4"",
""block_id"": 10,
""walking_distance"": 596
},
{
""site_id"": ""F4"",
""block_id"": 11,
""walking_distance"": 272
},
{
""site_id"": ""F5"",
""block_id"": 0,
""walking_distance"": 433
},
{
""site_id"": ""F5"",
""block_id"": 1,
""walking_distance"": 869
},
{
""site_id"": ""F5"",
""block_id"": 2,
""walking_distance"": 965
},
{
""site_id"": ""F5"",
""block_id"": 3,
""walking_distance"": 492
},
{
""site_id"": ""F5"",
""block_id"": 4,
""walking_distance"": 16
},
{
""site_id"": ""F5"",
""block_id"": 5,
""walking_distance"": 629
},
{
""site_id"": ""F5"",
""block_id"": 6,
""walking_distance"": 994
},
{
""site_id"": ""F5"",
""block_id"": 7,
""walking_distance"": 576
},
{
""site_id"": ""F5"",
""block_id"": 8,
""walking_distance"": 888
},
{
""site_id"": ""F5"",
""block_id"": 9,
""walking_distance"": 817
},
{
""site_id"": ""F5"",
""block_id"": 10,
""walking_distance"": 11
},
{
""site_id"": ""F5"",
""block_id"": 11,
""walking_distance"": 429
},
{
""site_id"": ""F6"",
""block_id"": 0,
""walking_distance"": 744
},
{
""site_id"": ""F6"",
""block_id"": 1,
""walking_distance"": 422
},
{
""site_id"": ""F6"",
""block_id"": 2,
""walking_distance"": 942
},
{
""site_id"": ""F6"",
""block_id"": 3,
""walking_distance"": 746
},
{
""site_id"": ""F6"",
""block_id"": 4,
""walking_distance"": 435
},
{
""site_id"": ""F6"",
""block_id"": 5,
""walking_distance"": 42
},
{
""site_id"": ""F6"",
""block_id"": 6,
""walking_distance"": 137
},
{
""site_id"": ""F6"",
""block_id"": 7,
""walking_distance"": 140
},
{
""site_id"": ""F6"",
""block_id"": 8,
""walking_distance"": 131
},
{
""site_id"": ""F6"",
""block_id"": 9,
""walking_distance"": 334
},
{
""site_id"": ""F6"",
""block_id"": 10,
""walking_distance"": 53
},
{
""site_id"": ""F6"",
""block_id"": 11,
""walking_distance"": 903
}
]
}
Also, when you send your plan back, please stick to this simple JSON layout so it's easy to check automatically.
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
Think of it like a short form: ""selected"" is the list of drop-off sites you decide to keep maintained, and ""assignments"" is, for each block in the same order as the instance, which maintained site that block will use. This JSON is just a sketch of the shape I expect — it’s not the real answer itself.
Please make sure every identifier you use matches exactly what’s in the instance input — don’t rename or invent labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1000, 1000, 1000, 1000, 1000, 1000], 'connection_costs': [[39, 160, 210, 289, 156, 65, 296, 631, 440, 359, 646, 451], [384, 663, 104, 271, 433, 126, 256, 70, 763, 4, 331, 619], [737, 325, 404, 190, 268, 79, 888, 119, 308, 165, 257, 409], [688, 502, 674, 208, 314, 714, 661, 365, 427, 1, 596, 272], [433, 869, 965, 492, 16, 629, 994, 576, 888, 817, 11, 429], [744, 422, 942, 746, 435, 42, 137, 140, 131, 334, 53, 903]], 'objective': 4142.0}","{'open_facilities': [0, 5], 'assignments': [0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 0]}",4142.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 12, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}, {'id': 'F5', 'opening_cost': 1000}, {'id': 'F6', 'opening_cost': 1000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 39}, {'facility': 'F1', 'customer': 1, 'cost': 160}, {'facility': 'F1', 'customer': 2, 'cost': 210}, {'facility': 'F1', 'customer': 3, 'cost': 289}, {'facility': 'F1', 'customer': 4, 'cost': 156}, {'facility': 'F1', 'customer': 5, 'cost': 65}, {'facility': 'F1', 'customer': 6, 'cost': 296}, {'facility': 'F1', 'customer': 7, 'cost': 631}, {'facility': 'F1', 'customer': 8, 'cost': 440}, {'facility': 'F1', 'customer': 9, 'cost': 359}, {'facility': 'F1', 'customer': 10, 'cost': 646}, {'facility': 'F1', 'customer': 11, 'cost': 451}, {'facility': 'F2', 'customer': 0, 'cost': 384}, {'facility': 'F2', 'customer': 1, 'cost': 663}, {'facility': 'F2', 'customer': 2, 'cost': 104}, {'facility': 'F2', 'customer': 3, 'cost': 271}, {'facility': 'F2', 'customer': 4, 'cost': 433}, {'facility': 'F2', 'customer': 5, 'cost': 126}, {'facility': 'F2', 'customer': 6, 'cost': 256}, {'facility': 'F2', 'customer': 7, 'cost': 70}, {'facility': 'F2', 'customer': 8, 'cost': 763}, {'facility': 'F2', 'customer': 9, 'cost': 4}, {'facility': 'F2', 'customer': 10, 'cost': 331}, {'facility': 'F2', 'customer': 11, 'cost': 619}, {'facility': 'F3', 'customer': 0, 'cost': 737}, {'facility': 'F3', 'customer': 1, 'cost': 325}, {'facility': 'F3', 'customer': 2, 'cost': 404}, {'facility': 'F3', 'customer': 3, 'cost': 190}, {'facility': 'F3', 'customer': 4, 'cost': 268}, {'facility': 'F3', 'customer': 5, 'cost': 79}, {'facility': 'F3', 'customer': 6, 'cost': 888}, {'facility': 'F3', 'customer': 7, 'cost': 119}, {'facility': 'F3', 'customer': 8, 'cost': 308}, {'facility': 'F3', 'customer': 9, 'cost': 165}, {'facility': 'F3', 'customer': 10, 'cost': 257}, {'facility': 'F3', 'customer': 11, 'cost': 409}, {'facility': 'F4', 'customer': 0, 'cost': 688}, {'facility': 'F4', 'customer': 1, 'cost': 502}, {'facility': 'F4', 'customer': 2, 'cost': 674}, {'facility': 'F4', 'customer': 3, 'cost': 208}, {'facility': 'F4', 'customer': 4, 'cost': 314}, {'facility': 'F4', 'customer': 5, 'cost': 714}, {'facility': 'F4', 'customer': 6, 'cost': 661}, {'facility': 'F4', 'customer': 7, 'cost': 365}, {'facility': 'F4', 'customer': 8, 'cost': 427}, {'facility': 'F4', 'customer': 9, 'cost': 1}, {'facility': 'F4', 'customer': 10, 'cost': 596}, {'facility': 'F4', 'customer': 11, 'cost': 272}, {'facility': 'F5', 'customer': 0, 'cost': 433}, {'facility': 'F5', 'customer': 1, 'cost': 869}, {'facility': 'F5', 'customer': 2, 'cost': 965}, {'facility': 'F5', 'customer': 3, 'cost': 492}, {'facility': 'F5', 'customer': 4, 'cost': 16}, {'facility': 'F5', 'customer': 5, 'cost': 629}, {'facility': 'F5', 'customer': 6, 'cost': 994}, {'facility': 'F5', 'customer': 7, 'cost': 576}, {'facility': 'F5', 'customer': 8, 'cost': 888}, {'facility': 'F5', 'customer': 9, 'cost': 817}, {'facility': 'F5', 'customer': 10, 'cost': 11}, {'facility': 'F5', 'customer': 11, 'cost': 429}, {'facility': 'F6', 'customer': 0, 'cost': 744}, {'facility': 'F6', 'customer': 1, 'cost': 422}, {'facility': 'F6', 'customer': 2, 'cost': 942}, {'facility': 'F6', 'customer': 3, 'cost': 746}, {'facility': 'F6', 'customer': 4, 'cost': 435}, {'facility': 'F6', 'customer': 5, 'cost': 42}, {'facility': 'F6', 'customer': 6, 'cost': 137}, {'facility': 'F6', 'customer': 7, 'cost': 140}, {'facility': 'F6', 'customer': 8, 'cost': 131}, {'facility': 'F6', 'customer': 9, 'cost': 334}, {'facility': 'F6', 'customer': 10, 'cost': 53}, {'facility': 'F6', 'customer': 11, 'cost': 903}], 'objective': 4142.0}","{'selected': ['F1', 'F6'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F6', 'F6', 'F6', 'F6', 'F6', 'F6', 'F1']}",15,json,0
UFLP,UFLP,"Someone managing the farm markets needs to pick which roadside produce stands will operate this season and assign each regular buyer to a single open stand. Better choices are those that cut the total expense, calculated by adding the operating costs for all stands left open plus the travel cost for each customer to their chosen stand. Each customer gets exactly one operating stand and nobody visits a closed one; stands aren’t capped on how many people they can serve. The exact numbers are shown below.
There are 4 candidate roadside produce stands, 9 regular buyers, and the stand opening costs are 5234, 3751, 6957, 3907.
Stand F1 has an opening cost of 5234.
Stand F2 has an opening cost of 3751.
Stand F3 has an opening cost of 6957.
Stand F4 has an opening cost of 3907.
Buyer 1 would incur travel cost 759 to visit stand F1.
Buyer 2 would incur travel cost 320 to visit stand F1.
Buyer 3 would incur travel cost 173 to visit stand F1.
Buyer 4 would incur travel cost 443 to visit stand F1.
Buyer 5 would incur travel cost 396 to visit stand F1.
Buyer 6 would incur travel cost 708 to visit stand F1.
Buyer 7 would incur travel cost 425 to visit stand F1.
Buyer 8 would incur travel cost 708 to visit stand F1.
Buyer 9 would incur travel cost 391 to visit stand F1.
Buyer 1 would incur travel cost 203 to visit stand F2.
Buyer 2 would incur travel cost 779 to visit stand F2.
Buyer 3 would incur travel cost 609 to visit stand F2.
Buyer 4 would incur travel cost 514 to visit stand F2.
Buyer 5 would incur travel cost 560 to visit stand F2.
Buyer 6 would incur travel cost 579 to visit stand F2.
Buyer 7 would incur travel cost 525 to visit stand F2.
Buyer 8 would incur travel cost 389 to visit stand F2.
Buyer 9 would incur travel cost 848 to visit stand F2.
Buyer 1 would incur travel cost 868 to visit stand F3.
Buyer 2 would incur travel cost 557 to visit stand F3.
Buyer 3 would incur travel cost 61 to visit stand F3.
Buyer 4 would incur travel cost 857 to visit stand F3.
Buyer 5 would incur travel cost 280 to visit stand F3.
Buyer 6 would incur travel cost 977 to visit stand F3.
Buyer 7 would incur travel cost 609 to visit stand F3.
Buyer 8 would incur travel cost 230 to visit stand F3.
Buyer 9 would incur travel cost 730 to visit stand F3.
Buyer 1 would incur travel cost 174 to visit stand F4.
Buyer 2 would incur travel cost 211 to visit stand F4.
Buyer 3 would incur travel cost 790 to visit stand F4.
Buyer 4 would incur travel cost 947 to visit stand F4.
Buyer 5 would incur travel cost 449 to visit stand F4.
Buyer 6 would incur travel cost 819 to visit stand F4.
Buyer 7 would incur travel cost 520 to visit stand F4.
Buyer 8 would incur travel cost 691 to visit stand F4.
Buyer 9 would incur travel cost 431 to visit stand F4.
These numbers are for the manager to use in choosing which stands to open and how to assign buyers so the total expense (stand opening costs plus travel costs) is minimized.
If you want to send me the plan in a tidy, machine-friendly way, just use this simple JSON shape below — it shows which stands to open and which open stand each buyer will go to.
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
""selected"" is the list of stands you'll keep operating this season. ""assignments"" says, for each regular buyer (in the same order as the instance), which open stand they go to. Think of it like filling out a short form: pick the open stands, then list each buyer's chosen stand. This is just a sketch of the shape I need, not the actual filled-in answer.
Please make sure to use the exact identifiers from the instance input — do not rename them or invent new ones.
Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".","{'opening_costs': [5234, 3751, 6957, 3907], 'connection_costs': [[759, 320, 173, 443, 396, 708, 425, 708, 391], [203, 779, 609, 514, 560, 579, 525, 389, 848], [868, 557, 61, 857, 280, 977, 609, 230, 730], [174, 211, 790, 947, 449, 819, 520, 691, 431]], 'objective': 8757.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1, 1, 1, 1]}",8757.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 9, 'facilities': [{'id': 'F1', 'opening_cost': 5234}, {'id': 'F2', 'opening_cost': 3751}, {'id': 'F3', 'opening_cost': 6957}, {'id': 'F4', 'opening_cost': 3907}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 759}, {'facility': 'F1', 'customer': 2, 'cost': 320}, {'facility': 'F1', 'customer': 3, 'cost': 173}, {'facility': 'F1', 'customer': 4, 'cost': 443}, {'facility': 'F1', 'customer': 5, 'cost': 396}, {'facility': 'F1', 'customer': 6, 'cost': 708}, {'facility': 'F1', 'customer': 7, 'cost': 425}, {'facility': 'F1', 'customer': 8, 'cost': 708}, {'facility': 'F1', 'customer': 9, 'cost': 391}, {'facility': 'F2', 'customer': 1, 'cost': 203}, {'facility': 'F2', 'customer': 2, 'cost': 779}, {'facility': 'F2', 'customer': 3, 'cost': 609}, {'facility': 'F2', 'customer': 4, 'cost': 514}, {'facility': 'F2', 'customer': 5, 'cost': 560}, {'facility': 'F2', 'customer': 6, 'cost': 579}, {'facility': 'F2', 'customer': 7, 'cost': 525}, {'facility': 'F2', 'customer': 8, 'cost': 389}, {'facility': 'F2', 'customer': 9, 'cost': 848}, {'facility': 'F3', 'customer': 1, 'cost': 868}, {'facility': 'F3', 'customer': 2, 'cost': 557}, {'facility': 'F3', 'customer': 3, 'cost': 61}, {'facility': 'F3', 'customer': 4, 'cost': 857}, {'facility': 'F3', 'customer': 5, 'cost': 280}, {'facility': 'F3', 'customer': 6, 'cost': 977}, {'facility': 'F3', 'customer': 7, 'cost': 609}, {'facility': 'F3', 'customer': 8, 'cost': 230}, {'facility': 'F3', 'customer': 9, 'cost': 730}, {'facility': 'F4', 'customer': 1, 'cost': 174}, {'facility': 'F4', 'customer': 2, 'cost': 211}, {'facility': 'F4', 'customer': 3, 'cost': 790}, {'facility': 'F4', 'customer': 4, 'cost': 947}, {'facility': 'F4', 'customer': 5, 'cost': 449}, {'facility': 'F4', 'customer': 6, 'cost': 819}, {'facility': 'F4', 'customer': 7, 'cost': 520}, {'facility': 'F4', 'customer': 8, 'cost': 691}, {'facility': 'F4', 'customer': 9, 'cost': 431}], 'objective': 8757.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",16,nl,1
UFLP,UFLP,"At the conservatory the director must decide which piano practice rooms to operate and then send every musician to one of those open rooms. The smart trade-off is obvious in plain terms: keep an eye on the sum of the room upkeep bills plus the walking time for all musicians, and choose the setup with the least total. Each musician is assigned to exactly one available room — closed rooms aren’t options — and open rooms can host multiple musicians without limit. The specific room costs and walking distances are listed below.
# num_rooms=5
# num_musicians=11
# ROOMS
room_id,room_upkeep_cost
F1,3855
F2,5518
F3,2501
F4,7315
F5,6976
# MUSICIANS
musician_id
0
1
2
3
4
5
6
7
8
9
10
# WALKING_TIMES
room_id,musician_id,walking_time
F1,0,968
F1,1,783
F1,2,346
F1,3,784
F1,4,10
F1,5,801
F1,6,306
F1,7,747
F1,8,674
F1,9,184
F1,10,261
F2,0,527
F2,1,560
F2,2,22
F2,3,109
F2,4,795
F2,5,712
F2,6,857
F2,7,105
F2,8,169
F2,9,450
F2,10,955
F3,0,207
F3,1,643
F3,2,696
F3,3,851
F3,4,41
F3,5,1
F3,6,330
F3,7,125
F3,8,747
F3,9,544
F3,10,110
F4,0,590
F4,1,346
F4,2,666
F4,3,701
F4,4,1
F4,5,680
F4,6,578
F4,7,480
F4,8,789
F4,9,99
F4,10,951
F5,0,451
F5,1,187
F5,2,511
F5,3,41
F5,4,678
F5,5,829
F5,6,547
F5,7,48
F5,8,371
F5,9,633
F5,10,432
You can just give the plan in a tiny JSON shape like this — it makes it easy to check which rooms get opened and where each musician is sent:
{
""solution"": {
""selected"": [<room_to_open>, <room_to_open>, ...],
""assignments"": [<chosen_open_room>, <chosen_open_room>, ...]
}
}
""selected"" is the list of practice rooms you decide to operate. ""assignments"" lists, for every musician in order, which open room they go to. Think of it like filling out a simple form: pick the rooms you’ll run, then list each musician’s room.
This is just a sketch of the shape I expect, not the actual answer. Please use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [3855, 5518, 2501, 7315, 6976], 'connection_costs': [[968, 783, 346, 784, 10, 801, 306, 747, 674, 184, 261], [527, 560, 22, 109, 795, 712, 857, 105, 169, 450, 955], [207, 643, 696, 851, 41, 1, 330, 125, 747, 544, 110], [590, 346, 666, 701, 1, 680, 578, 480, 789, 99, 951], [451, 187, 511, 41, 678, 829, 547, 48, 371, 633, 432]], 'objective': 6796.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}",6796.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 3855}, {'id': 'F2', 'opening_cost': 5518}, {'id': 'F3', 'opening_cost': 2501}, {'id': 'F4', 'opening_cost': 7315}, {'id': 'F5', 'opening_cost': 6976}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 968}, {'facility': 'F1', 'customer': 1, 'cost': 783}, {'facility': 'F1', 'customer': 2, 'cost': 346}, {'facility': 'F1', 'customer': 3, 'cost': 784}, {'facility': 'F1', 'customer': 4, 'cost': 10}, {'facility': 'F1', 'customer': 5, 'cost': 801}, {'facility': 'F1', 'customer': 6, 'cost': 306}, {'facility': 'F1', 'customer': 7, 'cost': 747}, {'facility': 'F1', 'customer': 8, 'cost': 674}, {'facility': 'F1', 'customer': 9, 'cost': 184}, {'facility': 'F1', 'customer': 10, 'cost': 261}, {'facility': 'F2', 'customer': 0, 'cost': 527}, {'facility': 'F2', 'customer': 1, 'cost': 560}, {'facility': 'F2', 'customer': 2, 'cost': 22}, {'facility': 'F2', 'customer': 3, 'cost': 109}, {'facility': 'F2', 'customer': 4, 'cost': 795}, {'facility': 'F2', 'customer': 5, 'cost': 712}, {'facility': 'F2', 'customer': 6, 'cost': 857}, {'facility': 'F2', 'customer': 7, 'cost': 105}, {'facility': 'F2', 'customer': 8, 'cost': 169}, {'facility': 'F2', 'customer': 9, 'cost': 450}, {'facility': 'F2', 'customer': 10, 'cost': 955}, {'facility': 'F3', 'customer': 0, 'cost': 207}, {'facility': 'F3', 'customer': 1, 'cost': 643}, {'facility': 'F3', 'customer': 2, 'cost': 696}, {'facility': 'F3', 'customer': 3, 'cost': 851}, {'facility': 'F3', 'customer': 4, 'cost': 41}, {'facility': 'F3', 'customer': 5, 'cost': 1}, {'facility': 'F3', 'customer': 6, 'cost': 330}, {'facility': 'F3', 'customer': 7, 'cost': 125}, {'facility': 'F3', 'customer': 8, 'cost': 747}, {'facility': 'F3', 'customer': 9, 'cost': 544}, {'facility': 'F3', 'customer': 10, 'cost': 110}, {'facility': 'F4', 'customer': 0, 'cost': 590}, {'facility': 'F4', 'customer': 1, 'cost': 346}, {'facility': 'F4', 'customer': 2, 'cost': 666}, {'facility': 'F4', 'customer': 3, 'cost': 701}, {'facility': 'F4', 'customer': 4, 'cost': 1}, {'facility': 'F4', 'customer': 5, 'cost': 680}, {'facility': 'F4', 'customer': 6, 'cost': 578}, {'facility': 'F4', 'customer': 7, 'cost': 480}, {'facility': 'F4', 'customer': 8, 'cost': 789}, {'facility': 'F4', 'customer': 9, 'cost': 99}, {'facility': 'F4', 'customer': 10, 'cost': 951}, {'facility': 'F5', 'customer': 0, 'cost': 451}, {'facility': 'F5', 'customer': 1, 'cost': 187}, {'facility': 'F5', 'customer': 2, 'cost': 511}, {'facility': 'F5', 'customer': 3, 'cost': 41}, {'facility': 'F5', 'customer': 4, 'cost': 678}, {'facility': 'F5', 'customer': 5, 'cost': 829}, {'facility': 'F5', 'customer': 6, 'cost': 547}, {'facility': 'F5', 'customer': 7, 'cost': 48}, {'facility': 'F5', 'customer': 8, 'cost': 371}, {'facility': 'F5', 'customer': 9, 'cost': 633}, {'facility': 'F5', 'customer': 10, 'cost': 432}], 'objective': 6796.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",17,csv,0
UFLP,UFLP,"We’re organizing a citywide donation drive and need to pick which potential drop-off boxes to install and then decide which installed box each donor will go to. Each possible box costs money to place, and each donor incurs some detour to reach the box they’re assigned to, so the trick is to keep the total cost down by adding all the installation fees and every donor’s extra travel; a lower total means a better rollout. Also, every donor must be routed to one single box that’s actually been installed — no duplicates, no unassigned donors, and nobody should be told to use a box that wasn’t put out. The specific locations, costs, and donor positions are listed below.
{
""total_candidate_boxes"": 6,
""total_donors"": 13,
""boxs"": [
{
""box_id"": ""F1"",
""installation_fee"": 1510
},
{
""box_id"": ""F2"",
""installation_fee"": 1032
},
{
""box_id"": ""F3"",
""installation_fee"": 1160
},
{
""box_id"": ""F4"",
""installation_fee"": 1687
},
{
""box_id"": ""F5"",
""installation_fee"": 1227
},
{
""box_id"": ""F6"",
""installation_fee"": 1784
}
],
""donors"": [
{
""donor_id"": ""A""
},
{
""donor_id"": ""B""
},
{
""donor_id"": ""C""
},
{
""donor_id"": ""D""
},
{
""donor_id"": ""E""
},
{
""donor_id"": ""F""
},
{
""donor_id"": ""G""
},
{
""donor_id"": ""H""
},
{
""donor_id"": ""I""
},
{
""donor_id"": ""J""
},
{
""donor_id"": ""K""
},
{
""donor_id"": ""L""
},
{
""donor_id"": ""M""
}
],
""donor_detours"": [
{
""box_id"": ""F1"",
""donor_id"": ""A"",
""donor_detour_cost"": 459
},
{
""box_id"": ""F1"",
""donor_id"": ""B"",
""donor_detour_cost"": 41
},
{
""box_id"": ""F1"",
""donor_id"": ""C"",
""donor_detour_cost"": 923
},
{
""box_id"": ""F1"",
""donor_id"": ""D"",
""donor_detour_cost"": 381
},
{
""box_id"": ""F1"",
""donor_id"": ""E"",
""donor_detour_cost"": 150
},
{
""box_id"": ""F1"",
""donor_id"": ""F"",
""donor_detour_cost"": 812
},
{
""box_id"": ""F1"",
""donor_id"": ""G"",
""donor_detour_cost"": 635
},
{
""box_id"": ""F1"",
""donor_id"": ""H"",
""donor_detour_cost"": 744
},
{
""box_id"": ""F1"",
""donor_id"": ""I"",
""donor_detour_cost"": 272
},
{
""box_id"": ""F1"",
""donor_id"": ""J"",
""donor_detour_cost"": 673
},
{
""box_id"": ""F1"",
""donor_id"": ""K"",
""donor_detour_cost"": 422
},
{
""box_id"": ""F1"",
""donor_id"": ""L"",
""donor_detour_cost"": 241
},
{
""box_id"": ""F1"",
""donor_id"": ""M"",
""donor_detour_cost"": 206
},
{
""box_id"": ""F2"",
""donor_id"": ""A"",
""donor_detour_cost"": 103
},
{
""box_id"": ""F2"",
""donor_id"": ""B"",
""donor_detour_cost"": 200
},
{
""box_id"": ""F2"",
""donor_id"": ""C"",
""donor_detour_cost"": 749
},
{
""box_id"": ""F2"",
""donor_id"": ""D"",
""donor_detour_cost"": 78
},
{
""box_id"": ""F2"",
""donor_id"": ""E"",
""donor_detour_cost"": 735
},
{
""box_id"": ""F2"",
""donor_id"": ""F"",
""donor_detour_cost"": 729
},
{
""box_id"": ""F2"",
""donor_id"": ""G"",
""donor_detour_cost"": 984
},
{
""box_id"": ""F2"",
""donor_id"": ""H"",
""donor_detour_cost"": 893
},
{
""box_id"": ""F2"",
""donor_id"": ""I"",
""donor_detour_cost"": 198
},
{
""box_id"": ""F2"",
""donor_id"": ""J"",
""donor_detour_cost"": 738
},
{
""box_id"": ""F2"",
""donor_id"": ""K"",
""donor_detour_cost"": 53
},
{
""box_id"": ""F2"",
""donor_id"": ""L"",
""donor_detour_cost"": 433
},
{
""box_id"": ""F2"",
""donor_id"": ""M"",
""donor_detour_cost"": 268
},
{
""box_id"": ""F3"",
""donor_id"": ""A"",
""donor_detour_cost"": 468
},
{
""box_id"": ""F3"",
""donor_id"": ""B"",
""donor_detour_cost"": 262
},
{
""box_id"": ""F3"",
""donor_id"": ""C"",
""donor_detour_cost"": 84
},
{
""box_id"": ""F3"",
""donor_id"": ""D"",
""donor_detour_cost"": 580
},
{
""box_id"": ""F3"",
""donor_id"": ""E"",
""donor_detour_cost"": 390
},
{
""box_id"": ""F3"",
""donor_id"": ""F"",
""donor_detour_cost"": 56
},
{
""box_id"": ""F3"",
""donor_id"": ""G"",
""donor_detour_cost"": 970
},
{
""box_id"": ""F3"",
""donor_id"": ""H"",
""donor_detour_cost"": 893
},
{
""box_id"": ""F3"",
""donor_id"": ""I"",
""donor_detour_cost"": 555
},
{
""box_id"": ""F3"",
""donor_id"": ""J"",
""donor_detour_cost"": 540
},
{
""box_id"": ""F3"",
""donor_id"": ""K"",
""donor_detour_cost"": 453
},
{
""box_id"": ""F3"",
""donor_id"": ""L"",
""donor_detour_cost"": 839
},
{
""box_id"": ""F3"",
""donor_id"": ""M"",
""donor_detour_cost"": 20
},
{
""box_id"": ""F4"",
""donor_id"": ""A"",
""donor_detour_cost"": 289
},
{
""box_id"": ""F4"",
""donor_id"": ""B"",
""donor_detour_cost"": 86
},
{
""box_id"": ""F4"",
""donor_id"": ""C"",
""donor_detour_cost"": 8
},
{
""box_id"": ""F4"",
""donor_id"": ""D"",
""donor_detour_cost"": 244
},
{
""box_id"": ""F4"",
""donor_id"": ""E"",
""donor_detour_cost"": 860
},
{
""box_id"": ""F4"",
""donor_id"": ""F"",
""donor_detour_cost"": 398
},
{
""box_id"": ""F4"",
""donor_id"": ""G"",
""donor_detour_cost"": 528
},
{
""box_id"": ""F4"",
""donor_id"": ""H"",
""donor_detour_cost"": 217
},
{
""box_id"": ""F4"",
""donor_id"": ""I"",
""donor_detour_cost"": 863
},
{
""box_id"": ""F4"",
""donor_id"": ""J"",
""donor_detour_cost"": 105
},
{
""box_id"": ""F4"",
""donor_id"": ""K"",
""donor_detour_cost"": 516
},
{
""box_id"": ""F4"",
""donor_id"": ""L"",
""donor_detour_cost"": 656
},
{
""box_id"": ""F4"",
""donor_id"": ""M"",
""donor_detour_cost"": 622
},
{
""box_id"": ""F5"",
""donor_id"": ""A"",
""donor_detour_cost"": 79
},
{
""box_id"": ""F5"",
""donor_id"": ""B"",
""donor_detour_cost"": 652
},
{
""box_id"": ""F5"",
""donor_id"": ""C"",
""donor_detour_cost"": 735
},
{
""box_id"": ""F5"",
""donor_id"": ""D"",
""donor_detour_cost"": 489
},
{
""box_id"": ""F5"",
""donor_id"": ""E"",
""donor_detour_cost"": 646
},
{
""box_id"": ""F5"",
""donor_id"": ""F"",
""donor_detour_cost"": 955
},
{
""box_id"": ""F5"",
""donor_id"": ""G"",
""donor_detour_cost"": 886
},
{
""box_id"": ""F5"",
""donor_id"": ""H"",
""donor_detour_cost"": 960
},
{
""box_id"": ""F5"",
""donor_id"": ""I"",
""donor_detour_cost"": 781
},
{
""box_id"": ""F5"",
""donor_id"": ""J"",
""donor_detour_cost"": 328
},
{
""box_id"": ""F5"",
""donor_id"": ""K"",
""donor_detour_cost"": 923
},
{
""box_id"": ""F5"",
""donor_id"": ""L"",
""donor_detour_cost"": 986
},
{
""box_id"": ""F5"",
""donor_id"": ""M"",
""donor_detour_cost"": 207
},
{
""box_id"": ""F6"",
""donor_id"": ""A"",
""donor_detour_cost"": 963
},
{
""box_id"": ""F6"",
""donor_id"": ""B"",
""donor_detour_cost"": 83
},
{
""box_id"": ""F6"",
""donor_id"": ""C"",
""donor_detour_cost"": 798
},
{
""box_id"": ""F6"",
""donor_id"": ""D"",
""donor_detour_cost"": 336
},
{
""box_id"": ""F6"",
""donor_id"": ""E"",
""donor_detour_cost"": 740
},
{
""box_id"": ""F6"",
""donor_id"": ""F"",
""donor_detour_cost"": 410
},
{
""box_id"": ""F6"",
""donor_id"": ""G"",
""donor_detour_cost"": 559
},
{
""box_id"": ""F6"",
""donor_id"": ""H"",
""donor_detour_cost"": 318
},
{
""box_id"": ""F6"",
""donor_id"": ""I"",
""donor_detour_cost"": 393
},
{
""box_id"": ""F6"",
""donor_id"": ""J"",
""donor_detour_cost"": 49
},
{
""box_id"": ""F6"",
""donor_id"": ""K"",
""donor_detour_cost"": 4
},
{
""box_id"": ""F6"",
""donor_id"": ""L"",
""donor_detour_cost"": 349
},
{
""box_id"": ""F6"",
""donor_id"": ""M"",
""donor_detour_cost"": 271
}
]
}
Oh, and one more practical thing — when you send the plan back, a tiny JSON sketch like the one below is perfect for me. It just lists which boxes we actually install and then, for each donor, which installed box they should go to.
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_dropbox>, <chosen_dropbox>, ...]
}
}
""selected"" is the list of drop-off box locations you decide to install. ""assignments"" is a list with one entry per donor saying which installed box they should use. Super casual: think of ""selected"" as the checklist of boxes we put out, and ""assignments"" as the little directions we hand each donor. This is just the expected shape — not the final plan itself.
Please use the exact identifiers from the instance input when filling those lists — do not rename identifiers or invent new ones.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1510, 1032, 1160, 1687, 1227, 1784], 'connection_costs': [[459, 41, 923, 381, 150, 812, 635, 744, 272, 673, 422, 241, 206], [103, 200, 749, 78, 735, 729, 984, 893, 198, 738, 53, 433, 268], [468, 262, 84, 580, 390, 56, 970, 893, 555, 540, 453, 839, 20], [289, 86, 8, 244, 860, 398, 528, 217, 863, 105, 516, 656, 622], [79, 652, 735, 489, 646, 955, 886, 960, 781, 328, 923, 986, 207], [963, 83, 798, 336, 740, 410, 559, 318, 393, 49, 4, 349, 271]], 'objective': 5929.0}","{'open_facilities': [1, 3], 'assignments': [1, 3, 3, 1, 1, 3, 3, 3, 1, 3, 1, 1, 1]}",5929.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 13, 'facilities': [{'id': 'F1', 'opening_cost': 1510}, {'id': 'F2', 'opening_cost': 1032}, {'id': 'F3', 'opening_cost': 1160}, {'id': 'F4', 'opening_cost': 1687}, {'id': 'F5', 'opening_cost': 1227}, {'id': 'F6', 'opening_cost': 1784}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}, {'id': 'L'}, {'id': 'M'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 459}, {'facility': 'F1', 'customer': 'B', 'cost': 41}, {'facility': 'F1', 'customer': 'C', 'cost': 923}, {'facility': 'F1', 'customer': 'D', 'cost': 381}, {'facility': 'F1', 'customer': 'E', 'cost': 150}, {'facility': 'F1', 'customer': 'F', 'cost': 812}, {'facility': 'F1', 'customer': 'G', 'cost': 635}, {'facility': 'F1', 'customer': 'H', 'cost': 744}, {'facility': 'F1', 'customer': 'I', 'cost': 272}, {'facility': 'F1', 'customer': 'J', 'cost': 673}, {'facility': 'F1', 'customer': 'K', 'cost': 422}, {'facility': 'F1', 'customer': 'L', 'cost': 241}, {'facility': 'F1', 'customer': 'M', 'cost': 206}, {'facility': 'F2', 'customer': 'A', 'cost': 103}, {'facility': 'F2', 'customer': 'B', 'cost': 200}, {'facility': 'F2', 'customer': 'C', 'cost': 749}, {'facility': 'F2', 'customer': 'D', 'cost': 78}, {'facility': 'F2', 'customer': 'E', 'cost': 735}, {'facility': 'F2', 'customer': 'F', 'cost': 729}, {'facility': 'F2', 'customer': 'G', 'cost': 984}, {'facility': 'F2', 'customer': 'H', 'cost': 893}, {'facility': 'F2', 'customer': 'I', 'cost': 198}, {'facility': 'F2', 'customer': 'J', 'cost': 738}, {'facility': 'F2', 'customer': 'K', 'cost': 53}, {'facility': 'F2', 'customer': 'L', 'cost': 433}, {'facility': 'F2', 'customer': 'M', 'cost': 268}, {'facility': 'F3', 'customer': 'A', 'cost': 468}, {'facility': 'F3', 'customer': 'B', 'cost': 262}, {'facility': 'F3', 'customer': 'C', 'cost': 84}, {'facility': 'F3', 'customer': 'D', 'cost': 580}, {'facility': 'F3', 'customer': 'E', 'cost': 390}, {'facility': 'F3', 'customer': 'F', 'cost': 56}, {'facility': 'F3', 'customer': 'G', 'cost': 970}, {'facility': 'F3', 'customer': 'H', 'cost': 893}, {'facility': 'F3', 'customer': 'I', 'cost': 555}, {'facility': 'F3', 'customer': 'J', 'cost': 540}, {'facility': 'F3', 'customer': 'K', 'cost': 453}, {'facility': 'F3', 'customer': 'L', 'cost': 839}, {'facility': 'F3', 'customer': 'M', 'cost': 20}, {'facility': 'F4', 'customer': 'A', 'cost': 289}, {'facility': 'F4', 'customer': 'B', 'cost': 86}, {'facility': 'F4', 'customer': 'C', 'cost': 8}, {'facility': 'F4', 'customer': 'D', 'cost': 244}, {'facility': 'F4', 'customer': 'E', 'cost': 860}, {'facility': 'F4', 'customer': 'F', 'cost': 398}, {'facility': 'F4', 'customer': 'G', 'cost': 528}, {'facility': 'F4', 'customer': 'H', 'cost': 217}, {'facility': 'F4', 'customer': 'I', 'cost': 863}, {'facility': 'F4', 'customer': 'J', 'cost': 105}, {'facility': 'F4', 'customer': 'K', 'cost': 516}, {'facility': 'F4', 'customer': 'L', 'cost': 656}, {'facility': 'F4', 'customer': 'M', 'cost': 622}, {'facility': 'F5', 'customer': 'A', 'cost': 79}, {'facility': 'F5', 'customer': 'B', 'cost': 652}, {'facility': 'F5', 'customer': 'C', 'cost': 735}, {'facility': 'F5', 'customer': 'D', 'cost': 489}, {'facility': 'F5', 'customer': 'E', 'cost': 646}, {'facility': 'F5', 'customer': 'F', 'cost': 955}, {'facility': 'F5', 'customer': 'G', 'cost': 886}, {'facility': 'F5', 'customer': 'H', 'cost': 960}, {'facility': 'F5', 'customer': 'I', 'cost': 781}, {'facility': 'F5', 'customer': 'J', 'cost': 328}, {'facility': 'F5', 'customer': 'K', 'cost': 923}, {'facility': 'F5', 'customer': 'L', 'cost': 986}, {'facility': 'F5', 'customer': 'M', 'cost': 207}, {'facility': 'F6', 'customer': 'A', 'cost': 963}, {'facility': 'F6', 'customer': 'B', 'cost': 83}, {'facility': 'F6', 'customer': 'C', 'cost': 798}, {'facility': 'F6', 'customer': 'D', 'cost': 336}, {'facility': 'F6', 'customer': 'E', 'cost': 740}, {'facility': 'F6', 'customer': 'F', 'cost': 410}, {'facility': 'F6', 'customer': 'G', 'cost': 559}, {'facility': 'F6', 'customer': 'H', 'cost': 318}, {'facility': 'F6', 'customer': 'I', 'cost': 393}, {'facility': 'F6', 'customer': 'J', 'cost': 49}, {'facility': 'F6', 'customer': 'K', 'cost': 4}, {'facility': 'F6', 'customer': 'L', 'cost': 349}, {'facility': 'F6', 'customer': 'M', 'cost': 271}], 'objective': 5929.0}","{'selected': ['F2', 'F4'], 'assignments': ['F2', 'F4', 'F4', 'F2', 'F2', 'F4', 'F4', 'F4', 'F2', 'F4', 'F2', 'F2', 'F2']}",18,json,names
UFLP,UFLP,"Recently the social services office was tasked with picking which evening soup kitchens to fund and assigning every nearby person in need to one of the funded kitchens. The rule is clear: only funded kitchens can receive people, everyone must be sent to one and only one kitchen, and any funded kitchen can serve as many people as needed. What they want is the cheapest overall arrangement — total up the funding commitments plus each person’s travel cost to their assigned kitchen, and keep that total as low as possible. Detailed numbers and locations are shown below.
There are 5 candidate evening soup kitchens, 11 nearby people in need, and the kitchen funding costs are 1000, 1000, 1000, 1000, 1000.
Kitchen F1 requires a funding commitment of 1000 to open.
Kitchen F2 requires a funding commitment of 1000 to open.
Kitchen F3 requires a funding commitment of 1000 to open.
Kitchen F4 requires a funding commitment of 1000 to open.
Kitchen F5 requires a funding commitment of 1000 to open.
Person 1 would incur a travel cost of 394 to go to kitchen F1.
Person 2 would incur a travel cost of 431 to go to kitchen F1.
Person 3 would incur a travel cost of 608 to go to kitchen F1.
Person 4 would incur a travel cost of 929 to go to kitchen F1.
Person 5 would incur a travel cost of 393 to go to kitchen F1.
Person 6 would incur a travel cost of 118 to go to kitchen F1.
Person 7 would incur a travel cost of 724 to go to kitchen F1.
Person 8 would incur a travel cost of 235 to go to kitchen F1.
Person 9 would incur a travel cost of 676 to go to kitchen F1.
Person 10 would incur a travel cost of 949 to go to kitchen F1.
Person 11 would incur a travel cost of 209 to go to kitchen F1.
Person 1 would incur a travel cost of 288 to go to kitchen F2.
Person 2 would incur a travel cost of 754 to go to kitchen F2.
Person 3 would incur a travel cost of 601 to go to kitchen F2.
Person 4 would incur a travel cost of 534 to go to kitchen F2.
Person 5 would incur a travel cost of 86 to go to kitchen F2.
Person 6 would incur a travel cost of 529 to go to kitchen F2.
Person 7 would incur a travel cost of 748 to go to kitchen F2.
Person 8 would incur a travel cost of 792 to go to kitchen F2.
Person 9 would incur a travel cost of 961 to go to kitchen F2.
Person 10 would incur a travel cost of 296 to go to kitchen F2.
Person 11 would incur a travel cost of 956 to go to kitchen F2.
Person 1 would incur a travel cost of 175 to go to kitchen F3.
Person 2 would incur a travel cost of 538 to go to kitchen F3.
Person 3 would incur a travel cost of 935 to go to kitchen F3.
Person 4 would incur a travel cost of 665 to go to kitchen F3.
Person 5 would incur a travel cost of 855 to go to kitchen F3.
Person 6 would incur a travel cost of 94 to go to kitchen F3.
Person 7 would incur a travel cost of 139 to go to kitchen F3.
Person 8 would incur a travel cost of 896 to go to kitchen F3.
Person 9 would incur a travel cost of 780 to go to kitchen F3.
Person 10 would incur a travel cost of 190 to go to kitchen F3.
Person 11 would incur a travel cost of 335 to go to kitchen F3.
Person 1 would incur a travel cost of 295 to go to kitchen F4.
Person 2 would incur a travel cost of 15 to go to kitchen F4.
Person 3 would incur a travel cost of 567 to go to kitchen F4.
Person 4 would incur a travel cost of 271 to go to kitchen F4.
Person 5 would incur a travel cost of 186 to go to kitchen F4.
Person 6 would incur a travel cost of 693 to go to kitchen F4.
Person 7 would incur a travel cost of 413 to go to kitchen F4.
Person 8 would incur a travel cost of 470 to go to kitchen F4.
Person 9 would incur a travel cost of 222 to go to kitchen F4.
Person 10 would incur a travel cost of 31 to go to kitchen F4.
Person 11 would incur a travel cost of 403 to go to kitchen F4.
Person 1 would incur a travel cost of 944 to go to kitchen F5.
Person 2 would incur a travel cost of 475 to go to kitchen F5.
Person 3 would incur a travel cost of 482 to go to kitchen F5.
Person 4 would incur a travel cost of 611 to go to kitchen F5.
Person 5 would incur a travel cost of 770 to go to kitchen F5.
Person 6 would incur a travel cost of 488 to go to kitchen F5.
Person 7 would incur a travel cost of 457 to go to kitchen F5.
Person 8 would incur a travel cost of 905 to go to kitchen F5.
Person 9 would incur a travel cost of 609 to go to kitchen F5.
Person 10 would incur a travel cost of 838 to go to kitchen F5.
Person 11 would incur a travel cost of 623 to go to kitchen F5.
The office will use these figures to choose which kitchens to fund and assign every person so the sum of funding commitments plus travel costs is minimized.
One quick thing before you go: it'd be great if you could return the final choice in a tiny JSON form so it's easy to read. Here's the relaxed shape I'm expecting — just a small sketch showing which kitchens we fund and which funded kitchen each person is sent to.
{
""solution"": {
""selected"": [<kitchen_to_fund>, <kitchen_to_fund>, ...],
""assignments"": [<assigned_kitchen>, <assigned_kitchen>, ...]
}
}
Think of it like a simple form: ""selected"" is the list of soup kitchens we decide to fund, and ""assignments"" lists, in the same order as the people in the instance, the funded kitchen each person is assigned to. This is only the expected shape — not the actual answer itself.
Please make sure all identifiers are used exactly as they appear in the instance input — do not rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1000, 1000, 1000, 1000, 1000], 'connection_costs': [[394, 431, 608, 929, 393, 118, 724, 235, 676, 949, 209], [288, 754, 601, 534, 86, 529, 748, 792, 961, 296, 956], [175, 538, 935, 665, 855, 94, 139, 896, 780, 190, 335], [295, 15, 567, 271, 186, 693, 413, 470, 222, 31, 403], [944, 475, 482, 611, 770, 488, 457, 905, 609, 838, 623]], 'objective': 4505.0}","{'open_facilities': [2, 3], 'assignments': [2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 2]}",4505.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}, {'id': 'F5', 'opening_cost': 1000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 394}, {'facility': 'F1', 'customer': 2, 'cost': 431}, {'facility': 'F1', 'customer': 3, 'cost': 608}, {'facility': 'F1', 'customer': 4, 'cost': 929}, {'facility': 'F1', 'customer': 5, 'cost': 393}, {'facility': 'F1', 'customer': 6, 'cost': 118}, {'facility': 'F1', 'customer': 7, 'cost': 724}, {'facility': 'F1', 'customer': 8, 'cost': 235}, {'facility': 'F1', 'customer': 9, 'cost': 676}, {'facility': 'F1', 'customer': 10, 'cost': 949}, {'facility': 'F1', 'customer': 11, 'cost': 209}, {'facility': 'F2', 'customer': 1, 'cost': 288}, {'facility': 'F2', 'customer': 2, 'cost': 754}, {'facility': 'F2', 'customer': 3, 'cost': 601}, {'facility': 'F2', 'customer': 4, 'cost': 534}, {'facility': 'F2', 'customer': 5, 'cost': 86}, {'facility': 'F2', 'customer': 6, 'cost': 529}, {'facility': 'F2', 'customer': 7, 'cost': 748}, {'facility': 'F2', 'customer': 8, 'cost': 792}, {'facility': 'F2', 'customer': 9, 'cost': 961}, {'facility': 'F2', 'customer': 10, 'cost': 296}, {'facility': 'F2', 'customer': 11, 'cost': 956}, {'facility': 'F3', 'customer': 1, 'cost': 175}, {'facility': 'F3', 'customer': 2, 'cost': 538}, {'facility': 'F3', 'customer': 3, 'cost': 935}, {'facility': 'F3', 'customer': 4, 'cost': 665}, {'facility': 'F3', 'customer': 5, 'cost': 855}, {'facility': 'F3', 'customer': 6, 'cost': 94}, {'facility': 'F3', 'customer': 7, 'cost': 139}, {'facility': 'F3', 'customer': 8, 'cost': 896}, {'facility': 'F3', 'customer': 9, 'cost': 780}, {'facility': 'F3', 'customer': 10, 'cost': 190}, {'facility': 'F3', 'customer': 11, 'cost': 335}, {'facility': 'F4', 'customer': 1, 'cost': 295}, {'facility': 'F4', 'customer': 2, 'cost': 15}, {'facility': 'F4', 'customer': 3, 'cost': 567}, {'facility': 'F4', 'customer': 4, 'cost': 271}, {'facility': 'F4', 'customer': 5, 'cost': 186}, {'facility': 'F4', 'customer': 6, 'cost': 693}, {'facility': 'F4', 'customer': 7, 'cost': 413}, {'facility': 'F4', 'customer': 8, 'cost': 470}, {'facility': 'F4', 'customer': 9, 'cost': 222}, {'facility': 'F4', 'customer': 10, 'cost': 31}, {'facility': 'F4', 'customer': 11, 'cost': 403}, {'facility': 'F5', 'customer': 1, 'cost': 944}, {'facility': 'F5', 'customer': 2, 'cost': 475}, {'facility': 'F5', 'customer': 3, 'cost': 482}, {'facility': 'F5', 'customer': 4, 'cost': 611}, {'facility': 'F5', 'customer': 5, 'cost': 770}, {'facility': 'F5', 'customer': 6, 'cost': 488}, {'facility': 'F5', 'customer': 7, 'cost': 457}, {'facility': 'F5', 'customer': 8, 'cost': 905}, {'facility': 'F5', 'customer': 9, 'cost': 609}, {'facility': 'F5', 'customer': 10, 'cost': 838}, {'facility': 'F5', 'customer': 11, 'cost': 623}], 'objective': 4505.0}","{'selected': ['F3', 'F4'], 'assignments': ['F3', 'F4', 'F4', 'F4', 'F4', 'F3', 'F3', 'F4', 'F4', 'F4', 'F3']}",19,nl,1
UFLP,UFLP,"Someone in charge of the building’s network has to pick which of the small servers around the floor to power, then bind each device to a single powered server. Each server has a startup cost and each device-server pair has a delay cost; the winning setup is simply the one with the lowest combined total of server power costs plus all the devices’ latency penalties. Every device must be attached to exactly one turned-on server, and the real numbers and map follow below.
They must choose among 4 candidate servers to power for 10 devices, with server startup costs 9895, 2122, 7733, 7070.
Candidate server F1 can be powered at startup cost 9895.
Candidate server F2 can be powered at startup cost 2122.
Candidate server F3 can be powered at startup cost 7733.
Candidate server F4 can be powered at startup cost 7070.
If device 0 is attached to server F1, it incurs latency cost 128.
If device 1 is attached to server F1, it incurs latency cost 22.
If device 2 is attached to server F1, it incurs latency cost 890.
If device 3 is attached to server F1, it incurs latency cost 707.
If device 4 is attached to server F1, it incurs latency cost 603.
If device 5 is attached to server F1, it incurs latency cost 436.
If device 6 is attached to server F1, it incurs latency cost 622.
If device 7 is attached to server F1, it incurs latency cost 727.
If device 8 is attached to server F1, it incurs latency cost 849.
If device 9 is attached to server F1, it incurs latency cost 254.
If device 0 is attached to server F2, it incurs latency cost 319.
If device 1 is attached to server F2, it incurs latency cost 400.
If device 2 is attached to server F2, it incurs latency cost 374.
If device 3 is attached to server F2, it incurs latency cost 803.
If device 4 is attached to server F2, it incurs latency cost 250.
If device 5 is attached to server F2, it incurs latency cost 410.
If device 6 is attached to server F2, it incurs latency cost 931.
If device 7 is attached to server F2, it incurs latency cost 464.
If device 8 is attached to server F2, it incurs latency cost 829.
If device 9 is attached to server F2, it incurs latency cost 622.
If device 0 is attached to server F3, it incurs latency cost 82.
If device 1 is attached to server F3, it incurs latency cost 793.
If device 2 is attached to server F3, it incurs latency cost 54.
If device 3 is attached to server F3, it incurs latency cost 21.
If device 4 is attached to server F3, it incurs latency cost 857.
If device 5 is attached to server F3, it incurs latency cost 625.
If device 6 is attached to server F3, it incurs latency cost 145.
If device 7 is attached to server F3, it incurs latency cost 347.
If device 8 is attached to server F3, it incurs latency cost 193.
If device 9 is attached to server F3, it incurs latency cost 565.
If device 0 is attached to server F4, it incurs latency cost 815.
If device 1 is attached to server F4, it incurs latency cost 793.
If device 2 is attached to server F4, it incurs latency cost 951.
If device 3 is attached to server F4, it incurs latency cost 12.
If device 4 is attached to server F4, it incurs latency cost 328.
If device 5 is attached to server F4, it incurs latency cost 339.
If device 6 is attached to server F4, it incurs latency cost 932.
If device 7 is attached to server F4, it incurs latency cost 132.
If device 8 is attached to server F4, it incurs latency cost 568.
If device 9 is attached to server F4, it incurs latency cost 53.
They will pick the powered servers and device attachments that minimize the total of the listed startup costs and latency penalties.
You can just hand me the answer in a tiny JSON form like this — nothing fancy, just which sites you flip on and then, for every device in order, which powered site it uses:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
""selected"" is the short list of servers (sites) you decide to power up. ""assignments"" lists, in the same order as the devices were given in the instance, the site each device is bound to. Think of it like filling out a simple form: first pick the open sites, then say where each device goes. This JSON is just the shape I need — not the real answer.
Please make sure to use the exact identifiers from the instance input — don't rename or invent labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [9895, 2122, 7733, 7070], 'connection_costs': [[128, 22, 890, 707, 603, 436, 622, 727, 849, 254], [319, 400, 374, 803, 250, 410, 931, 464, 829, 622], [82, 793, 54, 21, 857, 625, 145, 347, 193, 565], [815, 793, 951, 12, 328, 339, 932, 132, 568, 53]], 'objective': 7524.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}",7524.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 10, 'facilities': [{'id': 'F1', 'opening_cost': 9895}, {'id': 'F2', 'opening_cost': 2122}, {'id': 'F3', 'opening_cost': 7733}, {'id': 'F4', 'opening_cost': 7070}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 128}, {'facility': 'F1', 'customer': 1, 'cost': 22}, {'facility': 'F1', 'customer': 2, 'cost': 890}, {'facility': 'F1', 'customer': 3, 'cost': 707}, {'facility': 'F1', 'customer': 4, 'cost': 603}, {'facility': 'F1', 'customer': 5, 'cost': 436}, {'facility': 'F1', 'customer': 6, 'cost': 622}, {'facility': 'F1', 'customer': 7, 'cost': 727}, {'facility': 'F1', 'customer': 8, 'cost': 849}, {'facility': 'F1', 'customer': 9, 'cost': 254}, {'facility': 'F2', 'customer': 0, 'cost': 319}, {'facility': 'F2', 'customer': 1, 'cost': 400}, {'facility': 'F2', 'customer': 2, 'cost': 374}, {'facility': 'F2', 'customer': 3, 'cost': 803}, {'facility': 'F2', 'customer': 4, 'cost': 250}, {'facility': 'F2', 'customer': 5, 'cost': 410}, {'facility': 'F2', 'customer': 6, 'cost': 931}, {'facility': 'F2', 'customer': 7, 'cost': 464}, {'facility': 'F2', 'customer': 8, 'cost': 829}, {'facility': 'F2', 'customer': 9, 'cost': 622}, {'facility': 'F3', 'customer': 0, 'cost': 82}, {'facility': 'F3', 'customer': 1, 'cost': 793}, {'facility': 'F3', 'customer': 2, 'cost': 54}, {'facility': 'F3', 'customer': 3, 'cost': 21}, {'facility': 'F3', 'customer': 4, 'cost': 857}, {'facility': 'F3', 'customer': 5, 'cost': 625}, {'facility': 'F3', 'customer': 6, 'cost': 145}, {'facility': 'F3', 'customer': 7, 'cost': 347}, {'facility': 'F3', 'customer': 8, 'cost': 193}, {'facility': 'F3', 'customer': 9, 'cost': 565}, {'facility': 'F4', 'customer': 0, 'cost': 815}, {'facility': 'F4', 'customer': 1, 'cost': 793}, {'facility': 'F4', 'customer': 2, 'cost': 951}, {'facility': 'F4', 'customer': 3, 'cost': 12}, {'facility': 'F4', 'customer': 4, 'cost': 328}, {'facility': 'F4', 'customer': 5, 'cost': 339}, {'facility': 'F4', 'customer': 6, 'cost': 932}, {'facility': 'F4', 'customer': 7, 'cost': 132}, {'facility': 'F4', 'customer': 8, 'cost': 568}, {'facility': 'F4', 'customer': 9, 'cost': 53}], 'objective': 7524.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",20,nl,0
UFLP,UFLP,"Out on the road the charging crew chooses which stations to fire up and which active station each customer will visit. Switching on a station costs money, and sending a customer there causes a detour cost — every customer needs exactly one station and can’t be split between stations. The smartest choice is the one that yields the lowest total bill: total activation costs plus total customer detour costs, and the scenario’s exact details are shown below.
There are 4 stations and 11 users in this instance.
**Stations**
| station_id | activation_cost |
|---|---|
| F1 | 1419 |
| F2 | 8670 |
| F3 | 4009 |
| F4 | 8389 |
**Users**
| user_id |
|---|
| 0 |
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| 7 |
| 8 |
| 9 |
| 10 |
**Detour Cost**
| station_id | user_id | detour_cost |
|---|---|---|
| F1 | 0 | 38 |
| F1 | 1 | 901 |
| F1 | 2 | 549 |
| F1 | 3 | 898 |
| F1 | 4 | 412 |
| F1 | 5 | 934 |
| F1 | 6 | 46 |
| F1 | 7 | 736 |
| F1 | 8 | 834 |
| F1 | 9 | 800 |
| F1 | 10 | 604 |
| F2 | 0 | 65 |
| F2 | 1 | 102 |
| F2 | 2 | 130 |
| F2 | 3 | 617 |
| F2 | 4 | 802 |
| F2 | 5 | 149 |
| F2 | 6 | 595 |
| F2 | 7 | 252 |
| F2 | 8 | 61 |
| F2 | 9 | 310 |
| F2 | 10 | 899 |
| F3 | 0 | 210 |
| F3 | 1 | 70 |
| F3 | 2 | 603 |
| F3 | 3 | 983 |
| F3 | 4 | 698 |
| F3 | 5 | 660 |
| F3 | 6 | 863 |
| F3 | 7 | 752 |
| F3 | 8 | 663 |
| F3 | 9 | 95 |
| F3 | 10 | 466 |
| F4 | 0 | 805 |
| F4 | 1 | 209 |
| F4 | 2 | 695 |
| F4 | 3 | 994 |
| F4 | 4 | 697 |
| F4 | 5 | 113 |
| F4 | 6 | 774 |
| F4 | 7 | 278 |
| F4 | 8 | 614 |
| F4 | 9 | 878 |
| F4 | 10 | 368 |
Also, to keep things tidy, please return your pick in this simple JSON shape — just a quick sketch of the form I’ll read. It should look like this:
{
""solution"": {
""selected"": [<station_to_open>, <station_to_open>, ...],
""assignments"": [<chosen_open_station>, <chosen_open_station>, ...]
}
}
""selected"" is the list of stations the crew decides to switch on. ""assignments"" lists, for each customer in the input order, which opened station that customer will visit. Think of it like a filled-in form: which stations are active, and for each customer where they go.
This JSON is just the expected shape — not the actual solution itself. And one more important note: use the exact identifiers from the instance input, do not rename them or invent new labels. Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".","{'opening_costs': [1419, 8670, 4009, 8389], 'connection_costs': [[38, 901, 549, 898, 412, 934, 46, 736, 834, 800, 604], [65, 102, 130, 617, 802, 149, 595, 252, 61, 310, 899], [210, 70, 603, 983, 698, 660, 863, 752, 663, 95, 466], [805, 209, 695, 994, 697, 113, 774, 278, 614, 878, 368]], 'objective': 8171.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}",8171.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 1419}, {'id': 'F2', 'opening_cost': 8670}, {'id': 'F3', 'opening_cost': 4009}, {'id': 'F4', 'opening_cost': 8389}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 38}, {'facility': 'F1', 'customer': 1, 'cost': 901}, {'facility': 'F1', 'customer': 2, 'cost': 549}, {'facility': 'F1', 'customer': 3, 'cost': 898}, {'facility': 'F1', 'customer': 4, 'cost': 412}, {'facility': 'F1', 'customer': 5, 'cost': 934}, {'facility': 'F1', 'customer': 6, 'cost': 46}, {'facility': 'F1', 'customer': 7, 'cost': 736}, {'facility': 'F1', 'customer': 8, 'cost': 834}, {'facility': 'F1', 'customer': 9, 'cost': 800}, {'facility': 'F1', 'customer': 10, 'cost': 604}, {'facility': 'F2', 'customer': 0, 'cost': 65}, {'facility': 'F2', 'customer': 1, 'cost': 102}, {'facility': 'F2', 'customer': 2, 'cost': 130}, {'facility': 'F2', 'customer': 3, 'cost': 617}, {'facility': 'F2', 'customer': 4, 'cost': 802}, {'facility': 'F2', 'customer': 5, 'cost': 149}, {'facility': 'F2', 'customer': 6, 'cost': 595}, {'facility': 'F2', 'customer': 7, 'cost': 252}, {'facility': 'F2', 'customer': 8, 'cost': 61}, {'facility': 'F2', 'customer': 9, 'cost': 310}, {'facility': 'F2', 'customer': 10, 'cost': 899}, {'facility': 'F3', 'customer': 0, 'cost': 210}, {'facility': 'F3', 'customer': 1, 'cost': 70}, {'facility': 'F3', 'customer': 2, 'cost': 603}, {'facility': 'F3', 'customer': 3, 'cost': 983}, {'facility': 'F3', 'customer': 4, 'cost': 698}, {'facility': 'F3', 'customer': 5, 'cost': 660}, {'facility': 'F3', 'customer': 6, 'cost': 863}, {'facility': 'F3', 'customer': 7, 'cost': 752}, {'facility': 'F3', 'customer': 8, 'cost': 663}, {'facility': 'F3', 'customer': 9, 'cost': 95}, {'facility': 'F3', 'customer': 10, 'cost': 466}, {'facility': 'F4', 'customer': 0, 'cost': 805}, {'facility': 'F4', 'customer': 1, 'cost': 209}, {'facility': 'F4', 'customer': 2, 'cost': 695}, {'facility': 'F4', 'customer': 3, 'cost': 994}, {'facility': 'F4', 'customer': 4, 'cost': 697}, {'facility': 'F4', 'customer': 5, 'cost': 113}, {'facility': 'F4', 'customer': 6, 'cost': 774}, {'facility': 'F4', 'customer': 7, 'cost': 278}, {'facility': 'F4', 'customer': 8, 'cost': 614}, {'facility': 'F4', 'customer': 9, 'cost': 878}, {'facility': 'F4', 'customer': 10, 'cost': 368}], 'objective': 8171.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",21,markdown_table,0
UFLP,UFLP,"Someone on the school staff is lining up afternoon tutoring and has to pick which rooms to open and where each student will go. What makes one plan better than another is simple: add together the rental charges for the chosen rooms and the travel burden for each student — the plan that gives the smallest combined amount is preferred. No student can be left unassigned or split between rooms; every student goes to one offered room, and rooms don’t have hard capacity limits. The concrete details follow below.
{
""num_rooms"": 5,
""num_students"": 11,
""rooms"": [
{
""room_id"": ""F1"",
""room_rental_cost"": 1525
},
{
""room_id"": ""F2"",
""room_rental_cost"": 1260
},
{
""room_id"": ""F3"",
""room_rental_cost"": 1134
},
{
""room_id"": ""F4"",
""room_rental_cost"": 1076
},
{
""room_id"": ""F5"",
""room_rental_cost"": 1831
}
],
""students"": [
{
""student_id"": 0
},
{
""student_id"": 1
},
{
""student_id"": 2
},
{
""student_id"": 3
},
{
""student_id"": 4
},
{
""student_id"": 5
},
{
""student_id"": 6
},
{
""student_id"": 7
},
{
""student_id"": 8
},
{
""student_id"": 9
},
{
""student_id"": 10
}
],
""student_travels"": [
{
""room_id"": ""F1"",
""student_id"": 0,
""student_travel_cost"": 536
},
{
""room_id"": ""F1"",
""student_id"": 1,
""student_travel_cost"": 917
},
{
""room_id"": ""F1"",
""student_id"": 2,
""student_travel_cost"": 595
},
{
""room_id"": ""F1"",
""student_id"": 3,
""student_travel_cost"": 764
},
{
""room_id"": ""F1"",
""student_id"": 4,
""student_travel_cost"": 521
},
{
""room_id"": ""F1"",
""student_id"": 5,
""student_travel_cost"": 456
},
{
""room_id"": ""F1"",
""student_id"": 6,
""student_travel_cost"": 688
},
{
""room_id"": ""F1"",
""student_id"": 7,
""student_travel_cost"": 291
},
{
""room_id"": ""F1"",
""student_id"": 8,
""student_travel_cost"": 468
},
{
""room_id"": ""F1"",
""student_id"": 9,
""student_travel_cost"": 771
},
{
""room_id"": ""F1"",
""student_id"": 10,
""student_travel_cost"": 285
},
{
""room_id"": ""F2"",
""student_id"": 0,
""student_travel_cost"": 853
},
{
""room_id"": ""F2"",
""student_id"": 1,
""student_travel_cost"": 156
},
{
""room_id"": ""F2"",
""student_id"": 2,
""student_travel_cost"": 118
},
{
""room_id"": ""F2"",
""student_id"": 3,
""student_travel_cost"": 22
},
{
""room_id"": ""F2"",
""student_id"": 4,
""student_travel_cost"": 85
},
{
""room_id"": ""F2"",
""student_id"": 5,
""student_travel_cost"": 220
},
{
""room_id"": ""F2"",
""student_id"": 6,
""student_travel_cost"": 879
},
{
""room_id"": ""F2"",
""student_id"": 7,
""student_travel_cost"": 450
},
{
""room_id"": ""F2"",
""student_id"": 8,
""student_travel_cost"": 89
},
{
""room_id"": ""F2"",
""student_id"": 9,
""student_travel_cost"": 489
},
{
""room_id"": ""F2"",
""student_id"": 10,
""student_travel_cost"": 919
},
{
""room_id"": ""F3"",
""student_id"": 0,
""student_travel_cost"": 345
},
{
""room_id"": ""F3"",
""student_id"": 1,
""student_travel_cost"": 950
},
{
""room_id"": ""F3"",
""student_id"": 2,
""student_travel_cost"": 660
},
{
""room_id"": ""F3"",
""student_id"": 3,
""student_travel_cost"": 210
},
{
""room_id"": ""F3"",
""student_id"": 4,
""student_travel_cost"": 568
},
{
""room_id"": ""F3"",
""student_id"": 5,
""student_travel_cost"": 72
},
{
""room_id"": ""F3"",
""student_id"": 6,
""student_travel_cost"": 790
},
{
""room_id"": ""F3"",
""student_id"": 7,
""student_travel_cost"": 835
},
{
""room_id"": ""F3"",
""student_id"": 8,
""student_travel_cost"": 293
},
{
""room_id"": ""F3"",
""student_id"": 9,
""student_travel_cost"": 827
},
{
""room_id"": ""F3"",
""student_id"": 10,
""student_travel_cost"": 158
},
{
""room_id"": ""F4"",
""student_id"": 0,
""student_travel_cost"": 416
},
{
""room_id"": ""F4"",
""student_id"": 1,
""student_travel_cost"": 90
},
{
""room_id"": ""F4"",
""student_id"": 2,
""student_travel_cost"": 265
},
{
""room_id"": ""F4"",
""student_id"": 3,
""student_travel_cost"": 638
},
{
""room_id"": ""F4"",
""student_id"": 4,
""student_travel_cost"": 283
},
{
""room_id"": ""F4"",
""student_id"": 5,
""student_travel_cost"": 320
},
{
""room_id"": ""F4"",
""student_id"": 6,
""student_travel_cost"": 198
},
{
""room_id"": ""F4"",
""student_id"": 7,
""student_travel_cost"": 149
},
{
""room_id"": ""F4"",
""student_id"": 8,
""student_travel_cost"": 151
},
{
""room_id"": ""F4"",
""student_id"": 9,
""student_travel_cost"": 191
},
{
""room_id"": ""F4"",
""student_id"": 10,
""student_travel_cost"": 644
},
{
""room_id"": ""F5"",
""student_id"": 0,
""student_travel_cost"": 150
},
{
""room_id"": ""F5"",
""student_id"": 1,
""student_travel_cost"": 190
},
{
""room_id"": ""F5"",
""student_id"": 2,
""student_travel_cost"": 552
},
{
""room_id"": ""F5"",
""student_id"": 3,
""student_travel_cost"": 762
},
{
""room_id"": ""F5"",
""student_id"": 4,
""student_travel_cost"": 737
},
{
""room_id"": ""F5"",
""student_id"": 5,
""student_travel_cost"": 284
},
{
""room_id"": ""F5"",
""student_id"": 6,
""student_travel_cost"": 824
},
{
""room_id"": ""F5"",
""student_id"": 7,
""student_travel_cost"": 985
},
{
""room_id"": ""F5"",
""student_id"": 8,
""student_travel_cost"": 201
},
{
""room_id"": ""F5"",
""student_id"": 9,
""student_travel_cost"": 968
},
{
""room_id"": ""F5"",
""student_id"": 10,
""student_travel_cost"": 80
}
]
}
If you want to hand me the plan, a small JSON sketch is easiest — something that lists which rooms you open and, for each student, which opened room they go to. Here’s the shape I expect:
{
""solution"": {
""selected"": [<room_to_open>, <room_to_open>, ...],
""assignments"": [<chosen_open_room>, <chosen_open_room>, ...]
}
}
""selected"" is just the list of room IDs you decide to open (the rental charges will be counted for those). ""assignments"" gives one entry per student showing the room they’ll attend — so the first entry is the room for the first student, the second for the second student, and so on. Easy, no extra fields needed.
This is just a sketch of the expected shape, not the actual answer — fill it in with the real IDs from the instance input.
Please use the exact identifiers from the instance input — do not rename them or invent new labels. For example: Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [1525, 1260, 1134, 1076, 1831], 'connection_costs': [[536, 917, 595, 764, 521, 456, 688, 291, 468, 771, 285], [853, 156, 118, 22, 85, 220, 879, 450, 89, 489, 919], [345, 950, 660, 210, 568, 72, 790, 835, 293, 827, 158], [416, 90, 265, 638, 283, 320, 198, 149, 151, 191, 644], [150, 190, 552, 762, 737, 284, 824, 985, 201, 968, 80]], 'objective': 4322.0}","{'open_facilities': [2, 3], 'assignments': [2, 3, 3, 2, 3, 2, 3, 3, 3, 3, 2]}",4322.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 1525}, {'id': 'F2', 'opening_cost': 1260}, {'id': 'F3', 'opening_cost': 1134}, {'id': 'F4', 'opening_cost': 1076}, {'id': 'F5', 'opening_cost': 1831}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 536}, {'facility': 'F1', 'customer': 1, 'cost': 917}, {'facility': 'F1', 'customer': 2, 'cost': 595}, {'facility': 'F1', 'customer': 3, 'cost': 764}, {'facility': 'F1', 'customer': 4, 'cost': 521}, {'facility': 'F1', 'customer': 5, 'cost': 456}, {'facility': 'F1', 'customer': 6, 'cost': 688}, {'facility': 'F1', 'customer': 7, 'cost': 291}, {'facility': 'F1', 'customer': 8, 'cost': 468}, {'facility': 'F1', 'customer': 9, 'cost': 771}, {'facility': 'F1', 'customer': 10, 'cost': 285}, {'facility': 'F2', 'customer': 0, 'cost': 853}, {'facility': 'F2', 'customer': 1, 'cost': 156}, {'facility': 'F2', 'customer': 2, 'cost': 118}, {'facility': 'F2', 'customer': 3, 'cost': 22}, {'facility': 'F2', 'customer': 4, 'cost': 85}, {'facility': 'F2', 'customer': 5, 'cost': 220}, {'facility': 'F2', 'customer': 6, 'cost': 879}, {'facility': 'F2', 'customer': 7, 'cost': 450}, {'facility': 'F2', 'customer': 8, 'cost': 89}, {'facility': 'F2', 'customer': 9, 'cost': 489}, {'facility': 'F2', 'customer': 10, 'cost': 919}, {'facility': 'F3', 'customer': 0, 'cost': 345}, {'facility': 'F3', 'customer': 1, 'cost': 950}, {'facility': 'F3', 'customer': 2, 'cost': 660}, {'facility': 'F3', 'customer': 3, 'cost': 210}, {'facility': 'F3', 'customer': 4, 'cost': 568}, {'facility': 'F3', 'customer': 5, 'cost': 72}, {'facility': 'F3', 'customer': 6, 'cost': 790}, {'facility': 'F3', 'customer': 7, 'cost': 835}, {'facility': 'F3', 'customer': 8, 'cost': 293}, {'facility': 'F3', 'customer': 9, 'cost': 827}, {'facility': 'F3', 'customer': 10, 'cost': 158}, {'facility': 'F4', 'customer': 0, 'cost': 416}, {'facility': 'F4', 'customer': 1, 'cost': 90}, {'facility': 'F4', 'customer': 2, 'cost': 265}, {'facility': 'F4', 'customer': 3, 'cost': 638}, {'facility': 'F4', 'customer': 4, 'cost': 283}, {'facility': 'F4', 'customer': 5, 'cost': 320}, {'facility': 'F4', 'customer': 6, 'cost': 198}, {'facility': 'F4', 'customer': 7, 'cost': 149}, {'facility': 'F4', 'customer': 8, 'cost': 151}, {'facility': 'F4', 'customer': 9, 'cost': 191}, {'facility': 'F4', 'customer': 10, 'cost': 644}, {'facility': 'F5', 'customer': 0, 'cost': 150}, {'facility': 'F5', 'customer': 1, 'cost': 190}, {'facility': 'F5', 'customer': 2, 'cost': 552}, {'facility': 'F5', 'customer': 3, 'cost': 762}, {'facility': 'F5', 'customer': 4, 'cost': 737}, {'facility': 'F5', 'customer': 5, 'cost': 284}, {'facility': 'F5', 'customer': 6, 'cost': 824}, {'facility': 'F5', 'customer': 7, 'cost': 985}, {'facility': 'F5', 'customer': 8, 'cost': 201}, {'facility': 'F5', 'customer': 9, 'cost': 968}, {'facility': 'F5', 'customer': 10, 'cost': 80}], 'objective': 4322.0}","{'selected': ['F3', 'F4'], 'assignments': ['F3', 'F4', 'F4', 'F3', 'F4', 'F3', 'F4', 'F4', 'F4', 'F4', 'F3']}",22,json,0
UFLP,UFLP,"Many people rely on the bookmobile, and the outreach team must pick from a list of possible stops, each with its own price to operate. Patrons are scattered around, so once stops are chosen each patron needs to be assigned to exactly one of those running stops. The smart choice is the one that minimizes the total cost — the running costs for chosen stops plus the combined travel distance of everyone — calculated by simply adding those two parts together. No patron can be assigned to more than one stop or be left out, and assignments only count if the stop is actually running. The specifics are shown below.
{
""num_candidate_stops"": 6,
""num_patrons"": 14,
""stops"": [
{
""stop_id"": ""F1"",
""stop_operating_cost"": 7433
},
{
""stop_id"": ""F2"",
""stop_operating_cost"": 8799
},
{
""stop_id"": ""F3"",
""stop_operating_cost"": 9182
},
{
""stop_id"": ""F4"",
""stop_operating_cost"": 9103
},
{
""stop_id"": ""F5"",
""stop_operating_cost"": 7198
},
{
""stop_id"": ""F6"",
""stop_operating_cost"": 9155
}
],
""patrons"": [
{
""patron_id"": 1
},
{
""patron_id"": 2
},
{
""patron_id"": 3
},
{
""patron_id"": 4
},
{
""patron_id"": 5
},
{
""patron_id"": 6
},
{
""patron_id"": 7
},
{
""patron_id"": 8
},
{
""patron_id"": 9
},
{
""patron_id"": 10
},
{
""patron_id"": 11
},
{
""patron_id"": 12
},
{
""patron_id"": 13
},
{
""patron_id"": 14
}
],
""travel_distances"": [
{
""stop_id"": ""F1"",
""patron_id"": 1,
""travel_distance_cost"": 711
},
{
""stop_id"": ""F1"",
""patron_id"": 2,
""travel_distance_cost"": 855
},
{
""stop_id"": ""F1"",
""patron_id"": 3,
""travel_distance_cost"": 642
},
{
""stop_id"": ""F1"",
""patron_id"": 4,
""travel_distance_cost"": 286
},
{
""stop_id"": ""F1"",
""patron_id"": 5,
""travel_distance_cost"": 639
},
{
""stop_id"": ""F1"",
""patron_id"": 6,
""travel_distance_cost"": 165
},
{
""stop_id"": ""F1"",
""patron_id"": 7,
""travel_distance_cost"": 998
},
{
""stop_id"": ""F1"",
""patron_id"": 8,
""travel_distance_cost"": 761
},
{
""stop_id"": ""F1"",
""patron_id"": 9,
""travel_distance_cost"": 368
},
{
""stop_id"": ""F1"",
""patron_id"": 10,
""travel_distance_cost"": 309
},
{
""stop_id"": ""F1"",
""patron_id"": 11,
""travel_distance_cost"": 772
},
{
""stop_id"": ""F1"",
""patron_id"": 12,
""travel_distance_cost"": 931
},
{
""stop_id"": ""F1"",
""patron_id"": 13,
""travel_distance_cost"": 260
},
{
""stop_id"": ""F1"",
""patron_id"": 14,
""travel_distance_cost"": 839
},
{
""stop_id"": ""F2"",
""patron_id"": 1,
""travel_distance_cost"": 882
},
{
""stop_id"": ""F2"",
""patron_id"": 2,
""travel_distance_cost"": 899
},
{
""stop_id"": ""F2"",
""patron_id"": 3,
""travel_distance_cost"": 880
},
{
""stop_id"": ""F2"",
""patron_id"": 4,
""travel_distance_cost"": 724
},
{
""stop_id"": ""F2"",
""patron_id"": 5,
""travel_distance_cost"": 468
},
{
""stop_id"": ""F2"",
""patron_id"": 6,
""travel_distance_cost"": 571
},
{
""stop_id"": ""F2"",
""patron_id"": 7,
""travel_distance_cost"": 393
},
{
""stop_id"": ""F2"",
""patron_id"": 8,
""travel_distance_cost"": 732
},
{
""stop_id"": ""F2"",
""patron_id"": 9,
""travel_distance_cost"": 757
},
{
""stop_id"": ""F2"",
""patron_id"": 10,
""travel_distance_cost"": 612
},
{
""stop_id"": ""F2"",
""patron_id"": 11,
""travel_distance_cost"": 980
},
{
""stop_id"": ""F2"",
""patron_id"": 12,
""travel_distance_cost"": 375
},
{
""stop_id"": ""F2"",
""patron_id"": 13,
""travel_distance_cost"": 671
},
{
""stop_id"": ""F2"",
""patron_id"": 14,
""travel_distance_cost"": 105
},
{
""stop_id"": ""F3"",
""patron_id"": 1,
""travel_distance_cost"": 390
},
{
""stop_id"": ""F3"",
""patron_id"": 2,
""travel_distance_cost"": 958
},
{
""stop_id"": ""F3"",
""patron_id"": 3,
""travel_distance_cost"": 633
},
{
""stop_id"": ""F3"",
""patron_id"": 4,
""travel_distance_cost"": 211
},
{
""stop_id"": ""F3"",
""patron_id"": 5,
""travel_distance_cost"": 914
},
{
""stop_id"": ""F3"",
""patron_id"": 6,
""travel_distance_cost"": 281
},
{
""stop_id"": ""F3"",
""patron_id"": 7,
""travel_distance_cost"": 352
},
{
""stop_id"": ""F3"",
""patron_id"": 8,
""travel_distance_cost"": 623
},
{
""stop_id"": ""F3"",
""patron_id"": 9,
""travel_distance_cost"": 516
},
{
""stop_id"": ""F3"",
""patron_id"": 10,
""travel_distance_cost"": 20
},
{
""stop_id"": ""F3"",
""patron_id"": 11,
""travel_distance_cost"": 944
},
{
""stop_id"": ""F3"",
""patron_id"": 12,
""travel_distance_cost"": 13
},
{
""stop_id"": ""F3"",
""patron_id"": 13,
""travel_distance_cost"": 287
},
{
""stop_id"": ""F3"",
""patron_id"": 14,
""travel_distance_cost"": 661
},
{
""stop_id"": ""F4"",
""patron_id"": 1,
""travel_distance_cost"": 353
},
{
""stop_id"": ""F4"",
""patron_id"": 2,
""travel_distance_cost"": 327
},
{
""stop_id"": ""F4"",
""patron_id"": 3,
""travel_distance_cost"": 624
},
{
""stop_id"": ""F4"",
""patron_id"": 4,
""travel_distance_cost"": 871
},
{
""stop_id"": ""F4"",
""patron_id"": 5,
""travel_distance_cost"": 864
},
{
""stop_id"": ""F4"",
""patron_id"": 6,
""travel_distance_cost"": 65
},
{
""stop_id"": ""F4"",
""patron_id"": 7,
""travel_distance_cost"": 768
},
{
""stop_id"": ""F4"",
""patron_id"": 8,
""travel_distance_cost"": 250
},
{
""stop_id"": ""F4"",
""patron_id"": 9,
""travel_distance_cost"": 548
},
{
""stop_id"": ""F4"",
""patron_id"": 10,
""travel_distance_cost"": 653
},
{
""stop_id"": ""F4"",
""patron_id"": 11,
""travel_distance_cost"": 357
},
{
""stop_id"": ""F4"",
""patron_id"": 12,
""travel_distance_cost"": 827
},
{
""stop_id"": ""F4"",
""patron_id"": 13,
""travel_distance_cost"": 416
},
{
""stop_id"": ""F4"",
""patron_id"": 14,
""travel_distance_cost"": 608
},
{
""stop_id"": ""F5"",
""patron_id"": 1,
""travel_distance_cost"": 788
},
{
""stop_id"": ""F5"",
""patron_id"": 2,
""travel_distance_cost"": 742
},
{
""stop_id"": ""F5"",
""patron_id"": 3,
""travel_distance_cost"": 55
},
{
""stop_id"": ""F5"",
""patron_id"": 4,
""travel_distance_cost"": 96
},
{
""stop_id"": ""F5"",
""patron_id"": 5,
""travel_distance_cost"": 904
},
{
""stop_id"": ""F5"",
""patron_id"": 6,
""travel_distance_cost"": 387
},
{
""stop_id"": ""F5"",
""patron_id"": 7,
""travel_distance_cost"": 130
},
{
""stop_id"": ""F5"",
""patron_id"": 8,
""travel_distance_cost"": 678
},
{
""stop_id"": ""F5"",
""patron_id"": 9,
""travel_distance_cost"": 424
},
{
""stop_id"": ""F5"",
""patron_id"": 10,
""travel_distance_cost"": 578
},
{
""stop_id"": ""F5"",
""patron_id"": 11,
""travel_distance_cost"": 342
},
{
""stop_id"": ""F5"",
""patron_id"": 12,
""travel_distance_cost"": 550
},
{
""stop_id"": ""F5"",
""patron_id"": 13,
""travel_distance_cost"": 103
},
{
""stop_id"": ""F5"",
""patron_id"": 14,
""travel_distance_cost"": 270
},
{
""stop_id"": ""F6"",
""patron_id"": 1,
""travel_distance_cost"": 669
},
{
""stop_id"": ""F6"",
""patron_id"": 2,
""travel_distance_cost"": 617
},
{
""stop_id"": ""F6"",
""patron_id"": 3,
""travel_distance_cost"": 499
},
{
""stop_id"": ""F6"",
""patron_id"": 4,
""travel_distance_cost"": 362
},
{
""stop_id"": ""F6"",
""patron_id"": 5,
""travel_distance_cost"": 682
},
{
""stop_id"": ""F6"",
""patron_id"": 6,
""travel_distance_cost"": 457
},
{
""stop_id"": ""F6"",
""patron_id"": 7,
""travel_distance_cost"": 609
},
{
""stop_id"": ""F6"",
""patron_id"": 8,
""travel_distance_cost"": 340
},
{
""stop_id"": ""F6"",
""patron_id"": 9,
""travel_distance_cost"": 149
},
{
""stop_id"": ""F6"",
""patron_id"": 10,
""travel_distance_cost"": 674
},
{
""stop_id"": ""F6"",
""patron_id"": 11,
""travel_distance_cost"": 890
},
{
""stop_id"": ""F6"",
""patron_id"": 12,
""travel_distance_cost"": 296
},
{
""stop_id"": ""F6"",
""patron_id"": 13,
""travel_distance_cost"": 495
},
{
""stop_id"": ""F6"",
""patron_id"": 14,
""travel_distance_cost"": 332
}
]
}
When you reply, just stick to this simple JSON layout so it's easy to parse and check.
{
""solution"": {
""selected"": [<stop_to_open>, <stop_to_open>, ...],
""assignments"": [<assigned_stop>, <assigned_stop>, ...]
}
}
""selected"" is where you list the stops you decide to run (the ones you pay to operate). ""assignments"" is a list, in the same order as the patrons in the instance, saying which running stop each patron will use. Think of it like filling out a form: pick the stops, then say for each patron which stop they're going to.
This JSON is just a sketch of the shape I need — not the final answer itself.
Please be careful: use the exact identifiers from the instance input, do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [7433, 8799, 9182, 9103, 7198, 9155], 'connection_costs': [[711, 855, 642, 286, 639, 165, 998, 761, 368, 309, 772, 931, 260, 839], [882, 899, 880, 724, 468, 571, 393, 732, 757, 612, 980, 375, 671, 105], [390, 958, 633, 211, 914, 281, 352, 623, 516, 20, 944, 13, 287, 661], [353, 327, 624, 871, 864, 65, 768, 250, 548, 653, 357, 827, 416, 608], [788, 742, 55, 96, 904, 387, 130, 678, 424, 578, 342, 550, 103, 270], [669, 617, 499, 362, 682, 457, 609, 340, 149, 674, 890, 296, 495, 332]], 'objective': 13245.0}","{'open_facilities': [4], 'assignments': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]}",13245.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 14, 'facilities': [{'id': 'F1', 'opening_cost': 7433}, {'id': 'F2', 'opening_cost': 8799}, {'id': 'F3', 'opening_cost': 9182}, {'id': 'F4', 'opening_cost': 9103}, {'id': 'F5', 'opening_cost': 7198}, {'id': 'F6', 'opening_cost': 9155}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}, {'id': 12}, {'id': 13}, {'id': 14}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 711}, {'facility': 'F1', 'customer': 2, 'cost': 855}, {'facility': 'F1', 'customer': 3, 'cost': 642}, {'facility': 'F1', 'customer': 4, 'cost': 286}, {'facility': 'F1', 'customer': 5, 'cost': 639}, {'facility': 'F1', 'customer': 6, 'cost': 165}, {'facility': 'F1', 'customer': 7, 'cost': 998}, {'facility': 'F1', 'customer': 8, 'cost': 761}, {'facility': 'F1', 'customer': 9, 'cost': 368}, {'facility': 'F1', 'customer': 10, 'cost': 309}, {'facility': 'F1', 'customer': 11, 'cost': 772}, {'facility': 'F1', 'customer': 12, 'cost': 931}, {'facility': 'F1', 'customer': 13, 'cost': 260}, {'facility': 'F1', 'customer': 14, 'cost': 839}, {'facility': 'F2', 'customer': 1, 'cost': 882}, {'facility': 'F2', 'customer': 2, 'cost': 899}, {'facility': 'F2', 'customer': 3, 'cost': 880}, {'facility': 'F2', 'customer': 4, 'cost': 724}, {'facility': 'F2', 'customer': 5, 'cost': 468}, {'facility': 'F2', 'customer': 6, 'cost': 571}, {'facility': 'F2', 'customer': 7, 'cost': 393}, {'facility': 'F2', 'customer': 8, 'cost': 732}, {'facility': 'F2', 'customer': 9, 'cost': 757}, {'facility': 'F2', 'customer': 10, 'cost': 612}, {'facility': 'F2', 'customer': 11, 'cost': 980}, {'facility': 'F2', 'customer': 12, 'cost': 375}, {'facility': 'F2', 'customer': 13, 'cost': 671}, {'facility': 'F2', 'customer': 14, 'cost': 105}, {'facility': 'F3', 'customer': 1, 'cost': 390}, {'facility': 'F3', 'customer': 2, 'cost': 958}, {'facility': 'F3', 'customer': 3, 'cost': 633}, {'facility': 'F3', 'customer': 4, 'cost': 211}, {'facility': 'F3', 'customer': 5, 'cost': 914}, {'facility': 'F3', 'customer': 6, 'cost': 281}, {'facility': 'F3', 'customer': 7, 'cost': 352}, {'facility': 'F3', 'customer': 8, 'cost': 623}, {'facility': 'F3', 'customer': 9, 'cost': 516}, {'facility': 'F3', 'customer': 10, 'cost': 20}, {'facility': 'F3', 'customer': 11, 'cost': 944}, {'facility': 'F3', 'customer': 12, 'cost': 13}, {'facility': 'F3', 'customer': 13, 'cost': 287}, {'facility': 'F3', 'customer': 14, 'cost': 661}, {'facility': 'F4', 'customer': 1, 'cost': 353}, {'facility': 'F4', 'customer': 2, 'cost': 327}, {'facility': 'F4', 'customer': 3, 'cost': 624}, {'facility': 'F4', 'customer': 4, 'cost': 871}, {'facility': 'F4', 'customer': 5, 'cost': 864}, {'facility': 'F4', 'customer': 6, 'cost': 65}, {'facility': 'F4', 'customer': 7, 'cost': 768}, {'facility': 'F4', 'customer': 8, 'cost': 250}, {'facility': 'F4', 'customer': 9, 'cost': 548}, {'facility': 'F4', 'customer': 10, 'cost': 653}, {'facility': 'F4', 'customer': 11, 'cost': 357}, {'facility': 'F4', 'customer': 12, 'cost': 827}, {'facility': 'F4', 'customer': 13, 'cost': 416}, {'facility': 'F4', 'customer': 14, 'cost': 608}, {'facility': 'F5', 'customer': 1, 'cost': 788}, {'facility': 'F5', 'customer': 2, 'cost': 742}, {'facility': 'F5', 'customer': 3, 'cost': 55}, {'facility': 'F5', 'customer': 4, 'cost': 96}, {'facility': 'F5', 'customer': 5, 'cost': 904}, {'facility': 'F5', 'customer': 6, 'cost': 387}, {'facility': 'F5', 'customer': 7, 'cost': 130}, {'facility': 'F5', 'customer': 8, 'cost': 678}, {'facility': 'F5', 'customer': 9, 'cost': 424}, {'facility': 'F5', 'customer': 10, 'cost': 578}, {'facility': 'F5', 'customer': 11, 'cost': 342}, {'facility': 'F5', 'customer': 12, 'cost': 550}, {'facility': 'F5', 'customer': 13, 'cost': 103}, {'facility': 'F5', 'customer': 14, 'cost': 270}, {'facility': 'F6', 'customer': 1, 'cost': 669}, {'facility': 'F6', 'customer': 2, 'cost': 617}, {'facility': 'F6', 'customer': 3, 'cost': 499}, {'facility': 'F6', 'customer': 4, 'cost': 362}, {'facility': 'F6', 'customer': 5, 'cost': 682}, {'facility': 'F6', 'customer': 6, 'cost': 457}, {'facility': 'F6', 'customer': 7, 'cost': 609}, {'facility': 'F6', 'customer': 8, 'cost': 340}, {'facility': 'F6', 'customer': 9, 'cost': 149}, {'facility': 'F6', 'customer': 10, 'cost': 674}, {'facility': 'F6', 'customer': 11, 'cost': 890}, {'facility': 'F6', 'customer': 12, 'cost': 296}, {'facility': 'F6', 'customer': 13, 'cost': 495}, {'facility': 'F6', 'customer': 14, 'cost': 332}], 'objective': 13245.0}","{'selected': ['F5'], 'assignments': ['F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5']}",23,json,1
UFLP,UFLP,"Many people don’t realize how much goes into choosing which distribution points to run for a farmers market network and how to route vendors there. Each candidate point has a cost to bring online, and each vendor has a cost to haul goods to whichever point they use. The goal is to keep the overall expense as small as possible — the total is simply the combined cost of the points we decide to run plus all vendors’ hauling costs — and every vendor must be sent to exactly one running point, with no duplicates or omissions. The concrete numbers appear below.
{
""num_distribution_points"": 4,
""num_vendors"": 9,
""distribution_points"": [
{
""distribution_point_id"": ""F1"",
""setup_cost"": 2000
},
{
""distribution_point_id"": ""F2"",
""setup_cost"": 2000
},
{
""distribution_point_id"": ""F3"",
""setup_cost"": 2000
},
{
""distribution_point_id"": ""F4"",
""setup_cost"": 2000
}
],
""vendors"": [
{
""vendor_id"": 1
},
{
""vendor_id"": 2
},
{
""vendor_id"": 3
},
{
""vendor_id"": 4
},
{
""vendor_id"": 5
},
{
""vendor_id"": 6
},
{
""vendor_id"": 7
},
{
""vendor_id"": 8
},
{
""vendor_id"": 9
}
],
""haulings"": [
{
""distribution_point_id"": ""F1"",
""vendor_id"": 1,
""hauling_cost"": 758
},
{
""distribution_point_id"": ""F1"",
""vendor_id"": 2,
""hauling_cost"": 457
},
{
""distribution_point_id"": ""F1"",
""vendor_id"": 3,
""hauling_cost"": 153
},
{
""distribution_point_id"": ""F1"",
""vendor_id"": 4,
""hauling_cost"": 36
},
{
""distribution_point_id"": ""F1"",
""vendor_id"": 5,
""hauling_cost"": 323
},
{
""distribution_point_id"": ""F1"",
""vendor_id"": 6,
""hauling_cost"": 853
},
{
""distribution_point_id"": ""F1"",
""vendor_id"": 7,
""hauling_cost"": 85
},
{
""distribution_point_id"": ""F1"",
""vendor_id"": 8,
""hauling_cost"": 117
},
{
""distribution_point_id"": ""F1"",
""vendor_id"": 9,
""hauling_cost"": 403
},
{
""distribution_point_id"": ""F2"",
""vendor_id"": 1,
""hauling_cost"": 624
},
{
""distribution_point_id"": ""F2"",
""vendor_id"": 2,
""hauling_cost"": 855
},
{
""distribution_point_id"": ""F2"",
""vendor_id"": 3,
""hauling_cost"": 382
},
{
""distribution_point_id"": ""F2"",
""vendor_id"": 4,
""hauling_cost"": 563
},
{
""distribution_point_id"": ""F2"",
""vendor_id"": 5,
""hauling_cost"": 409
},
{
""distribution_point_id"": ""F2"",
""vendor_id"": 6,
""hauling_cost"": 228
},
{
""distribution_point_id"": ""F2"",
""vendor_id"": 7,
""hauling_cost"": 742
},
{
""distribution_point_id"": ""F2"",
""vendor_id"": 8,
""hauling_cost"": 25
},
{
""distribution_point_id"": ""F2"",
""vendor_id"": 9,
""hauling_cost"": 559
},
{
""distribution_point_id"": ""F3"",
""vendor_id"": 1,
""hauling_cost"": 73
},
{
""distribution_point_id"": ""F3"",
""vendor_id"": 2,
""hauling_cost"": 55
},
{
""distribution_point_id"": ""F3"",
""vendor_id"": 3,
""hauling_cost"": 379
},
{
""distribution_point_id"": ""F3"",
""vendor_id"": 4,
""hauling_cost"": 963
},
{
""distribution_point_id"": ""F3"",
""vendor_id"": 5,
""hauling_cost"": 301
},
{
""distribution_point_id"": ""F3"",
""vendor_id"": 6,
""hauling_cost"": 270
},
{
""distribution_point_id"": ""F3"",
""vendor_id"": 7,
""hauling_cost"": 947
},
{
""distribution_point_id"": ""F3"",
""vendor_id"": 8,
""hauling_cost"": 11
},
{
""distribution_point_id"": ""F3"",
""vendor_id"": 9,
""hauling_cost"": 837
},
{
""distribution_point_id"": ""F4"",
""vendor_id"": 1,
""hauling_cost"": 631
},
{
""distribution_point_id"": ""F4"",
""vendor_id"": 2,
""hauling_cost"": 990
},
{
""distribution_point_id"": ""F4"",
""vendor_id"": 3,
""hauling_cost"": 161
},
{
""distribution_point_id"": ""F4"",
""vendor_id"": 4,
""hauling_cost"": 471
},
{
""distribution_point_id"": ""F4"",
""vendor_id"": 5,
""hauling_cost"": 934
},
{
""distribution_point_id"": ""F4"",
""vendor_id"": 6,
""hauling_cost"": 329
},
{
""distribution_point_id"": ""F4"",
""vendor_id"": 7,
""hauling_cost"": 475
},
{
""distribution_point_id"": ""F4"",
""vendor_id"": 8,
""hauling_cost"": 644
},
{
""distribution_point_id"": ""F4"",
""vendor_id"": 9,
""hauling_cost"": 320
}
]
}
Also, I’ll keep my reply in a simple JSON layout so it’s easy to fill in — here’s the shape I expect you to follow:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
""selected"" is the list of market points you decide to run (put the exact identifiers from the instance there). ""assignments"" is a list, one entry per vendor in the same order as the instance, showing which open point that vendor goes to. It’s just a quick form-like sketch of the expected shape, not the real answer.
Please use the exact identifiers from the instance input — don’t rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000], 'connection_costs': [[758, 457, 153, 36, 323, 853, 85, 117, 403], [624, 855, 382, 563, 409, 228, 742, 25, 559], [73, 55, 379, 963, 301, 270, 947, 11, 837], [631, 990, 161, 471, 934, 329, 475, 644, 320]], 'objective': 5185.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0, 0, 0]}",5185.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 9, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 758}, {'facility': 'F1', 'customer': 2, 'cost': 457}, {'facility': 'F1', 'customer': 3, 'cost': 153}, {'facility': 'F1', 'customer': 4, 'cost': 36}, {'facility': 'F1', 'customer': 5, 'cost': 323}, {'facility': 'F1', 'customer': 6, 'cost': 853}, {'facility': 'F1', 'customer': 7, 'cost': 85}, {'facility': 'F1', 'customer': 8, 'cost': 117}, {'facility': 'F1', 'customer': 9, 'cost': 403}, {'facility': 'F2', 'customer': 1, 'cost': 624}, {'facility': 'F2', 'customer': 2, 'cost': 855}, {'facility': 'F2', 'customer': 3, 'cost': 382}, {'facility': 'F2', 'customer': 4, 'cost': 563}, {'facility': 'F2', 'customer': 5, 'cost': 409}, {'facility': 'F2', 'customer': 6, 'cost': 228}, {'facility': 'F2', 'customer': 7, 'cost': 742}, {'facility': 'F2', 'customer': 8, 'cost': 25}, {'facility': 'F2', 'customer': 9, 'cost': 559}, {'facility': 'F3', 'customer': 1, 'cost': 73}, {'facility': 'F3', 'customer': 2, 'cost': 55}, {'facility': 'F3', 'customer': 3, 'cost': 379}, {'facility': 'F3', 'customer': 4, 'cost': 963}, {'facility': 'F3', 'customer': 5, 'cost': 301}, {'facility': 'F3', 'customer': 6, 'cost': 270}, {'facility': 'F3', 'customer': 7, 'cost': 947}, {'facility': 'F3', 'customer': 8, 'cost': 11}, {'facility': 'F3', 'customer': 9, 'cost': 837}, {'facility': 'F4', 'customer': 1, 'cost': 631}, {'facility': 'F4', 'customer': 2, 'cost': 990}, {'facility': 'F4', 'customer': 3, 'cost': 161}, {'facility': 'F4', 'customer': 4, 'cost': 471}, {'facility': 'F4', 'customer': 5, 'cost': 934}, {'facility': 'F4', 'customer': 6, 'cost': 329}, {'facility': 'F4', 'customer': 7, 'cost': 475}, {'facility': 'F4', 'customer': 8, 'cost': 644}, {'facility': 'F4', 'customer': 9, 'cost': 320}], 'objective': 5185.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",24,json,1
UFLP,UFLP,"Backstage it’s being decided which candidate info tables to put people at and how to route each festivalgoer to a single staffed table so the combined hit — staffing fees plus everyone’s walking burden — is as small as possible. To measure a plan, total the staffing costs for the tables that are opened and then add every visitor’s walk cost based on which table they’re sent to. No one can be left unassigned or sent to an unstaffed table, and any staffed table can serve any number of visitors. The specific details and numbers are listed below.
There are 5 booths and 14 attendees in this instance.
**Booths**
| booth_id | staffing_fee |
|---|---|
| F1 | 1716 |
| F2 | 1060 |
| F3 | 1691 |
| F4 | 1742 |
| F5 | 1031 |
**Attendees**
| attendee_id |
|---|
| A |
| B |
| C |
| D |
| E |
| F |
| G |
| H |
| I |
| J |
| K |
| L |
| M |
| N |
**Walking Cost**
| booth_id | attendee_id | walking_cost |
|---|---|---|
| F1 | A | 677 |
| F1 | B | 698 |
| F1 | C | 48 |
| F1 | D | 791 |
| F1 | E | 709 |
| F1 | F | 39 |
| F1 | G | 733 |
| F1 | H | 670 |
| F1 | I | 413 |
| F1 | J | 983 |
| F1 | K | 675 |
| F1 | L | 908 |
| F1 | M | 756 |
| F1 | N | 568 |
| F2 | A | 95 |
| F2 | B | 222 |
| F2 | C | 530 |
| F2 | D | 949 |
| F2 | E | 236 |
| F2 | F | 113 |
| F2 | G | 464 |
| F2 | H | 360 |
| F2 | I | 872 |
| F2 | J | 224 |
| F2 | K | 449 |
| F2 | L | 565 |
| F2 | M | 233 |
| F2 | N | 687 |
| F3 | A | 168 |
| F3 | B | 464 |
| F3 | C | 192 |
| F3 | D | 247 |
| F3 | E | 470 |
| F3 | F | 434 |
| F3 | G | 888 |
| F3 | H | 716 |
| F3 | I | 963 |
| F3 | J | 429 |
| F3 | K | 937 |
| F3 | L | 857 |
| F3 | M | 465 |
| F3 | N | 43 |
| F4 | A | 104 |
| F4 | B | 121 |
| F4 | C | 517 |
| F4 | D | 893 |
| F4 | E | 964 |
| F4 | F | 497 |
| F4 | G | 443 |
| F4 | H | 611 |
| F4 | I | 115 |
| F4 | J | 524 |
| F4 | K | 912 |
| F4 | L | 201 |
| F4 | M | 407 |
| F4 | N | 812 |
| F5 | A | 471 |
| F5 | B | 405 |
| F5 | C | 729 |
| F5 | D | 349 |
| F5 | E | 507 |
| F5 | F | 148 |
| F5 | G | 739 |
| F5 | H | 99 |
| F5 | I | 594 |
| F5 | J | 674 |
| F5 | K | 250 |
| F5 | L | 973 |
| F5 | M | 154 |
| F5 | N | 207 |
Quick heads-up: when you send back your plan, use this little JSON layout so I can read it reliably.
{
""solution"": {
""selected"": [<info_table_to_open>, <info_table_to_open>, ...],
""assignments"": [<assigned_info_table>, <assigned_info_table>, ...]
}
}
""selected"" is where you list which info tables you're opening, and ""assignments"" is a list that, for each festivalgoer in the order they appear in the instance, says which opened table they get sent to. Think of it as a simple form: open these tables, and these people go to those tables.
This JSON is just the expected shape — a sketch of how your answer should be formatted, not the actual choices.
All identifiers in your actual answer must match the instance input exactly — do not rename them or invent new labels. For example: Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [1716, 1060, 1691, 1742, 1031], 'connection_costs': [[677, 698, 48, 791, 709, 39, 733, 670, 413, 983, 675, 908, 756, 568], [95, 222, 530, 949, 236, 113, 464, 360, 872, 224, 449, 565, 233, 687], [168, 464, 192, 247, 470, 434, 888, 716, 963, 429, 937, 857, 465, 43], [104, 121, 517, 893, 964, 497, 443, 611, 115, 524, 912, 201, 407, 812], [471, 405, 729, 349, 507, 148, 739, 99, 594, 674, 250, 973, 154, 207]], 'objective': 6193.0}","{'open_facilities': [1, 4], 'assignments': [1, 1, 1, 4, 1, 1, 1, 4, 4, 1, 4, 1, 4, 4]}",6193.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 14, 'facilities': [{'id': 'F1', 'opening_cost': 1716}, {'id': 'F2', 'opening_cost': 1060}, {'id': 'F3', 'opening_cost': 1691}, {'id': 'F4', 'opening_cost': 1742}, {'id': 'F5', 'opening_cost': 1031}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}, {'id': 'L'}, {'id': 'M'}, {'id': 'N'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 677}, {'facility': 'F1', 'customer': 'B', 'cost': 698}, {'facility': 'F1', 'customer': 'C', 'cost': 48}, {'facility': 'F1', 'customer': 'D', 'cost': 791}, {'facility': 'F1', 'customer': 'E', 'cost': 709}, {'facility': 'F1', 'customer': 'F', 'cost': 39}, {'facility': 'F1', 'customer': 'G', 'cost': 733}, {'facility': 'F1', 'customer': 'H', 'cost': 670}, {'facility': 'F1', 'customer': 'I', 'cost': 413}, {'facility': 'F1', 'customer': 'J', 'cost': 983}, {'facility': 'F1', 'customer': 'K', 'cost': 675}, {'facility': 'F1', 'customer': 'L', 'cost': 908}, {'facility': 'F1', 'customer': 'M', 'cost': 756}, {'facility': 'F1', 'customer': 'N', 'cost': 568}, {'facility': 'F2', 'customer': 'A', 'cost': 95}, {'facility': 'F2', 'customer': 'B', 'cost': 222}, {'facility': 'F2', 'customer': 'C', 'cost': 530}, {'facility': 'F2', 'customer': 'D', 'cost': 949}, {'facility': 'F2', 'customer': 'E', 'cost': 236}, {'facility': 'F2', 'customer': 'F', 'cost': 113}, {'facility': 'F2', 'customer': 'G', 'cost': 464}, {'facility': 'F2', 'customer': 'H', 'cost': 360}, {'facility': 'F2', 'customer': 'I', 'cost': 872}, {'facility': 'F2', 'customer': 'J', 'cost': 224}, {'facility': 'F2', 'customer': 'K', 'cost': 449}, {'facility': 'F2', 'customer': 'L', 'cost': 565}, {'facility': 'F2', 'customer': 'M', 'cost': 233}, {'facility': 'F2', 'customer': 'N', 'cost': 687}, {'facility': 'F3', 'customer': 'A', 'cost': 168}, {'facility': 'F3', 'customer': 'B', 'cost': 464}, {'facility': 'F3', 'customer': 'C', 'cost': 192}, {'facility': 'F3', 'customer': 'D', 'cost': 247}, {'facility': 'F3', 'customer': 'E', 'cost': 470}, {'facility': 'F3', 'customer': 'F', 'cost': 434}, {'facility': 'F3', 'customer': 'G', 'cost': 888}, {'facility': 'F3', 'customer': 'H', 'cost': 716}, {'facility': 'F3', 'customer': 'I', 'cost': 963}, {'facility': 'F3', 'customer': 'J', 'cost': 429}, {'facility': 'F3', 'customer': 'K', 'cost': 937}, {'facility': 'F3', 'customer': 'L', 'cost': 857}, {'facility': 'F3', 'customer': 'M', 'cost': 465}, {'facility': 'F3', 'customer': 'N', 'cost': 43}, {'facility': 'F4', 'customer': 'A', 'cost': 104}, {'facility': 'F4', 'customer': 'B', 'cost': 121}, {'facility': 'F4', 'customer': 'C', 'cost': 517}, {'facility': 'F4', 'customer': 'D', 'cost': 893}, {'facility': 'F4', 'customer': 'E', 'cost': 964}, {'facility': 'F4', 'customer': 'F', 'cost': 497}, {'facility': 'F4', 'customer': 'G', 'cost': 443}, {'facility': 'F4', 'customer': 'H', 'cost': 611}, {'facility': 'F4', 'customer': 'I', 'cost': 115}, {'facility': 'F4', 'customer': 'J', 'cost': 524}, {'facility': 'F4', 'customer': 'K', 'cost': 912}, {'facility': 'F4', 'customer': 'L', 'cost': 201}, {'facility': 'F4', 'customer': 'M', 'cost': 407}, {'facility': 'F4', 'customer': 'N', 'cost': 812}, {'facility': 'F5', 'customer': 'A', 'cost': 471}, {'facility': 'F5', 'customer': 'B', 'cost': 405}, {'facility': 'F5', 'customer': 'C', 'cost': 729}, {'facility': 'F5', 'customer': 'D', 'cost': 349}, {'facility': 'F5', 'customer': 'E', 'cost': 507}, {'facility': 'F5', 'customer': 'F', 'cost': 148}, {'facility': 'F5', 'customer': 'G', 'cost': 739}, {'facility': 'F5', 'customer': 'H', 'cost': 99}, {'facility': 'F5', 'customer': 'I', 'cost': 594}, {'facility': 'F5', 'customer': 'J', 'cost': 674}, {'facility': 'F5', 'customer': 'K', 'cost': 250}, {'facility': 'F5', 'customer': 'L', 'cost': 973}, {'facility': 'F5', 'customer': 'M', 'cost': 154}, {'facility': 'F5', 'customer': 'N', 'cost': 207}], 'objective': 6193.0}","{'selected': ['F2', 'F5'], 'assignments': ['F2', 'F2', 'F2', 'F5', 'F2', 'F2', 'F2', 'F5', 'F5', 'F2', 'F5', 'F2', 'F5', 'F5']}",25,markdown_table,names
UFLP,UFLP,"Someone running a neighborhood parcel service is weighing which depots to switch on and which depot should handle each delivery. Each depot has a startup cost and each delivery carries a cost depending on the chosen depot, so decisions are judged by the total spend: depot startup costs plus the sum of all delivery costs. Every single delivery needs to be tied to one opened depot and not more. The full list of depots, costs, and deliveries appears below.
{
""num_depots"": 3,
""num_deliveries"": 9,
""depots"": [
{
""depot_id"": ""F1"",
""depot_startup_cost"": 1424
},
{
""depot_id"": ""F2"",
""depot_startup_cost"": 1477
},
{
""depot_id"": ""F3"",
""depot_startup_cost"": 1106
}
],
""deliverys"": [
{
""depot_id"": ""F1"",
""delivery_id"": 1,
""delivery_cost"": 665
},
{
""depot_id"": ""F1"",
""delivery_id"": 2,
""delivery_cost"": 847
},
{
""depot_id"": ""F1"",
""delivery_id"": 3,
""delivery_cost"": 128
},
{
""depot_id"": ""F1"",
""delivery_id"": 4,
""delivery_cost"": 201
},
{
""depot_id"": ""F1"",
""delivery_id"": 5,
""delivery_cost"": 309
},
{
""depot_id"": ""F1"",
""delivery_id"": 6,
""delivery_cost"": 904
},
{
""depot_id"": ""F1"",
""delivery_id"": 7,
""delivery_cost"": 566
},
{
""depot_id"": ""F1"",
""delivery_id"": 8,
""delivery_cost"": 378
},
{
""depot_id"": ""F1"",
""delivery_id"": 9,
""delivery_cost"": 837
},
{
""depot_id"": ""F2"",
""delivery_id"": 1,
""delivery_cost"": 542
},
{
""depot_id"": ""F2"",
""delivery_id"": 2,
""delivery_cost"": 40
},
{
""depot_id"": ""F2"",
""delivery_id"": 3,
""delivery_cost"": 998
},
{
""depot_id"": ""F2"",
""delivery_id"": 4,
""delivery_cost"": 41
},
{
""depot_id"": ""F2"",
""delivery_id"": 5,
""delivery_cost"": 610
},
{
""depot_id"": ""F2"",
""delivery_id"": 6,
""delivery_cost"": 125
},
{
""depot_id"": ""F2"",
""delivery_id"": 7,
""delivery_cost"": 426
},
{
""depot_id"": ""F2"",
""delivery_id"": 8,
""delivery_cost"": 919
},
{
""depot_id"": ""F2"",
""delivery_id"": 9,
""delivery_cost"": 196
},
{
""depot_id"": ""F3"",
""delivery_id"": 1,
""delivery_cost"": 917
},
{
""depot_id"": ""F3"",
""delivery_id"": 2,
""delivery_cost"": 978
},
{
""depot_id"": ""F3"",
""delivery_id"": 3,
""delivery_cost"": 705
},
{
""depot_id"": ""F3"",
""delivery_id"": 4,
""delivery_cost"": 232
},
{
""depot_id"": ""F3"",
""delivery_id"": 5,
""delivery_cost"": 710
},
{
""depot_id"": ""F3"",
""delivery_id"": 6,
""delivery_cost"": 23
},
{
""depot_id"": ""F3"",
""delivery_id"": 7,
""delivery_cost"": 325
},
{
""depot_id"": ""F3"",
""delivery_id"": 8,
""delivery_cost"": 128
},
{
""depot_id"": ""F3"",
""delivery_id"": 9,
""delivery_cost"": 603
}
]
}
You can just send back the choices in a tiny JSON snippet like this:
{
""solution"": {
""selected"": [<depot_to_open>, <depot_to_open>, ...],
""assignments"": [<chosen_open_depot>, <chosen_open_depot>, ...]
}
}
Think of ""selected"" as the list of depots you decide to switch on, and ""assignments"" as, for each delivery in order, which opened depot will handle it. Super casual sketch — not the final picks, just the shape I need.
Please make sure you use the exact depot and delivery identifiers from the instance input — don't rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [1424, 1477, 1106], 'connection_costs': [[665, 847, 128, 201, 309, 904, 566, 378, 837], [542, 40, 998, 41, 610, 125, 426, 919, 196], [917, 978, 705, 232, 710, 23, 325, 128, 603]], 'objective': 5086.0}","{'open_facilities': [0, 1], 'assignments': [1, 1, 0, 1, 0, 1, 1, 0, 1]}",5086.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 9, 'facilities': [{'id': 'F1', 'opening_cost': 1424}, {'id': 'F2', 'opening_cost': 1477}, {'id': 'F3', 'opening_cost': 1106}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 665}, {'facility': 'F1', 'customer': 2, 'cost': 847}, {'facility': 'F1', 'customer': 3, 'cost': 128}, {'facility': 'F1', 'customer': 4, 'cost': 201}, {'facility': 'F1', 'customer': 5, 'cost': 309}, {'facility': 'F1', 'customer': 6, 'cost': 904}, {'facility': 'F1', 'customer': 7, 'cost': 566}, {'facility': 'F1', 'customer': 8, 'cost': 378}, {'facility': 'F1', 'customer': 9, 'cost': 837}, {'facility': 'F2', 'customer': 1, 'cost': 542}, {'facility': 'F2', 'customer': 2, 'cost': 40}, {'facility': 'F2', 'customer': 3, 'cost': 998}, {'facility': 'F2', 'customer': 4, 'cost': 41}, {'facility': 'F2', 'customer': 5, 'cost': 610}, {'facility': 'F2', 'customer': 6, 'cost': 125}, {'facility': 'F2', 'customer': 7, 'cost': 426}, {'facility': 'F2', 'customer': 8, 'cost': 919}, {'facility': 'F2', 'customer': 9, 'cost': 196}, {'facility': 'F3', 'customer': 1, 'cost': 917}, {'facility': 'F3', 'customer': 2, 'cost': 978}, {'facility': 'F3', 'customer': 3, 'cost': 705}, {'facility': 'F3', 'customer': 4, 'cost': 232}, {'facility': 'F3', 'customer': 5, 'cost': 710}, {'facility': 'F3', 'customer': 6, 'cost': 23}, {'facility': 'F3', 'customer': 7, 'cost': 325}, {'facility': 'F3', 'customer': 8, 'cost': 128}, {'facility': 'F3', 'customer': 9, 'cost': 603}], 'objective': 5086.0}","{'selected': ['F1', 'F2'], 'assignments': ['F2', 'F2', 'F1', 'F2', 'F1', 'F2', 'F2', 'F1', 'F2']}",26,json,1
UFLP,UFLP,"There’s a community project to roll out lending lockers for a local tool library so people can pick up items at convenient spots. The job is to pick which lockers to install and then attach every borrower to exactly one of the installed lockers — nobody should be missing or duplicated in the sign-up list. Effectiveness is judged by the sum of two things: the cost of installing the chosen lockers plus the sum of each borrower’s effort to fetch their tools; the lower that combined sum, the better the plan. The specific locker locations, installation costs, and borrower list will be shown below.
Details: 5 candidate locker locations, 11 borrowers, installation costs 2000, 2000, 2000, 2000, 2000.
Locker F1: installation cost 2000.
Locker F2: installation cost 2000.
Locker F3: installation cost 2000.
Locker F4: installation cost 2000.
Locker F5: installation cost 2000.
Borrower A to locker F1: retrieval effort 655.
Borrower B to locker F1: retrieval effort 421.
Borrower C to locker F1: retrieval effort 156.
Borrower D to locker F1: retrieval effort 515.
Borrower E to locker F1: retrieval effort 696.
Borrower F to locker F1: retrieval effort 187.
Borrower G to locker F1: retrieval effort 141.
Borrower H to locker F1: retrieval effort 166.
Borrower I to locker F1: retrieval effort 691.
Borrower J to locker F1: retrieval effort 130.
Borrower K to locker F1: retrieval effort 377.
Borrower A to locker F2: retrieval effort 370.
Borrower B to locker F2: retrieval effort 462.
Borrower C to locker F2: retrieval effort 148.
Borrower D to locker F2: retrieval effort 369.
Borrower E to locker F2: retrieval effort 176.
Borrower F to locker F2: retrieval effort 565.
Borrower G to locker F2: retrieval effort 43.
Borrower H to locker F2: retrieval effort 667.
Borrower I to locker F2: retrieval effort 933.
Borrower J to locker F2: retrieval effort 849.
Borrower K to locker F2: retrieval effort 60.
Borrower A to locker F3: retrieval effort 878.
Borrower B to locker F3: retrieval effort 82.
Borrower C to locker F3: retrieval effort 169.
Borrower D to locker F3: retrieval effort 19.
Borrower E to locker F3: retrieval effort 768.
Borrower F to locker F3: retrieval effort 282.
Borrower G to locker F3: retrieval effort 170.
Borrower H to locker F3: retrieval effort 564.
Borrower I to locker F3: retrieval effort 20.
Borrower J to locker F3: retrieval effort 445.
Borrower K to locker F3: retrieval effort 396.
Borrower A to locker F4: retrieval effort 323.
Borrower B to locker F4: retrieval effort 323.
Borrower C to locker F4: retrieval effort 358.
Borrower D to locker F4: retrieval effort 776.
Borrower E to locker F4: retrieval effort 558.
Borrower F to locker F4: retrieval effort 829.
Borrower G to locker F4: retrieval effort 243.
Borrower H to locker F4: retrieval effort 324.
Borrower I to locker F4: retrieval effort 244.
Borrower J to locker F4: retrieval effort 857.
Borrower K to locker F4: retrieval effort 851.
Borrower A to locker F5: retrieval effort 452.
Borrower B to locker F5: retrieval effort 665.
Borrower C to locker F5: retrieval effort 349.
Borrower D to locker F5: retrieval effort 361.
Borrower E to locker F5: retrieval effort 72.
Borrower F to locker F5: retrieval effort 36.
Borrower G to locker F5: retrieval effort 309.
Borrower H to locker F5: retrieval effort 388.
Borrower I to locker F5: retrieval effort 256.
Borrower J to locker F5: retrieval effort 479.
Borrower K to locker F5: retrieval effort 328.
The lists below enumerate each locker and each borrower-locker retrieval effort.
I’ll send the plan back in a simple JSON layout so it’s easy to read and use. It will follow this shape:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_site_to_open>, <chosen_site_to_open>, ...]
}
}
""selected"" is where I’ll list which locker sites we decide to install. ""assignments"" is a list, in borrower order, saying which opened site each borrower is attached to. Think of it as a short form — a sketch of the shape I’ll fill with the actual choices.
Please make sure to use the exact identifiers from the instance input — do not rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000, 2000], 'connection_costs': [[655, 421, 156, 515, 696, 187, 141, 166, 691, 130, 377], [370, 462, 148, 369, 176, 565, 43, 667, 933, 849, 60], [878, 82, 169, 19, 768, 282, 170, 564, 20, 445, 396], [323, 323, 358, 776, 558, 829, 243, 324, 244, 857, 851], [452, 665, 349, 361, 72, 36, 309, 388, 256, 479, 328]], 'objective': 5695.0}","{'open_facilities': [4], 'assignments': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]}",5695.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 655}, {'facility': 'F1', 'customer': 'B', 'cost': 421}, {'facility': 'F1', 'customer': 'C', 'cost': 156}, {'facility': 'F1', 'customer': 'D', 'cost': 515}, {'facility': 'F1', 'customer': 'E', 'cost': 696}, {'facility': 'F1', 'customer': 'F', 'cost': 187}, {'facility': 'F1', 'customer': 'G', 'cost': 141}, {'facility': 'F1', 'customer': 'H', 'cost': 166}, {'facility': 'F1', 'customer': 'I', 'cost': 691}, {'facility': 'F1', 'customer': 'J', 'cost': 130}, {'facility': 'F1', 'customer': 'K', 'cost': 377}, {'facility': 'F2', 'customer': 'A', 'cost': 370}, {'facility': 'F2', 'customer': 'B', 'cost': 462}, {'facility': 'F2', 'customer': 'C', 'cost': 148}, {'facility': 'F2', 'customer': 'D', 'cost': 369}, {'facility': 'F2', 'customer': 'E', 'cost': 176}, {'facility': 'F2', 'customer': 'F', 'cost': 565}, {'facility': 'F2', 'customer': 'G', 'cost': 43}, {'facility': 'F2', 'customer': 'H', 'cost': 667}, {'facility': 'F2', 'customer': 'I', 'cost': 933}, {'facility': 'F2', 'customer': 'J', 'cost': 849}, {'facility': 'F2', 'customer': 'K', 'cost': 60}, {'facility': 'F3', 'customer': 'A', 'cost': 878}, {'facility': 'F3', 'customer': 'B', 'cost': 82}, {'facility': 'F3', 'customer': 'C', 'cost': 169}, {'facility': 'F3', 'customer': 'D', 'cost': 19}, {'facility': 'F3', 'customer': 'E', 'cost': 768}, {'facility': 'F3', 'customer': 'F', 'cost': 282}, {'facility': 'F3', 'customer': 'G', 'cost': 170}, {'facility': 'F3', 'customer': 'H', 'cost': 564}, {'facility': 'F3', 'customer': 'I', 'cost': 20}, {'facility': 'F3', 'customer': 'J', 'cost': 445}, {'facility': 'F3', 'customer': 'K', 'cost': 396}, {'facility': 'F4', 'customer': 'A', 'cost': 323}, {'facility': 'F4', 'customer': 'B', 'cost': 323}, {'facility': 'F4', 'customer': 'C', 'cost': 358}, {'facility': 'F4', 'customer': 'D', 'cost': 776}, {'facility': 'F4', 'customer': 'E', 'cost': 558}, {'facility': 'F4', 'customer': 'F', 'cost': 829}, {'facility': 'F4', 'customer': 'G', 'cost': 243}, {'facility': 'F4', 'customer': 'H', 'cost': 324}, {'facility': 'F4', 'customer': 'I', 'cost': 244}, {'facility': 'F4', 'customer': 'J', 'cost': 857}, {'facility': 'F4', 'customer': 'K', 'cost': 851}, {'facility': 'F5', 'customer': 'A', 'cost': 452}, {'facility': 'F5', 'customer': 'B', 'cost': 665}, {'facility': 'F5', 'customer': 'C', 'cost': 349}, {'facility': 'F5', 'customer': 'D', 'cost': 361}, {'facility': 'F5', 'customer': 'E', 'cost': 72}, {'facility': 'F5', 'customer': 'F', 'cost': 36}, {'facility': 'F5', 'customer': 'G', 'cost': 309}, {'facility': 'F5', 'customer': 'H', 'cost': 388}, {'facility': 'F5', 'customer': 'I', 'cost': 256}, {'facility': 'F5', 'customer': 'J', 'cost': 479}, {'facility': 'F5', 'customer': 'K', 'cost': 328}], 'objective': 5695.0}","{'selected': ['F5'], 'assignments': ['F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5']}",27,nl,names
UFLP,UFLP,"Recently the county asked us to choose which vaccination sites to operate and to assign each resident to a single chosen site. The winning setup is the one with the smallest total cost — that total comes from the sum of the sites’ operating costs we use plus the travel cost for each resident to their assigned spot. Make sure everyone has one assigned site and no one is assigned twice; the concrete figures are shown below.
For our decision we have 5 candidate sites, 13 residents, and the sequence of site operating costs 2000, 2000, 2000, 2000, 2000.
Site F1: if we open it its operating cost is 2000.
Site F2: if we open it its operating cost is 2000.
Site F3: if we open it its operating cost is 2000.
Site F4: if we open it its operating cost is 2000.
Site F5: if we open it its operating cost is 2000.
Resident 1 — if we assign them to site F1 — would incur travel cost 942.
Resident 2 — if we assign them to site F1 — would incur travel cost 968.
Resident 3 — if we assign them to site F1 — would incur travel cost 326.
Resident 4 — if we assign them to site F1 — would incur travel cost 930.
Resident 5 — if we assign them to site F1 — would incur travel cost 220.
Resident 6 — if we assign them to site F1 — would incur travel cost 42.
Resident 7 — if we assign them to site F1 — would incur travel cost 762.
Resident 8 — if we assign them to site F1 — would incur travel cost 648.
Resident 9 — if we assign them to site F1 — would incur travel cost 388.
Resident 10 — if we assign them to site F1 — would incur travel cost 762.
Resident 11 — if we assign them to site F1 — would incur travel cost 161.
Resident 12 — if we assign them to site F1 — would incur travel cost 849.
Resident 13 — if we assign them to site F1 — would incur travel cost 271.
Resident 1 — if we assign them to site F2 — would incur travel cost 433.
Resident 2 — if we assign them to site F2 — would incur travel cost 330.
Resident 3 — if we assign them to site F2 — would incur travel cost 625.
Resident 4 — if we assign them to site F2 — would incur travel cost 360.
Resident 5 — if we assign them to site F2 — would incur travel cost 532.
Resident 6 — if we assign them to site F2 — would incur travel cost 740.
Resident 7 — if we assign them to site F2 — would incur travel cost 781.
Resident 8 — if we assign them to site F2 — would incur travel cost 804.
Resident 9 — if we assign them to site F2 — would incur travel cost 858.
Resident 10 — if we assign them to site F2 — would incur travel cost 176.
Resident 11 — if we assign them to site F2 — would incur travel cost 162.
Resident 12 — if we assign them to site F2 — would incur travel cost 694.
Resident 13 — if we assign them to site F2 — would incur travel cost 467.
Resident 1 — if we assign them to site F3 — would incur travel cost 117.
Resident 2 — if we assign them to site F3 — would incur travel cost 238.
Resident 3 — if we assign them to site F3 — would incur travel cost 491.
Resident 4 — if we assign them to site F3 — would incur travel cost 409.
Resident 5 — if we assign them to site F3 — would incur travel cost 20.
Resident 6 — if we assign them to site F3 — would incur travel cost 697.
Resident 7 — if we assign them to site F3 — would incur travel cost 174.
Resident 8 — if we assign them to site F3 — would incur travel cost 239.
Resident 9 — if we assign them to site F3 — would incur travel cost 836.
Resident 10 — if we assign them to site F3 — would incur travel cost 912.
Resident 11 — if we assign them to site F3 — would incur travel cost 501.
Resident 12 — if we assign them to site F3 — would incur travel cost 175.
Resident 13 — if we assign them to site F3 — would incur travel cost 766.
Resident 1 — if we assign them to site F4 — would incur travel cost 177.
Resident 2 — if we assign them to site F4 — would incur travel cost 60.
Resident 3 — if we assign them to site F4 — would incur travel cost 150.
Resident 4 — if we assign them to site F4 — would incur travel cost 703.
Resident 5 — if we assign them to site F4 — would incur travel cost 903.
Resident 6 — if we assign them to site F4 — would incur travel cost 680.
Resident 7 — if we assign them to site F4 — would incur travel cost 58.
Resident 8 — if we assign them to site F4 — would incur travel cost 464.
Resident 9 — if we assign them to site F4 — would incur travel cost 257.
Resident 10 — if we assign them to site F4 — would incur travel cost 509.
Resident 11 — if we assign them to site F4 — would incur travel cost 937.
Resident 12 — if we assign them to site F4 — would incur travel cost 670.
Resident 13 — if we assign them to site F4 — would incur travel cost 606.
Resident 1 — if we assign them to site F5 — would incur travel cost 353.
Resident 2 — if we assign them to site F5 — would incur travel cost 279.
Resident 3 — if we assign them to site F5 — would incur travel cost 843.
Resident 4 — if we assign them to site F5 — would incur travel cost 178.
Resident 5 — if we assign them to site F5 — would incur travel cost 699.
Resident 6 — if we assign them to site F5 — would incur travel cost 783.
Resident 7 — if we assign them to site F5 — would incur travel cost 51.
Resident 8 — if we assign them to site F5 — would incur travel cost 66.
Resident 9 — if we assign them to site F5 — would incur travel cost 392.
Resident 10 — if we assign them to site F5 — would incur travel cost 526.
Resident 11 — if we assign them to site F5 — would incur travel cost 30.
Resident 12 — if we assign them to site F5 — would incur travel cost 240.
Resident 13 — if we assign them to site F5 — would incur travel cost 96.
We'll use these figures to choose which sites to operate and to assign every resident to exactly one opened site.
Just send back your answer in this little JSON shape so I can read it programmatically — nothing fancy, just the keys below.
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
""selected"" is where you list the vaccination sites you choose to operate. ""assignments"" is a list, in the same order as the residents in the instance, saying which chosen site each resident will go to. Think of it like filling out a simple form: which sites are open, and which site each person is assigned to.
This JSON is just a sketch of the expected shape — please return the actual choices and assignments when you answer.
All identifiers must be used exactly as they appear in the instance input — no renaming and no new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000, 2000], 'connection_costs': [[942, 968, 326, 930, 220, 42, 762, 648, 388, 762, 161, 849, 271], [433, 330, 625, 360, 532, 740, 781, 804, 858, 176, 162, 694, 467], [117, 238, 491, 409, 20, 697, 174, 239, 836, 912, 501, 175, 766], [177, 60, 150, 703, 903, 680, 58, 464, 257, 509, 937, 670, 606], [353, 279, 843, 178, 699, 783, 51, 66, 392, 526, 30, 240, 96]], 'objective': 6536.0}","{'open_facilities': [4], 'assignments': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]}",6536.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 13, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}, {'id': 12}, {'id': 13}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 942}, {'facility': 'F1', 'customer': 2, 'cost': 968}, {'facility': 'F1', 'customer': 3, 'cost': 326}, {'facility': 'F1', 'customer': 4, 'cost': 930}, {'facility': 'F1', 'customer': 5, 'cost': 220}, {'facility': 'F1', 'customer': 6, 'cost': 42}, {'facility': 'F1', 'customer': 7, 'cost': 762}, {'facility': 'F1', 'customer': 8, 'cost': 648}, {'facility': 'F1', 'customer': 9, 'cost': 388}, {'facility': 'F1', 'customer': 10, 'cost': 762}, {'facility': 'F1', 'customer': 11, 'cost': 161}, {'facility': 'F1', 'customer': 12, 'cost': 849}, {'facility': 'F1', 'customer': 13, 'cost': 271}, {'facility': 'F2', 'customer': 1, 'cost': 433}, {'facility': 'F2', 'customer': 2, 'cost': 330}, {'facility': 'F2', 'customer': 3, 'cost': 625}, {'facility': 'F2', 'customer': 4, 'cost': 360}, {'facility': 'F2', 'customer': 5, 'cost': 532}, {'facility': 'F2', 'customer': 6, 'cost': 740}, {'facility': 'F2', 'customer': 7, 'cost': 781}, {'facility': 'F2', 'customer': 8, 'cost': 804}, {'facility': 'F2', 'customer': 9, 'cost': 858}, {'facility': 'F2', 'customer': 10, 'cost': 176}, {'facility': 'F2', 'customer': 11, 'cost': 162}, {'facility': 'F2', 'customer': 12, 'cost': 694}, {'facility': 'F2', 'customer': 13, 'cost': 467}, {'facility': 'F3', 'customer': 1, 'cost': 117}, {'facility': 'F3', 'customer': 2, 'cost': 238}, {'facility': 'F3', 'customer': 3, 'cost': 491}, {'facility': 'F3', 'customer': 4, 'cost': 409}, {'facility': 'F3', 'customer': 5, 'cost': 20}, {'facility': 'F3', 'customer': 6, 'cost': 697}, {'facility': 'F3', 'customer': 7, 'cost': 174}, {'facility': 'F3', 'customer': 8, 'cost': 239}, {'facility': 'F3', 'customer': 9, 'cost': 836}, {'facility': 'F3', 'customer': 10, 'cost': 912}, {'facility': 'F3', 'customer': 11, 'cost': 501}, {'facility': 'F3', 'customer': 12, 'cost': 175}, {'facility': 'F3', 'customer': 13, 'cost': 766}, {'facility': 'F4', 'customer': 1, 'cost': 177}, {'facility': 'F4', 'customer': 2, 'cost': 60}, {'facility': 'F4', 'customer': 3, 'cost': 150}, {'facility': 'F4', 'customer': 4, 'cost': 703}, {'facility': 'F4', 'customer': 5, 'cost': 903}, {'facility': 'F4', 'customer': 6, 'cost': 680}, {'facility': 'F4', 'customer': 7, 'cost': 58}, {'facility': 'F4', 'customer': 8, 'cost': 464}, {'facility': 'F4', 'customer': 9, 'cost': 257}, {'facility': 'F4', 'customer': 10, 'cost': 509}, {'facility': 'F4', 'customer': 11, 'cost': 937}, {'facility': 'F4', 'customer': 12, 'cost': 670}, {'facility': 'F4', 'customer': 13, 'cost': 606}, {'facility': 'F5', 'customer': 1, 'cost': 353}, {'facility': 'F5', 'customer': 2, 'cost': 279}, {'facility': 'F5', 'customer': 3, 'cost': 843}, {'facility': 'F5', 'customer': 4, 'cost': 178}, {'facility': 'F5', 'customer': 5, 'cost': 699}, {'facility': 'F5', 'customer': 6, 'cost': 783}, {'facility': 'F5', 'customer': 7, 'cost': 51}, {'facility': 'F5', 'customer': 8, 'cost': 66}, {'facility': 'F5', 'customer': 9, 'cost': 392}, {'facility': 'F5', 'customer': 10, 'cost': 526}, {'facility': 'F5', 'customer': 11, 'cost': 30}, {'facility': 'F5', 'customer': 12, 'cost': 240}, {'facility': 'F5', 'customer': 13, 'cost': 96}], 'objective': 6536.0}","{'selected': ['F5'], 'assignments': ['F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5', 'F5']}",28,nl,1
UFLP,UFLP,"I run a fleet of mobile pet groomers and have to pick which pop-up grooming tents to put up around town and then send every client to one of those tents. The trick is that each tent costs money to set up, and every client has a travel or pickup cost to get to the tent they use, so the better plan is the one that keeps the overall bill as low as possible — add up the setup fees for the tents that are put up plus the travel/pickup cost for every client. Each client has to be assigned to exactly one of the tents we actually set up (no one gets skipped and nobody goes to two places), and tents can handle as many pets as needed. The concrete details are shown below.
# num_candidate_tents=5
# num_clients=12
# TENTS
tent_id,tent_setup_cost
F1,1000
F2,1000
F3,1000
F4,1000
F5,1000
# CLIENTS
client_id
0
1
2
3
4
5
6
7
8
9
10
11
# CLIENT_TRAVELS
tent_id,client_id,client_travel_cost
F1,0,144
F1,1,51
F1,2,498
F1,3,601
F1,4,254
F1,5,19
F1,6,73
F1,7,892
F1,8,703
F1,9,999
F1,10,673
F1,11,843
F2,0,557
F2,1,600
F2,2,313
F2,3,729
F2,4,312
F2,5,506
F2,6,702
F2,7,437
F2,8,229
F2,9,415
F2,10,50
F2,11,60
F3,0,145
F3,1,609
F3,2,10
F3,3,700
F3,4,61
F3,5,938
F3,6,79
F3,7,139
F3,8,336
F3,9,644
F3,10,30
F3,11,783
F4,0,88
F4,1,654
F4,2,933
F4,3,119
F4,4,671
F4,5,407
F4,6,141
F4,7,384
F4,8,683
F4,9,495
F4,10,137
F4,11,594
F5,0,24
F5,1,732
F5,2,47
F5,3,573
F5,4,986
F5,5,102
F5,6,103
F5,7,402
F5,8,883
F5,9,524
F5,10,715
F5,11,229
Also, just so everything comes back to me in a predictable shape, please put the plan in this little JSON layout when you reply — just the same structure, nice and simple:
{
""solution"": {
""selected"": [<tent_to_open>, <tent_to_open>, ...],
""assignments"": [<chosen_open_tent>, <chosen_open_tent>, ...]
}
}
""selected"" is where you list the tents you decide to set up. ""assignments"" is a client-by-client list (in the same order as the input) saying which opened tent each client will go to. Think of it like filling out a short form: which tents are up, and for every client which tent they use.
This JSON is just a sketch of the expected shape — not the actual answer itself.
Please make sure to use the exact identifiers from the instance input when you fill this in — don't rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1000, 1000, 1000, 1000, 1000], 'connection_costs': [[144, 51, 498, 601, 254, 19, 73, 892, 703, 999, 673, 843], [557, 600, 313, 729, 312, 506, 702, 437, 229, 415, 50, 60], [145, 609, 10, 700, 61, 938, 79, 139, 336, 644, 30, 783], [88, 654, 933, 119, 671, 407, 141, 384, 683, 495, 137, 594], [24, 732, 47, 573, 986, 102, 103, 402, 883, 524, 715, 229]], 'objective': 4646.0}","{'open_facilities': [0, 1], 'assignments': [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]}",4646.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 12, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}, {'id': 'F5', 'opening_cost': 1000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 144}, {'facility': 'F1', 'customer': 1, 'cost': 51}, {'facility': 'F1', 'customer': 2, 'cost': 498}, {'facility': 'F1', 'customer': 3, 'cost': 601}, {'facility': 'F1', 'customer': 4, 'cost': 254}, {'facility': 'F1', 'customer': 5, 'cost': 19}, {'facility': 'F1', 'customer': 6, 'cost': 73}, {'facility': 'F1', 'customer': 7, 'cost': 892}, {'facility': 'F1', 'customer': 8, 'cost': 703}, {'facility': 'F1', 'customer': 9, 'cost': 999}, {'facility': 'F1', 'customer': 10, 'cost': 673}, {'facility': 'F1', 'customer': 11, 'cost': 843}, {'facility': 'F2', 'customer': 0, 'cost': 557}, {'facility': 'F2', 'customer': 1, 'cost': 600}, {'facility': 'F2', 'customer': 2, 'cost': 313}, {'facility': 'F2', 'customer': 3, 'cost': 729}, {'facility': 'F2', 'customer': 4, 'cost': 312}, {'facility': 'F2', 'customer': 5, 'cost': 506}, {'facility': 'F2', 'customer': 6, 'cost': 702}, {'facility': 'F2', 'customer': 7, 'cost': 437}, {'facility': 'F2', 'customer': 8, 'cost': 229}, {'facility': 'F2', 'customer': 9, 'cost': 415}, {'facility': 'F2', 'customer': 10, 'cost': 50}, {'facility': 'F2', 'customer': 11, 'cost': 60}, {'facility': 'F3', 'customer': 0, 'cost': 145}, {'facility': 'F3', 'customer': 1, 'cost': 609}, {'facility': 'F3', 'customer': 2, 'cost': 10}, {'facility': 'F3', 'customer': 3, 'cost': 700}, {'facility': 'F3', 'customer': 4, 'cost': 61}, {'facility': 'F3', 'customer': 5, 'cost': 938}, {'facility': 'F3', 'customer': 6, 'cost': 79}, {'facility': 'F3', 'customer': 7, 'cost': 139}, {'facility': 'F3', 'customer': 8, 'cost': 336}, {'facility': 'F3', 'customer': 9, 'cost': 644}, {'facility': 'F3', 'customer': 10, 'cost': 30}, {'facility': 'F3', 'customer': 11, 'cost': 783}, {'facility': 'F4', 'customer': 0, 'cost': 88}, {'facility': 'F4', 'customer': 1, 'cost': 654}, {'facility': 'F4', 'customer': 2, 'cost': 933}, {'facility': 'F4', 'customer': 3, 'cost': 119}, {'facility': 'F4', 'customer': 4, 'cost': 671}, {'facility': 'F4', 'customer': 5, 'cost': 407}, {'facility': 'F4', 'customer': 6, 'cost': 141}, {'facility': 'F4', 'customer': 7, 'cost': 384}, {'facility': 'F4', 'customer': 8, 'cost': 683}, {'facility': 'F4', 'customer': 9, 'cost': 495}, {'facility': 'F4', 'customer': 10, 'cost': 137}, {'facility': 'F4', 'customer': 11, 'cost': 594}, {'facility': 'F5', 'customer': 0, 'cost': 24}, {'facility': 'F5', 'customer': 1, 'cost': 732}, {'facility': 'F5', 'customer': 2, 'cost': 47}, {'facility': 'F5', 'customer': 3, 'cost': 573}, {'facility': 'F5', 'customer': 4, 'cost': 986}, {'facility': 'F5', 'customer': 5, 'cost': 102}, {'facility': 'F5', 'customer': 6, 'cost': 103}, {'facility': 'F5', 'customer': 7, 'cost': 402}, {'facility': 'F5', 'customer': 8, 'cost': 883}, {'facility': 'F5', 'customer': 9, 'cost': 524}, {'facility': 'F5', 'customer': 10, 'cost': 715}, {'facility': 'F5', 'customer': 11, 'cost': 229}], 'objective': 4646.0}","{'selected': ['F1', 'F2'], 'assignments': ['F1', 'F1', 'F2', 'F1', 'F1', 'F1', 'F1', 'F2', 'F2', 'F2', 'F2', 'F2']}",29,csv,0
UFLP,UFLP,"I’m looking after the city’s waste dropoff network and need to choose which pickup sites to keep open and which to close. Each site kept costs money to maintain, and every household has some effort or travel distance to get to whichever site they use. A good plan is simply one that costs less overall: add up the upkeep costs for the sites that stay open plus the travel burden for every household to its assigned site, and keep that total as small as possible. Every household has to be assigned to exactly one of the sites that are kept open — nobody can be left without a dropoff or sent to a closed one. The exact list of sites, their maintenance fees, and household travel numbers are shown below.
There are 5 dropoff sites and 12 households in this instance.
**Dropoff Sites**
| dropoff_site_id | site_maintenance_cost |
|---|---|
| F1 | 2000 |
| F2 | 2000 |
| F3 | 2000 |
| F4 | 2000 |
| F5 | 2000 |
**Households**
| household_id |
|---|
| 0 |
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| 7 |
| 8 |
| 9 |
| 10 |
| 11 |
**Household Travel Cost**
| dropoff_site_id | household_id | household_travel_cost |
|---|---|---|
| F1 | 0 | 808 |
| F1 | 1 | 23 |
| F1 | 2 | 582 |
| F1 | 3 | 478 |
| F1 | 4 | 566 |
| F1 | 5 | 190 |
| F1 | 6 | 624 |
| F1 | 7 | 265 |
| F1 | 8 | 549 |
| F1 | 9 | 497 |
| F1 | 10 | 840 |
| F1 | 11 | 18 |
| F2 | 0 | 132 |
| F2 | 1 | 742 |
| F2 | 2 | 728 |
| F2 | 3 | 457 |
| F2 | 4 | 702 |
| F2 | 5 | 219 |
| F2 | 6 | 924 |
| F2 | 7 | 594 |
| F2 | 8 | 923 |
| F2 | 9 | 617 |
| F2 | 10 | 679 |
| F2 | 11 | 983 |
| F3 | 0 | 367 |
| F3 | 1 | 749 |
| F3 | 2 | 787 |
| F3 | 3 | 545 |
| F3 | 4 | 958 |
| F3 | 5 | 423 |
| F3 | 6 | 478 |
| F3 | 7 | 688 |
| F3 | 8 | 952 |
| F3 | 9 | 124 |
| F3 | 10 | 420 |
| F3 | 11 | 367 |
| F4 | 0 | 723 |
| F4 | 1 | 136 |
| F4 | 2 | 317 |
| F4 | 3 | 883 |
| F4 | 4 | 15 |
| F4 | 5 | 689 |
| F4 | 6 | 333 |
| F4 | 7 | 733 |
| F4 | 8 | 162 |
| F4 | 9 | 136 |
| F4 | 10 | 711 |
| F4 | 11 | 12 |
| F5 | 0 | 213 |
| F5 | 1 | 858 |
| F5 | 2 | 792 |
| F5 | 3 | 385 |
| F5 | 4 | 637 |
| F5 | 5 | 849 |
| F5 | 6 | 829 |
| F5 | 7 | 469 |
| F5 | 8 | 909 |
| F5 | 9 | 205 |
| F5 | 10 | 862 |
| F5 | 11 | 684 |
I’ll show the shape I want the answer in so it’s easy to read and plug into whatever tool you’re using. Keep the layout exactly like this:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
""selected"" is the list of pickup sites you’ll keep open. ""assignments"" lists, for each household in the same order as the input, which open site that household uses. This is just a sketch of the expected shape — not the real solution.
Please make sure all identifiers come straight from the instance and are not changed or invented. No renaming or new labels — use them exactly as given.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000, 2000], 'connection_costs': [[808, 23, 582, 478, 566, 190, 624, 265, 549, 497, 840, 18], [132, 742, 728, 457, 702, 219, 924, 594, 923, 617, 679, 983], [367, 749, 787, 545, 958, 423, 478, 688, 952, 124, 420, 367], [723, 136, 317, 883, 15, 689, 333, 733, 162, 136, 711, 12], [213, 858, 792, 385, 637, 849, 829, 469, 909, 205, 862, 684]], 'objective': 6850.0}","{'open_facilities': [3], 'assignments': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]}",6850.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 12, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 808}, {'facility': 'F1', 'customer': 1, 'cost': 23}, {'facility': 'F1', 'customer': 2, 'cost': 582}, {'facility': 'F1', 'customer': 3, 'cost': 478}, {'facility': 'F1', 'customer': 4, 'cost': 566}, {'facility': 'F1', 'customer': 5, 'cost': 190}, {'facility': 'F1', 'customer': 6, 'cost': 624}, {'facility': 'F1', 'customer': 7, 'cost': 265}, {'facility': 'F1', 'customer': 8, 'cost': 549}, {'facility': 'F1', 'customer': 9, 'cost': 497}, {'facility': 'F1', 'customer': 10, 'cost': 840}, {'facility': 'F1', 'customer': 11, 'cost': 18}, {'facility': 'F2', 'customer': 0, 'cost': 132}, {'facility': 'F2', 'customer': 1, 'cost': 742}, {'facility': 'F2', 'customer': 2, 'cost': 728}, {'facility': 'F2', 'customer': 3, 'cost': 457}, {'facility': 'F2', 'customer': 4, 'cost': 702}, {'facility': 'F2', 'customer': 5, 'cost': 219}, {'facility': 'F2', 'customer': 6, 'cost': 924}, {'facility': 'F2', 'customer': 7, 'cost': 594}, {'facility': 'F2', 'customer': 8, 'cost': 923}, {'facility': 'F2', 'customer': 9, 'cost': 617}, {'facility': 'F2', 'customer': 10, 'cost': 679}, {'facility': 'F2', 'customer': 11, 'cost': 983}, {'facility': 'F3', 'customer': 0, 'cost': 367}, {'facility': 'F3', 'customer': 1, 'cost': 749}, {'facility': 'F3', 'customer': 2, 'cost': 787}, {'facility': 'F3', 'customer': 3, 'cost': 545}, {'facility': 'F3', 'customer': 4, 'cost': 958}, {'facility': 'F3', 'customer': 5, 'cost': 423}, {'facility': 'F3', 'customer': 6, 'cost': 478}, {'facility': 'F3', 'customer': 7, 'cost': 688}, {'facility': 'F3', 'customer': 8, 'cost': 952}, {'facility': 'F3', 'customer': 9, 'cost': 124}, {'facility': 'F3', 'customer': 10, 'cost': 420}, {'facility': 'F3', 'customer': 11, 'cost': 367}, {'facility': 'F4', 'customer': 0, 'cost': 723}, {'facility': 'F4', 'customer': 1, 'cost': 136}, {'facility': 'F4', 'customer': 2, 'cost': 317}, {'facility': 'F4', 'customer': 3, 'cost': 883}, {'facility': 'F4', 'customer': 4, 'cost': 15}, {'facility': 'F4', 'customer': 5, 'cost': 689}, {'facility': 'F4', 'customer': 6, 'cost': 333}, {'facility': 'F4', 'customer': 7, 'cost': 733}, {'facility': 'F4', 'customer': 8, 'cost': 162}, {'facility': 'F4', 'customer': 9, 'cost': 136}, {'facility': 'F4', 'customer': 10, 'cost': 711}, {'facility': 'F4', 'customer': 11, 'cost': 12}, {'facility': 'F5', 'customer': 0, 'cost': 213}, {'facility': 'F5', 'customer': 1, 'cost': 858}, {'facility': 'F5', 'customer': 2, 'cost': 792}, {'facility': 'F5', 'customer': 3, 'cost': 385}, {'facility': 'F5', 'customer': 4, 'cost': 637}, {'facility': 'F5', 'customer': 5, 'cost': 849}, {'facility': 'F5', 'customer': 6, 'cost': 829}, {'facility': 'F5', 'customer': 7, 'cost': 469}, {'facility': 'F5', 'customer': 8, 'cost': 909}, {'facility': 'F5', 'customer': 9, 'cost': 205}, {'facility': 'F5', 'customer': 10, 'cost': 862}, {'facility': 'F5', 'customer': 11, 'cost': 684}], 'objective': 6850.0}","{'selected': ['F4'], 'assignments': ['F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4']}",30,markdown_table,0
UFLP,UFLP,"Many people assumed the answer was “turn on everything,” but the ops crew knew better: only some nodes should be enabled, and each user should be assigned to one enabled node. Switching on a node costs money, and each user routed pays a latency cost — the overall amount to watch is the sum of those activation fees plus the users’ latency costs, so a plan that lowers that sum wins. Each user needs a single assigned active node (no doubling up or leaving anyone out), and capacity isn’t a constraint. The specifics are given below.
# total_edge_nodes=4
# total_users=10
# NODES
node_id,node_activation_cost
F1,2000
F2,2000
F3,2000
F4,2000
# USERS
user_id
0
1
2
3
4
5
6
7
8
9
# LATENCYS
node_id,user_id,latency_cost
F1,0,964
F1,1,973
F1,2,891
F1,3,613
F1,4,258
F1,5,333
F1,6,293
F1,7,22
F1,8,188
F1,9,609
F2,0,293
F2,1,317
F2,2,916
F2,3,880
F2,4,872
F2,5,473
F2,6,548
F2,7,279
F2,8,896
F2,9,894
F3,0,334
F3,1,142
F3,2,185
F3,3,61
F3,4,91
F3,5,420
F3,6,6
F3,7,410
F3,8,963
F3,9,492
F4,0,343
F4,1,166
F4,2,59
F4,3,818
F4,4,9
F4,5,748
F4,6,322
F4,7,23
F4,8,117
F4,9,758
If you want to reply with the plan, please stick to this simple JSON shape so it's easy to parse — just a tiny sketch of which nodes you turn on and who goes where.
{
""solution"": {
""selected"": [<node_to_enable>, <node_to_enable>, ...],
""assignments"": [<assigned_node>, <assigned_node>, ...]
}
}
""selected"" is the list of nodes you switch on (the activation fees you pay). ""assignments"" is a per-user list — for each user in the same order as the input, put the one active node they're routed to. Think of it like filling out a short form: which nodes are enabled, and then, for each user, which enabled node they use. This JSON is just the expected shape — not the actual answer.
Please make sure to use the identifiers exactly as they appear in the instance input — do not rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000], 'connection_costs': [[964, 973, 891, 613, 258, 333, 293, 22, 188, 609], [293, 317, 916, 880, 872, 473, 548, 279, 896, 894], [334, 142, 185, 61, 91, 420, 6, 410, 963, 492], [343, 166, 59, 818, 9, 748, 322, 23, 117, 758]], 'objective': 5104.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}",5104.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 10, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 964}, {'facility': 'F1', 'customer': 1, 'cost': 973}, {'facility': 'F1', 'customer': 2, 'cost': 891}, {'facility': 'F1', 'customer': 3, 'cost': 613}, {'facility': 'F1', 'customer': 4, 'cost': 258}, {'facility': 'F1', 'customer': 5, 'cost': 333}, {'facility': 'F1', 'customer': 6, 'cost': 293}, {'facility': 'F1', 'customer': 7, 'cost': 22}, {'facility': 'F1', 'customer': 8, 'cost': 188}, {'facility': 'F1', 'customer': 9, 'cost': 609}, {'facility': 'F2', 'customer': 0, 'cost': 293}, {'facility': 'F2', 'customer': 1, 'cost': 317}, {'facility': 'F2', 'customer': 2, 'cost': 916}, {'facility': 'F2', 'customer': 3, 'cost': 880}, {'facility': 'F2', 'customer': 4, 'cost': 872}, {'facility': 'F2', 'customer': 5, 'cost': 473}, {'facility': 'F2', 'customer': 6, 'cost': 548}, {'facility': 'F2', 'customer': 7, 'cost': 279}, {'facility': 'F2', 'customer': 8, 'cost': 896}, {'facility': 'F2', 'customer': 9, 'cost': 894}, {'facility': 'F3', 'customer': 0, 'cost': 334}, {'facility': 'F3', 'customer': 1, 'cost': 142}, {'facility': 'F3', 'customer': 2, 'cost': 185}, {'facility': 'F3', 'customer': 3, 'cost': 61}, {'facility': 'F3', 'customer': 4, 'cost': 91}, {'facility': 'F3', 'customer': 5, 'cost': 420}, {'facility': 'F3', 'customer': 6, 'cost': 6}, {'facility': 'F3', 'customer': 7, 'cost': 410}, {'facility': 'F3', 'customer': 8, 'cost': 963}, {'facility': 'F3', 'customer': 9, 'cost': 492}, {'facility': 'F4', 'customer': 0, 'cost': 343}, {'facility': 'F4', 'customer': 1, 'cost': 166}, {'facility': 'F4', 'customer': 2, 'cost': 59}, {'facility': 'F4', 'customer': 3, 'cost': 818}, {'facility': 'F4', 'customer': 4, 'cost': 9}, {'facility': 'F4', 'customer': 5, 'cost': 748}, {'facility': 'F4', 'customer': 6, 'cost': 322}, {'facility': 'F4', 'customer': 7, 'cost': 23}, {'facility': 'F4', 'customer': 8, 'cost': 117}, {'facility': 'F4', 'customer': 9, 'cost': 758}], 'objective': 5104.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",31,csv,0
UFLP,UFLP,"Many people depend on our local meal pickup program, and part of running it is choosing which kitchens to turn on and deciding a single kitchen for each recipient. Turning on a kitchen costs a set amount, and getting a meal from that kitchen to a person has its own cost — the grand total is the sum of the kitchens we open plus all the individual pickup/delivery charges. Every recipient must be paired with one open kitchen (no doubles, no omissions), and open kitchens can take unlimited orders. The concrete numbers and options are listed below.
{
""total_kitchens"": 6,
""total_recipients"": 12,
""kitchens"": [
{
""kitchen_id"": ""F1"",
""kitchen_opening_cost"": 2000
},
{
""kitchen_id"": ""F2"",
""kitchen_opening_cost"": 2000
},
{
""kitchen_id"": ""F3"",
""kitchen_opening_cost"": 2000
},
{
""kitchen_id"": ""F4"",
""kitchen_opening_cost"": 2000
},
{
""kitchen_id"": ""F5"",
""kitchen_opening_cost"": 2000
},
{
""kitchen_id"": ""F6"",
""kitchen_opening_cost"": 2000
}
],
""recipients"": [
{
""recipient_id"": 0
},
{
""recipient_id"": 1
},
{
""recipient_id"": 2
},
{
""recipient_id"": 3
},
{
""recipient_id"": 4
},
{
""recipient_id"": 5
},
{
""recipient_id"": 6
},
{
""recipient_id"": 7
},
{
""recipient_id"": 8
},
{
""recipient_id"": 9
},
{
""recipient_id"": 10
},
{
""recipient_id"": 11
}
],
""pickup_deliverys"": [
{
""kitchen_id"": ""F1"",
""recipient_id"": 0,
""pickup_delivery_cost"": 63
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 1,
""pickup_delivery_cost"": 653
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 2,
""pickup_delivery_cost"": 90
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 3,
""pickup_delivery_cost"": 509
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 4,
""pickup_delivery_cost"": 741
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 5,
""pickup_delivery_cost"": 649
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 6,
""pickup_delivery_cost"": 405
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 7,
""pickup_delivery_cost"": 579
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 8,
""pickup_delivery_cost"": 975
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 9,
""pickup_delivery_cost"": 353
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 10,
""pickup_delivery_cost"": 481
},
{
""kitchen_id"": ""F1"",
""recipient_id"": 11,
""pickup_delivery_cost"": 434
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 0,
""pickup_delivery_cost"": 24
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 1,
""pickup_delivery_cost"": 138
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 2,
""pickup_delivery_cost"": 304
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 3,
""pickup_delivery_cost"": 842
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 4,
""pickup_delivery_cost"": 149
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 5,
""pickup_delivery_cost"": 676
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 6,
""pickup_delivery_cost"": 913
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 7,
""pickup_delivery_cost"": 919
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 8,
""pickup_delivery_cost"": 217
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 9,
""pickup_delivery_cost"": 689
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 10,
""pickup_delivery_cost"": 337
},
{
""kitchen_id"": ""F2"",
""recipient_id"": 11,
""pickup_delivery_cost"": 323
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 0,
""pickup_delivery_cost"": 401
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 1,
""pickup_delivery_cost"": 690
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 2,
""pickup_delivery_cost"": 280
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 3,
""pickup_delivery_cost"": 169
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 4,
""pickup_delivery_cost"": 830
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 5,
""pickup_delivery_cost"": 98
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 6,
""pickup_delivery_cost"": 335
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 7,
""pickup_delivery_cost"": 927
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 8,
""pickup_delivery_cost"": 276
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 9,
""pickup_delivery_cost"": 451
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 10,
""pickup_delivery_cost"": 84
},
{
""kitchen_id"": ""F3"",
""recipient_id"": 11,
""pickup_delivery_cost"": 315
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 0,
""pickup_delivery_cost"": 263
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 1,
""pickup_delivery_cost"": 535
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 2,
""pickup_delivery_cost"": 971
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 3,
""pickup_delivery_cost"": 846
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 4,
""pickup_delivery_cost"": 216
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 5,
""pickup_delivery_cost"": 589
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 6,
""pickup_delivery_cost"": 462
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 7,
""pickup_delivery_cost"": 91
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 8,
""pickup_delivery_cost"": 269
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 9,
""pickup_delivery_cost"": 416
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 10,
""pickup_delivery_cost"": 219
},
{
""kitchen_id"": ""F4"",
""recipient_id"": 11,
""pickup_delivery_cost"": 44
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 0,
""pickup_delivery_cost"": 570
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 1,
""pickup_delivery_cost"": 93
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 2,
""pickup_delivery_cost"": 701
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 3,
""pickup_delivery_cost"": 401
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 4,
""pickup_delivery_cost"": 303
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 5,
""pickup_delivery_cost"": 223
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 6,
""pickup_delivery_cost"": 497
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 7,
""pickup_delivery_cost"": 575
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 8,
""pickup_delivery_cost"": 880
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 9,
""pickup_delivery_cost"": 230
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 10,
""pickup_delivery_cost"": 328
},
{
""kitchen_id"": ""F5"",
""recipient_id"": 11,
""pickup_delivery_cost"": 899
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 0,
""pickup_delivery_cost"": 89
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 1,
""pickup_delivery_cost"": 718
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 2,
""pickup_delivery_cost"": 30
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 3,
""pickup_delivery_cost"": 307
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 4,
""pickup_delivery_cost"": 852
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 5,
""pickup_delivery_cost"": 282
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 6,
""pickup_delivery_cost"": 70
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 7,
""pickup_delivery_cost"": 703
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 8,
""pickup_delivery_cost"": 888
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 9,
""pickup_delivery_cost"": 406
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 10,
""pickup_delivery_cost"": 14
},
{
""kitchen_id"": ""F6"",
""recipient_id"": 11,
""pickup_delivery_cost"": 584
}
]
}
If you prefer a neat, copy-pastable format for the result, I'll use a tiny JSON sketch like this so it's easy to read and check:
{
""solution"": {
""selected"": [<kitchen_to_open>, <kitchen_to_open>, ...],
""assignments"": [<kitchen_chosen_for_recipient>, <kitchen_chosen_for_recipient>, ...]
}
}
""selected"" is where I'll list the kitchens we decide to turn on. ""assignments"" is a list, one entry per recipient in the same order as the instance, showing which open kitchen each person will use. This is just the shape I’ll follow — not the final choices.
Please use the exact identifiers from the instance input for every entry — don't rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000, 2000, 2000], 'connection_costs': [[63, 653, 90, 509, 741, 649, 405, 579, 975, 353, 481, 434], [24, 138, 304, 842, 149, 676, 913, 919, 217, 689, 337, 323], [401, 690, 280, 169, 830, 98, 335, 927, 276, 451, 84, 315], [263, 535, 971, 846, 216, 589, 462, 91, 269, 416, 219, 44], [570, 93, 701, 401, 303, 223, 497, 575, 880, 230, 328, 899], [89, 718, 30, 307, 852, 282, 70, 703, 888, 406, 14, 584]], 'objective': 6353.0}","{'open_facilities': [3, 5], 'assignments': [5, 3, 5, 5, 3, 5, 5, 3, 3, 5, 5, 3]}",6353.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 12, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}, {'id': 'F6', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 63}, {'facility': 'F1', 'customer': 1, 'cost': 653}, {'facility': 'F1', 'customer': 2, 'cost': 90}, {'facility': 'F1', 'customer': 3, 'cost': 509}, {'facility': 'F1', 'customer': 4, 'cost': 741}, {'facility': 'F1', 'customer': 5, 'cost': 649}, {'facility': 'F1', 'customer': 6, 'cost': 405}, {'facility': 'F1', 'customer': 7, 'cost': 579}, {'facility': 'F1', 'customer': 8, 'cost': 975}, {'facility': 'F1', 'customer': 9, 'cost': 353}, {'facility': 'F1', 'customer': 10, 'cost': 481}, {'facility': 'F1', 'customer': 11, 'cost': 434}, {'facility': 'F2', 'customer': 0, 'cost': 24}, {'facility': 'F2', 'customer': 1, 'cost': 138}, {'facility': 'F2', 'customer': 2, 'cost': 304}, {'facility': 'F2', 'customer': 3, 'cost': 842}, {'facility': 'F2', 'customer': 4, 'cost': 149}, {'facility': 'F2', 'customer': 5, 'cost': 676}, {'facility': 'F2', 'customer': 6, 'cost': 913}, {'facility': 'F2', 'customer': 7, 'cost': 919}, {'facility': 'F2', 'customer': 8, 'cost': 217}, {'facility': 'F2', 'customer': 9, 'cost': 689}, {'facility': 'F2', 'customer': 10, 'cost': 337}, {'facility': 'F2', 'customer': 11, 'cost': 323}, {'facility': 'F3', 'customer': 0, 'cost': 401}, {'facility': 'F3', 'customer': 1, 'cost': 690}, {'facility': 'F3', 'customer': 2, 'cost': 280}, {'facility': 'F3', 'customer': 3, 'cost': 169}, {'facility': 'F3', 'customer': 4, 'cost': 830}, {'facility': 'F3', 'customer': 5, 'cost': 98}, {'facility': 'F3', 'customer': 6, 'cost': 335}, {'facility': 'F3', 'customer': 7, 'cost': 927}, {'facility': 'F3', 'customer': 8, 'cost': 276}, {'facility': 'F3', 'customer': 9, 'cost': 451}, {'facility': 'F3', 'customer': 10, 'cost': 84}, {'facility': 'F3', 'customer': 11, 'cost': 315}, {'facility': 'F4', 'customer': 0, 'cost': 263}, {'facility': 'F4', 'customer': 1, 'cost': 535}, {'facility': 'F4', 'customer': 2, 'cost': 971}, {'facility': 'F4', 'customer': 3, 'cost': 846}, {'facility': 'F4', 'customer': 4, 'cost': 216}, {'facility': 'F4', 'customer': 5, 'cost': 589}, {'facility': 'F4', 'customer': 6, 'cost': 462}, {'facility': 'F4', 'customer': 7, 'cost': 91}, {'facility': 'F4', 'customer': 8, 'cost': 269}, {'facility': 'F4', 'customer': 9, 'cost': 416}, {'facility': 'F4', 'customer': 10, 'cost': 219}, {'facility': 'F4', 'customer': 11, 'cost': 44}, {'facility': 'F5', 'customer': 0, 'cost': 570}, {'facility': 'F5', 'customer': 1, 'cost': 93}, {'facility': 'F5', 'customer': 2, 'cost': 701}, {'facility': 'F5', 'customer': 3, 'cost': 401}, {'facility': 'F5', 'customer': 4, 'cost': 303}, {'facility': 'F5', 'customer': 5, 'cost': 223}, {'facility': 'F5', 'customer': 6, 'cost': 497}, {'facility': 'F5', 'customer': 7, 'cost': 575}, {'facility': 'F5', 'customer': 8, 'cost': 880}, {'facility': 'F5', 'customer': 9, 'cost': 230}, {'facility': 'F5', 'customer': 10, 'cost': 328}, {'facility': 'F5', 'customer': 11, 'cost': 899}, {'facility': 'F6', 'customer': 0, 'cost': 89}, {'facility': 'F6', 'customer': 1, 'cost': 718}, {'facility': 'F6', 'customer': 2, 'cost': 30}, {'facility': 'F6', 'customer': 3, 'cost': 307}, {'facility': 'F6', 'customer': 4, 'cost': 852}, {'facility': 'F6', 'customer': 5, 'cost': 282}, {'facility': 'F6', 'customer': 6, 'cost': 70}, {'facility': 'F6', 'customer': 7, 'cost': 703}, {'facility': 'F6', 'customer': 8, 'cost': 888}, {'facility': 'F6', 'customer': 9, 'cost': 406}, {'facility': 'F6', 'customer': 10, 'cost': 14}, {'facility': 'F6', 'customer': 11, 'cost': 584}], 'objective': 6353.0}","{'selected': ['F4', 'F6'], 'assignments': ['F6', 'F4', 'F6', 'F6', 'F4', 'F6', 'F6', 'F4', 'F4', 'F6', 'F6', 'F4']}",32,json,0
UFLP,UFLP,"Someone on the events crew has to map out which pop-up booths get rented and then tie each customer group to a single one of those booths. Each group must end up at exactly one open booth (no leftovers, no multiple assignments), and booths can host as many groups as needed. The deciding factor is total cost: take the fees for the booths that are opened and add the travel/service cost for every group to its assigned booth — the configuration with the smallest total is the one to pick. The precise details are shown below.
# num_booths=6
# num_customer_groups=12
# BOOTHS
booth_id,booth_rental_fee
F1,1032
F2,1691
F3,1393
F4,1496
F5,1566
F6,1361
# GROUPS
group_id
1
2
3
4
5
6
7
8
9
10
11
12
# GROUP_TRAVEL_SERVICES
booth_id,group_id,group_travel_service_cost
F1,1,165
F1,2,200
F1,3,839
F1,4,962
F1,5,174
F1,6,417
F1,7,164
F1,8,735
F1,9,985
F1,10,854
F1,11,148
F1,12,268
F2,1,101
F2,2,426
F2,3,929
F2,4,848
F2,5,599
F2,6,888
F2,7,537
F2,8,90
F2,9,963
F2,10,3
F2,11,709
F2,12,738
F3,1,78
F3,2,879
F3,3,30
F3,4,221
F3,5,145
F3,6,596
F3,7,498
F3,8,374
F3,9,936
F3,10,632
F3,11,734
F3,12,267
F4,1,841
F4,2,99
F4,3,274
F4,4,915
F4,5,433
F4,6,92
F4,7,310
F4,8,653
F4,9,973
F4,10,778
F4,11,474
F4,12,971
F5,1,546
F5,2,933
F5,3,953
F5,4,259
F5,5,203
F5,6,65
F5,7,881
F5,8,601
F5,9,680
F5,10,400
F5,11,388
F5,12,204
F6,1,738
F6,2,41
F6,3,721
F6,4,132
F6,5,508
F6,6,177
F6,7,797
F6,8,380
F6,9,589
F6,10,256
F6,11,669
F6,12,437
When you answer, just return the picks in a tiny JSON blob like the one below so it's easy to parse — nothing fancy, just the two lists we need.
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<assigned_site>, <assigned_site>, ...]
}
}
Think of ""selected"" as the booths we decide to rent, and ""assignments"" as a simple one-entry-per-group list saying which rented booth each group goes to. Super casual: selected = which booths are open, assignments = which open booth each group is tied to.
This JSON is just a sketch of the shape I want back — not the real answer. Also, please use the exact identifiers from the instance input with no renaming and no new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1032, 1691, 1393, 1496, 1566, 1361], 'connection_costs': [[165, 200, 839, 962, 174, 417, 164, 735, 985, 854, 148, 268], [101, 426, 929, 848, 599, 888, 537, 90, 963, 3, 709, 738], [78, 879, 30, 221, 145, 596, 498, 374, 936, 632, 734, 267], [841, 99, 274, 915, 433, 92, 310, 653, 973, 778, 474, 971], [546, 933, 953, 259, 203, 65, 881, 601, 680, 400, 388, 204], [738, 41, 721, 132, 508, 177, 797, 380, 589, 256, 669, 437]], 'objective': 5608.0}","{'open_facilities': [0, 5], 'assignments': [0, 5, 5, 5, 0, 5, 0, 5, 5, 5, 0, 0]}",5608.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 12, 'facilities': [{'id': 'F1', 'opening_cost': 1032}, {'id': 'F2', 'opening_cost': 1691}, {'id': 'F3', 'opening_cost': 1393}, {'id': 'F4', 'opening_cost': 1496}, {'id': 'F5', 'opening_cost': 1566}, {'id': 'F6', 'opening_cost': 1361}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}, {'id': 12}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 165}, {'facility': 'F1', 'customer': 2, 'cost': 200}, {'facility': 'F1', 'customer': 3, 'cost': 839}, {'facility': 'F1', 'customer': 4, 'cost': 962}, {'facility': 'F1', 'customer': 5, 'cost': 174}, {'facility': 'F1', 'customer': 6, 'cost': 417}, {'facility': 'F1', 'customer': 7, 'cost': 164}, {'facility': 'F1', 'customer': 8, 'cost': 735}, {'facility': 'F1', 'customer': 9, 'cost': 985}, {'facility': 'F1', 'customer': 10, 'cost': 854}, {'facility': 'F1', 'customer': 11, 'cost': 148}, {'facility': 'F1', 'customer': 12, 'cost': 268}, {'facility': 'F2', 'customer': 1, 'cost': 101}, {'facility': 'F2', 'customer': 2, 'cost': 426}, {'facility': 'F2', 'customer': 3, 'cost': 929}, {'facility': 'F2', 'customer': 4, 'cost': 848}, {'facility': 'F2', 'customer': 5, 'cost': 599}, {'facility': 'F2', 'customer': 6, 'cost': 888}, {'facility': 'F2', 'customer': 7, 'cost': 537}, {'facility': 'F2', 'customer': 8, 'cost': 90}, {'facility': 'F2', 'customer': 9, 'cost': 963}, {'facility': 'F2', 'customer': 10, 'cost': 3}, {'facility': 'F2', 'customer': 11, 'cost': 709}, {'facility': 'F2', 'customer': 12, 'cost': 738}, {'facility': 'F3', 'customer': 1, 'cost': 78}, {'facility': 'F3', 'customer': 2, 'cost': 879}, {'facility': 'F3', 'customer': 3, 'cost': 30}, {'facility': 'F3', 'customer': 4, 'cost': 221}, {'facility': 'F3', 'customer': 5, 'cost': 145}, {'facility': 'F3', 'customer': 6, 'cost': 596}, {'facility': 'F3', 'customer': 7, 'cost': 498}, {'facility': 'F3', 'customer': 8, 'cost': 374}, {'facility': 'F3', 'customer': 9, 'cost': 936}, {'facility': 'F3', 'customer': 10, 'cost': 632}, {'facility': 'F3', 'customer': 11, 'cost': 734}, {'facility': 'F3', 'customer': 12, 'cost': 267}, {'facility': 'F4', 'customer': 1, 'cost': 841}, {'facility': 'F4', 'customer': 2, 'cost': 99}, {'facility': 'F4', 'customer': 3, 'cost': 274}, {'facility': 'F4', 'customer': 4, 'cost': 915}, {'facility': 'F4', 'customer': 5, 'cost': 433}, {'facility': 'F4', 'customer': 6, 'cost': 92}, {'facility': 'F4', 'customer': 7, 'cost': 310}, {'facility': 'F4', 'customer': 8, 'cost': 653}, {'facility': 'F4', 'customer': 9, 'cost': 973}, {'facility': 'F4', 'customer': 10, 'cost': 778}, {'facility': 'F4', 'customer': 11, 'cost': 474}, {'facility': 'F4', 'customer': 12, 'cost': 971}, {'facility': 'F5', 'customer': 1, 'cost': 546}, {'facility': 'F5', 'customer': 2, 'cost': 933}, {'facility': 'F5', 'customer': 3, 'cost': 953}, {'facility': 'F5', 'customer': 4, 'cost': 259}, {'facility': 'F5', 'customer': 5, 'cost': 203}, {'facility': 'F5', 'customer': 6, 'cost': 65}, {'facility': 'F5', 'customer': 7, 'cost': 881}, {'facility': 'F5', 'customer': 8, 'cost': 601}, {'facility': 'F5', 'customer': 9, 'cost': 680}, {'facility': 'F5', 'customer': 10, 'cost': 400}, {'facility': 'F5', 'customer': 11, 'cost': 388}, {'facility': 'F5', 'customer': 12, 'cost': 204}, {'facility': 'F6', 'customer': 1, 'cost': 738}, {'facility': 'F6', 'customer': 2, 'cost': 41}, {'facility': 'F6', 'customer': 3, 'cost': 721}, {'facility': 'F6', 'customer': 4, 'cost': 132}, {'facility': 'F6', 'customer': 5, 'cost': 508}, {'facility': 'F6', 'customer': 6, 'cost': 177}, {'facility': 'F6', 'customer': 7, 'cost': 797}, {'facility': 'F6', 'customer': 8, 'cost': 380}, {'facility': 'F6', 'customer': 9, 'cost': 589}, {'facility': 'F6', 'customer': 10, 'cost': 256}, {'facility': 'F6', 'customer': 11, 'cost': 669}, {'facility': 'F6', 'customer': 12, 'cost': 437}], 'objective': 5608.0}","{'selected': ['F1', 'F6'], 'assignments': ['F1', 'F6', 'F6', 'F6', 'F1', 'F6', 'F1', 'F6', 'F6', 'F6', 'F1', 'F1']}",33,csv,1
UFLP,UFLP,"Recently the bike-share folks have been mapping out which docks to open and which dock every rider should be linked to. There’s a cost to open any dock and a separate inconvenience score for each rider depending on which opened dock they use, so the winning plan is simply the one with the smallest combined cost: the total of all dock-opening fees plus the total of all riders’ access costs. Nobody can be left without a registered dock or assigned to a dock that wasn’t opened, and docks don’t have limits on how many riders they can handle. The concrete details are shown below.
{
""num_stations"": 5,
""num_riders"": 10,
""stations"": [
{
""station_id"": ""F1"",
""station_opening_fee"": 3814
},
{
""station_id"": ""F2"",
""station_opening_fee"": 4790
},
{
""station_id"": ""F3"",
""station_opening_fee"": 4967
},
{
""station_id"": ""F4"",
""station_opening_fee"": 2487
},
{
""station_id"": ""F5"",
""station_opening_fee"": 3191
}
],
""riders"": [
{
""rider_id"": ""A""
},
{
""rider_id"": ""B""
},
{
""rider_id"": ""C""
},
{
""rider_id"": ""D""
},
{
""rider_id"": ""E""
},
{
""rider_id"": ""F""
},
{
""rider_id"": ""G""
},
{
""rider_id"": ""H""
},
{
""rider_id"": ""I""
},
{
""rider_id"": ""J""
}
],
""access_inconveniences"": [
{
""station_id"": ""F1"",
""rider_id"": ""A"",
""access_inconvenience"": 774
},
{
""station_id"": ""F1"",
""rider_id"": ""B"",
""access_inconvenience"": 647
},
{
""station_id"": ""F1"",
""rider_id"": ""C"",
""access_inconvenience"": 850
},
{
""station_id"": ""F1"",
""rider_id"": ""D"",
""access_inconvenience"": 391
},
{
""station_id"": ""F1"",
""rider_id"": ""E"",
""access_inconvenience"": 247
},
{
""station_id"": ""F1"",
""rider_id"": ""F"",
""access_inconvenience"": 25
},
{
""station_id"": ""F1"",
""rider_id"": ""G"",
""access_inconvenience"": 825
},
{
""station_id"": ""F1"",
""rider_id"": ""H"",
""access_inconvenience"": 433
},
{
""station_id"": ""F1"",
""rider_id"": ""I"",
""access_inconvenience"": 9
},
{
""station_id"": ""F1"",
""rider_id"": ""J"",
""access_inconvenience"": 395
},
{
""station_id"": ""F2"",
""rider_id"": ""A"",
""access_inconvenience"": 897
},
{
""station_id"": ""F2"",
""rider_id"": ""B"",
""access_inconvenience"": 563
},
{
""station_id"": ""F2"",
""rider_id"": ""C"",
""access_inconvenience"": 68
},
{
""station_id"": ""F2"",
""rider_id"": ""D"",
""access_inconvenience"": 456
},
{
""station_id"": ""F2"",
""rider_id"": ""E"",
""access_inconvenience"": 138
},
{
""station_id"": ""F2"",
""rider_id"": ""F"",
""access_inconvenience"": 470
},
{
""station_id"": ""F2"",
""rider_id"": ""G"",
""access_inconvenience"": 670
},
{
""station_id"": ""F2"",
""rider_id"": ""H"",
""access_inconvenience"": 686
},
{
""station_id"": ""F2"",
""rider_id"": ""I"",
""access_inconvenience"": 401
},
{
""station_id"": ""F2"",
""rider_id"": ""J"",
""access_inconvenience"": 61
},
{
""station_id"": ""F3"",
""rider_id"": ""A"",
""access_inconvenience"": 986
},
{
""station_id"": ""F3"",
""rider_id"": ""B"",
""access_inconvenience"": 275
},
{
""station_id"": ""F3"",
""rider_id"": ""C"",
""access_inconvenience"": 481
},
{
""station_id"": ""F3"",
""rider_id"": ""D"",
""access_inconvenience"": 1
},
{
""station_id"": ""F3"",
""rider_id"": ""E"",
""access_inconvenience"": 254
},
{
""station_id"": ""F3"",
""rider_id"": ""F"",
""access_inconvenience"": 716
},
{
""station_id"": ""F3"",
""rider_id"": ""G"",
""access_inconvenience"": 115
},
{
""station_id"": ""F3"",
""rider_id"": ""H"",
""access_inconvenience"": 308
},
{
""station_id"": ""F3"",
""rider_id"": ""I"",
""access_inconvenience"": 308
},
{
""station_id"": ""F3"",
""rider_id"": ""J"",
""access_inconvenience"": 665
},
{
""station_id"": ""F4"",
""rider_id"": ""A"",
""access_inconvenience"": 981
},
{
""station_id"": ""F4"",
""rider_id"": ""B"",
""access_inconvenience"": 465
},
{
""station_id"": ""F4"",
""rider_id"": ""C"",
""access_inconvenience"": 40
},
{
""station_id"": ""F4"",
""rider_id"": ""D"",
""access_inconvenience"": 751
},
{
""station_id"": ""F4"",
""rider_id"": ""E"",
""access_inconvenience"": 607
},
{
""station_id"": ""F4"",
""rider_id"": ""F"",
""access_inconvenience"": 262
},
{
""station_id"": ""F4"",
""rider_id"": ""G"",
""access_inconvenience"": 477
},
{
""station_id"": ""F4"",
""rider_id"": ""H"",
""access_inconvenience"": 823
},
{
""station_id"": ""F4"",
""rider_id"": ""I"",
""access_inconvenience"": 586
},
{
""station_id"": ""F4"",
""rider_id"": ""J"",
""access_inconvenience"": 436
},
{
""station_id"": ""F5"",
""rider_id"": ""A"",
""access_inconvenience"": 281
},
{
""station_id"": ""F5"",
""rider_id"": ""B"",
""access_inconvenience"": 105
},
{
""station_id"": ""F5"",
""rider_id"": ""C"",
""access_inconvenience"": 733
},
{
""station_id"": ""F5"",
""rider_id"": ""D"",
""access_inconvenience"": 993
},
{
""station_id"": ""F5"",
""rider_id"": ""E"",
""access_inconvenience"": 54
},
{
""station_id"": ""F5"",
""rider_id"": ""F"",
""access_inconvenience"": 466
},
{
""station_id"": ""F5"",
""rider_id"": ""G"",
""access_inconvenience"": 592
},
{
""station_id"": ""F5"",
""rider_id"": ""H"",
""access_inconvenience"": 47
},
{
""station_id"": ""F5"",
""rider_id"": ""I"",
""access_inconvenience"": 637
},
{
""station_id"": ""F5"",
""rider_id"": ""J"",
""access_inconvenience"": 838
}
]
}
Oh, and when you send the plan back, just use this simple JSON shape so I can read it easily:
{
""solution"": {
""selected"": [<dock_to_open>, <dock_to_open>, ...],
""assignments"": [<assigned_dock>, <assigned_dock>, ...]
}
}
""selected"" is where you list the docks you choose to open. ""assignments"" is a parallel list (one entry per rider, in the same order as the input) saying which opened dock each rider is linked to. Think of it like filling out a form: which docks are active, and who goes to which one.
This is just a sketch of the expected shape, not the actual answer—I'll need the real identifiers from the instance to produce a concrete plan. Please make sure you use the identifiers exactly as they appear in the input — no renaming and no new labels.
For example: Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [3814, 4790, 4967, 2487, 3191], 'connection_costs': [[774, 647, 850, 391, 247, 25, 825, 433, 9, 395], [897, 563, 68, 456, 138, 470, 670, 686, 401, 61], [986, 275, 481, 1, 254, 716, 115, 308, 308, 665], [981, 465, 40, 751, 607, 262, 477, 823, 586, 436], [281, 105, 733, 993, 54, 466, 592, 47, 637, 838]], 'objective': 7915.0}","{'open_facilities': [3], 'assignments': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]}",7915.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 10, 'facilities': [{'id': 'F1', 'opening_cost': 3814}, {'id': 'F2', 'opening_cost': 4790}, {'id': 'F3', 'opening_cost': 4967}, {'id': 'F4', 'opening_cost': 2487}, {'id': 'F5', 'opening_cost': 3191}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 774}, {'facility': 'F1', 'customer': 'B', 'cost': 647}, {'facility': 'F1', 'customer': 'C', 'cost': 850}, {'facility': 'F1', 'customer': 'D', 'cost': 391}, {'facility': 'F1', 'customer': 'E', 'cost': 247}, {'facility': 'F1', 'customer': 'F', 'cost': 25}, {'facility': 'F1', 'customer': 'G', 'cost': 825}, {'facility': 'F1', 'customer': 'H', 'cost': 433}, {'facility': 'F1', 'customer': 'I', 'cost': 9}, {'facility': 'F1', 'customer': 'J', 'cost': 395}, {'facility': 'F2', 'customer': 'A', 'cost': 897}, {'facility': 'F2', 'customer': 'B', 'cost': 563}, {'facility': 'F2', 'customer': 'C', 'cost': 68}, {'facility': 'F2', 'customer': 'D', 'cost': 456}, {'facility': 'F2', 'customer': 'E', 'cost': 138}, {'facility': 'F2', 'customer': 'F', 'cost': 470}, {'facility': 'F2', 'customer': 'G', 'cost': 670}, {'facility': 'F2', 'customer': 'H', 'cost': 686}, {'facility': 'F2', 'customer': 'I', 'cost': 401}, {'facility': 'F2', 'customer': 'J', 'cost': 61}, {'facility': 'F3', 'customer': 'A', 'cost': 986}, {'facility': 'F3', 'customer': 'B', 'cost': 275}, {'facility': 'F3', 'customer': 'C', 'cost': 481}, {'facility': 'F3', 'customer': 'D', 'cost': 1}, {'facility': 'F3', 'customer': 'E', 'cost': 254}, {'facility': 'F3', 'customer': 'F', 'cost': 716}, {'facility': 'F3', 'customer': 'G', 'cost': 115}, {'facility': 'F3', 'customer': 'H', 'cost': 308}, {'facility': 'F3', 'customer': 'I', 'cost': 308}, {'facility': 'F3', 'customer': 'J', 'cost': 665}, {'facility': 'F4', 'customer': 'A', 'cost': 981}, {'facility': 'F4', 'customer': 'B', 'cost': 465}, {'facility': 'F4', 'customer': 'C', 'cost': 40}, {'facility': 'F4', 'customer': 'D', 'cost': 751}, {'facility': 'F4', 'customer': 'E', 'cost': 607}, {'facility': 'F4', 'customer': 'F', 'cost': 262}, {'facility': 'F4', 'customer': 'G', 'cost': 477}, {'facility': 'F4', 'customer': 'H', 'cost': 823}, {'facility': 'F4', 'customer': 'I', 'cost': 586}, {'facility': 'F4', 'customer': 'J', 'cost': 436}, {'facility': 'F5', 'customer': 'A', 'cost': 281}, {'facility': 'F5', 'customer': 'B', 'cost': 105}, {'facility': 'F5', 'customer': 'C', 'cost': 733}, {'facility': 'F5', 'customer': 'D', 'cost': 993}, {'facility': 'F5', 'customer': 'E', 'cost': 54}, {'facility': 'F5', 'customer': 'F', 'cost': 466}, {'facility': 'F5', 'customer': 'G', 'cost': 592}, {'facility': 'F5', 'customer': 'H', 'cost': 47}, {'facility': 'F5', 'customer': 'I', 'cost': 637}, {'facility': 'F5', 'customer': 'J', 'cost': 838}], 'objective': 7915.0}","{'selected': ['F4'], 'assignments': ['F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4']}",34,json,names
UFLP,UFLP,"We coordinate a network of volunteer tutoring spots and are deciding which spots to activate and which active spot each student should go to. Activating a spot costs money, and each student has a travel cost depending on which active spot they’re sent to. Better choices are those where the sum of the activation costs plus all students’ travel costs ends up lowest. Each student must go to one, and only one, active spot; nobody gets skipped. The concrete details are listed below.
We have 6 candidate hubs, 13 learners, and hub activation costs 6554, 6022, 6957, 7764, 7198, 2961.
Hub F1 has an activation cost of 6554.
Hub F2 has an activation cost of 6022.
Hub F3 has an activation cost of 6957.
Hub F4 has an activation cost of 7764.
Hub F5 has an activation cost of 7198.
Hub F6 has an activation cost of 2961.
Learner 0 would incur travel cost 299 if assigned to hub F1.
Learner 1 would incur travel cost 276 if assigned to hub F1.
Learner 2 would incur travel cost 194 if assigned to hub F1.
Learner 3 would incur travel cost 948 if assigned to hub F1.
Learner 4 would incur travel cost 842 if assigned to hub F1.
Learner 5 would incur travel cost 406 if assigned to hub F1.
Learner 6 would incur travel cost 252 if assigned to hub F1.
Learner 7 would incur travel cost 463 if assigned to hub F1.
Learner 8 would incur travel cost 160 if assigned to hub F1.
Learner 9 would incur travel cost 43 if assigned to hub F1.
Learner 10 would incur travel cost 404 if assigned to hub F1.
Learner 11 would incur travel cost 461 if assigned to hub F1.
Learner 12 would incur travel cost 219 if assigned to hub F1.
Learner 0 would incur travel cost 288 if assigned to hub F2.
Learner 1 would incur travel cost 855 if assigned to hub F2.
Learner 2 would incur travel cost 402 if assigned to hub F2.
Learner 3 would incur travel cost 597 if assigned to hub F2.
Learner 4 would incur travel cost 225 if assigned to hub F2.
Learner 5 would incur travel cost 474 if assigned to hub F2.
Learner 6 would incur travel cost 144 if assigned to hub F2.
Learner 7 would incur travel cost 131 if assigned to hub F2.
Learner 8 would incur travel cost 101 if assigned to hub F2.
Learner 9 would incur travel cost 463 if assigned to hub F2.
Learner 10 would incur travel cost 637 if assigned to hub F2.
Learner 11 would incur travel cost 578 if assigned to hub F2.
Learner 12 would incur travel cost 211 if assigned to hub F2.
Learner 0 would incur travel cost 954 if assigned to hub F3.
Learner 1 would incur travel cost 215 if assigned to hub F3.
Learner 2 would incur travel cost 83 if assigned to hub F3.
Learner 3 would incur travel cost 970 if assigned to hub F3.
Learner 4 would incur travel cost 28 if assigned to hub F3.
Learner 5 would incur travel cost 519 if assigned to hub F3.
Learner 6 would incur travel cost 776 if assigned to hub F3.
Learner 7 would incur travel cost 10 if assigned to hub F3.
Learner 8 would incur travel cost 857 if assigned to hub F3.
Learner 9 would incur travel cost 454 if assigned to hub F3.
Learner 10 would incur travel cost 948 if assigned to hub F3.
Learner 11 would incur travel cost 273 if assigned to hub F3.
Learner 12 would incur travel cost 166 if assigned to hub F3.
Learner 0 would incur travel cost 112 if assigned to hub F4.
Learner 1 would incur travel cost 391 if assigned to hub F4.
Learner 2 would incur travel cost 855 if assigned to hub F4.
Learner 3 would incur travel cost 911 if assigned to hub F4.
Learner 4 would incur travel cost 529 if assigned to hub F4.
Learner 5 would incur travel cost 332 if assigned to hub F4.
Learner 6 would incur travel cost 648 if assigned to hub F4.
Learner 7 would incur travel cost 126 if assigned to hub F4.
Learner 8 would incur travel cost 623 if assigned to hub F4.
Learner 9 would incur travel cost 143 if assigned to hub F4.
Learner 10 would incur travel cost 97 if assigned to hub F4.
Learner 11 would incur travel cost 169 if assigned to hub F4.
Learner 12 would incur travel cost 505 if assigned to hub F4.
Learner 0 would incur travel cost 273 if assigned to hub F5.
Learner 1 would incur travel cost 266 if assigned to hub F5.
Learner 2 would incur travel cost 398 if assigned to hub F5.
Learner 3 would incur travel cost 515 if assigned to hub F5.
Learner 4 would incur travel cost 365 if assigned to hub F5.
Learner 5 would incur travel cost 833 if assigned to hub F5.
Learner 6 would incur travel cost 895 if assigned to hub F5.
Learner 7 would incur travel cost 578 if assigned to hub F5.
Learner 8 would incur travel cost 89 if assigned to hub F5.
Learner 9 would incur travel cost 7 if assigned to hub F5.
Learner 10 would incur travel cost 103 if assigned to hub F5.
Learner 11 would incur travel cost 756 if assigned to hub F5.
Learner 12 would incur travel cost 984 if assigned to hub F5.
Learner 0 would incur travel cost 523 if assigned to hub F6.
Learner 1 would incur travel cost 222 if assigned to hub F6.
Learner 2 would incur travel cost 883 if assigned to hub F6.
Learner 3 would incur travel cost 7 if assigned to hub F6.
Learner 4 would incur travel cost 648 if assigned to hub F6.
Learner 5 would incur travel cost 322 if assigned to hub F6.
Learner 6 would incur travel cost 271 if assigned to hub F6.
Learner 7 would incur travel cost 260 if assigned to hub F6.
Learner 8 would incur travel cost 541 if assigned to hub F6.
Learner 9 would incur travel cost 870 if assigned to hub F6.
Learner 10 would incur travel cost 672 if assigned to hub F6.
Learner 11 would incur travel cost 700 if assigned to hub F6.
Learner 12 would incur travel cost 108 if assigned to hub F6.
We will use these details to pick which hubs to open and assign each learner so total activation plus travel costs is minimized.
Also, when you send back the actual choices, please use a tiny JSON snippet like this to tell us which spots you activate and which active spot each student goes to.
{
""solution"": {
""selected"": [<spot_to_activate>, <spot_to_activate>, ...],
""assignments"": [<assigned_spot>, <assigned_spot>, ...]
}
}
This just sketches the shape we want: ""selected"" is the list of spots you decide to activate (one placeholder per spot), and ""assignments"" lists, in order, which active spot each student is sent to. Think of it like filling out a short form — which locations are turned on, and for each student which turned-on spot they’ll use.
The JSON above is only an example of the shape we need, not the answer itself.
One more important thing — use the exact identifiers from the instance input, do not rename them or invent new ones. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [6554, 6022, 6957, 7764, 7198, 2961], 'connection_costs': [[299, 276, 194, 948, 842, 406, 252, 463, 160, 43, 404, 461, 219], [288, 855, 402, 597, 225, 474, 144, 131, 101, 463, 637, 578, 211], [954, 215, 83, 970, 28, 519, 776, 10, 857, 454, 948, 273, 166], [112, 391, 855, 911, 529, 332, 648, 126, 623, 143, 97, 169, 505], [273, 266, 398, 515, 365, 833, 895, 578, 89, 7, 103, 756, 984], [523, 222, 883, 7, 648, 322, 271, 260, 541, 870, 672, 700, 108]], 'objective': 8988.0}","{'open_facilities': [5], 'assignments': [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]}",8988.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 13, 'facilities': [{'id': 'F1', 'opening_cost': 6554}, {'id': 'F2', 'opening_cost': 6022}, {'id': 'F3', 'opening_cost': 6957}, {'id': 'F4', 'opening_cost': 7764}, {'id': 'F5', 'opening_cost': 7198}, {'id': 'F6', 'opening_cost': 2961}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}, {'id': 12}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 299}, {'facility': 'F1', 'customer': 1, 'cost': 276}, {'facility': 'F1', 'customer': 2, 'cost': 194}, {'facility': 'F1', 'customer': 3, 'cost': 948}, {'facility': 'F1', 'customer': 4, 'cost': 842}, {'facility': 'F1', 'customer': 5, 'cost': 406}, {'facility': 'F1', 'customer': 6, 'cost': 252}, {'facility': 'F1', 'customer': 7, 'cost': 463}, {'facility': 'F1', 'customer': 8, 'cost': 160}, {'facility': 'F1', 'customer': 9, 'cost': 43}, {'facility': 'F1', 'customer': 10, 'cost': 404}, {'facility': 'F1', 'customer': 11, 'cost': 461}, {'facility': 'F1', 'customer': 12, 'cost': 219}, {'facility': 'F2', 'customer': 0, 'cost': 288}, {'facility': 'F2', 'customer': 1, 'cost': 855}, {'facility': 'F2', 'customer': 2, 'cost': 402}, {'facility': 'F2', 'customer': 3, 'cost': 597}, {'facility': 'F2', 'customer': 4, 'cost': 225}, {'facility': 'F2', 'customer': 5, 'cost': 474}, {'facility': 'F2', 'customer': 6, 'cost': 144}, {'facility': 'F2', 'customer': 7, 'cost': 131}, {'facility': 'F2', 'customer': 8, 'cost': 101}, {'facility': 'F2', 'customer': 9, 'cost': 463}, {'facility': 'F2', 'customer': 10, 'cost': 637}, {'facility': 'F2', 'customer': 11, 'cost': 578}, {'facility': 'F2', 'customer': 12, 'cost': 211}, {'facility': 'F3', 'customer': 0, 'cost': 954}, {'facility': 'F3', 'customer': 1, 'cost': 215}, {'facility': 'F3', 'customer': 2, 'cost': 83}, {'facility': 'F3', 'customer': 3, 'cost': 970}, {'facility': 'F3', 'customer': 4, 'cost': 28}, {'facility': 'F3', 'customer': 5, 'cost': 519}, {'facility': 'F3', 'customer': 6, 'cost': 776}, {'facility': 'F3', 'customer': 7, 'cost': 10}, {'facility': 'F3', 'customer': 8, 'cost': 857}, {'facility': 'F3', 'customer': 9, 'cost': 454}, {'facility': 'F3', 'customer': 10, 'cost': 948}, {'facility': 'F3', 'customer': 11, 'cost': 273}, {'facility': 'F3', 'customer': 12, 'cost': 166}, {'facility': 'F4', 'customer': 0, 'cost': 112}, {'facility': 'F4', 'customer': 1, 'cost': 391}, {'facility': 'F4', 'customer': 2, 'cost': 855}, {'facility': 'F4', 'customer': 3, 'cost': 911}, {'facility': 'F4', 'customer': 4, 'cost': 529}, {'facility': 'F4', 'customer': 5, 'cost': 332}, {'facility': 'F4', 'customer': 6, 'cost': 648}, {'facility': 'F4', 'customer': 7, 'cost': 126}, {'facility': 'F4', 'customer': 8, 'cost': 623}, {'facility': 'F4', 'customer': 9, 'cost': 143}, {'facility': 'F4', 'customer': 10, 'cost': 97}, {'facility': 'F4', 'customer': 11, 'cost': 169}, {'facility': 'F4', 'customer': 12, 'cost': 505}, {'facility': 'F5', 'customer': 0, 'cost': 273}, {'facility': 'F5', 'customer': 1, 'cost': 266}, {'facility': 'F5', 'customer': 2, 'cost': 398}, {'facility': 'F5', 'customer': 3, 'cost': 515}, {'facility': 'F5', 'customer': 4, 'cost': 365}, {'facility': 'F5', 'customer': 5, 'cost': 833}, {'facility': 'F5', 'customer': 6, 'cost': 895}, {'facility': 'F5', 'customer': 7, 'cost': 578}, {'facility': 'F5', 'customer': 8, 'cost': 89}, {'facility': 'F5', 'customer': 9, 'cost': 7}, {'facility': 'F5', 'customer': 10, 'cost': 103}, {'facility': 'F5', 'customer': 11, 'cost': 756}, {'facility': 'F5', 'customer': 12, 'cost': 984}, {'facility': 'F6', 'customer': 0, 'cost': 523}, {'facility': 'F6', 'customer': 1, 'cost': 222}, {'facility': 'F6', 'customer': 2, 'cost': 883}, {'facility': 'F6', 'customer': 3, 'cost': 7}, {'facility': 'F6', 'customer': 4, 'cost': 648}, {'facility': 'F6', 'customer': 5, 'cost': 322}, {'facility': 'F6', 'customer': 6, 'cost': 271}, {'facility': 'F6', 'customer': 7, 'cost': 260}, {'facility': 'F6', 'customer': 8, 'cost': 541}, {'facility': 'F6', 'customer': 9, 'cost': 870}, {'facility': 'F6', 'customer': 10, 'cost': 672}, {'facility': 'F6', 'customer': 11, 'cost': 700}, {'facility': 'F6', 'customer': 12, 'cost': 108}], 'objective': 8988.0}","{'selected': ['F6'], 'assignments': ['F6', 'F6', 'F6', 'F6', 'F6', 'F6', 'F6', 'F6', 'F6', 'F6', 'F6', 'F6', 'F6']}",35,nl,0
UFLP,UFLP,"Recently during the response phase it became clear: decide which depots to activate and assign every affected household to one of the open depots. Activating a depot comes with a price, and every household will incur some effort to reach the depot they’re sent to. The plan that wins is the one with the lowest overall sum — add together the operating cost for every opened depot and the pickup effort for every household. Every household has to be assigned to exactly one open depot; nothing is omitted or duplicated. The concrete details appear below.
# num_depots=5
# num_households=12
# DEPOTS
depot_id,depot_opening_cost
F1,2000
F2,2000
F3,2000
F4,2000
F5,2000
# HOUSEHOLDS
household_id
0
1
2
3
4
5
6
7
8
9
10
11
# PICKUP_EFFORTS
depot_id,household_id,pickup_effort
F1,0,105
F1,1,418
F1,2,251
F1,3,839
F1,4,733
F1,5,237
F1,6,371
F1,7,86
F1,8,809
F1,9,430
F1,10,63
F1,11,745
F2,0,859
F2,1,313
F2,2,978
F2,3,597
F2,4,309
F2,5,734
F2,6,352
F2,7,198
F2,8,330
F2,9,222
F2,10,816
F2,11,302
F3,0,923
F3,1,216
F3,2,205
F3,3,570
F3,4,386
F3,5,763
F3,6,618
F3,7,214
F3,8,130
F3,9,739
F3,10,278
F3,11,379
F4,0,554
F4,1,989
F4,2,395
F4,3,869
F4,4,675
F4,5,523
F4,6,243
F4,7,228
F4,8,440
F4,9,867
F4,10,561
F4,11,344
F5,0,136
F5,1,825
F5,2,757
F5,3,734
F5,4,616
F5,5,892
F5,6,139
F5,7,345
F5,8,969
F5,9,910
F5,10,259
F5,11,665
Oh, and when you send the plan back, just use a tiny JSON object like this — nothing fancy, just that shape:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
""selected"" is the list of depots/depots-to-activate (the ones we pay to open). ""assignments"" lists, in order, which open depot each household is sent to. Super simple, like filling out a form — which depots, and which depot for each household.
This is just a sketch of the shape I need, not the actual answer. Please make sure all identifiers you use match the instance input exactly — don't rename or invent labels. Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".","{'opening_costs': [2000, 2000, 2000, 2000, 2000], 'connection_costs': [[105, 418, 251, 839, 733, 237, 371, 86, 809, 430, 63, 745], [859, 313, 978, 597, 309, 734, 352, 198, 330, 222, 816, 302], [923, 216, 205, 570, 386, 763, 618, 214, 130, 739, 278, 379], [554, 989, 395, 869, 675, 523, 243, 228, 440, 867, 561, 344], [136, 825, 757, 734, 616, 892, 139, 345, 969, 910, 259, 665]], 'objective': 7087.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}",7087.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 12, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 105}, {'facility': 'F1', 'customer': 1, 'cost': 418}, {'facility': 'F1', 'customer': 2, 'cost': 251}, {'facility': 'F1', 'customer': 3, 'cost': 839}, {'facility': 'F1', 'customer': 4, 'cost': 733}, {'facility': 'F1', 'customer': 5, 'cost': 237}, {'facility': 'F1', 'customer': 6, 'cost': 371}, {'facility': 'F1', 'customer': 7, 'cost': 86}, {'facility': 'F1', 'customer': 8, 'cost': 809}, {'facility': 'F1', 'customer': 9, 'cost': 430}, {'facility': 'F1', 'customer': 10, 'cost': 63}, {'facility': 'F1', 'customer': 11, 'cost': 745}, {'facility': 'F2', 'customer': 0, 'cost': 859}, {'facility': 'F2', 'customer': 1, 'cost': 313}, {'facility': 'F2', 'customer': 2, 'cost': 978}, {'facility': 'F2', 'customer': 3, 'cost': 597}, {'facility': 'F2', 'customer': 4, 'cost': 309}, {'facility': 'F2', 'customer': 5, 'cost': 734}, {'facility': 'F2', 'customer': 6, 'cost': 352}, {'facility': 'F2', 'customer': 7, 'cost': 198}, {'facility': 'F2', 'customer': 8, 'cost': 330}, {'facility': 'F2', 'customer': 9, 'cost': 222}, {'facility': 'F2', 'customer': 10, 'cost': 816}, {'facility': 'F2', 'customer': 11, 'cost': 302}, {'facility': 'F3', 'customer': 0, 'cost': 923}, {'facility': 'F3', 'customer': 1, 'cost': 216}, {'facility': 'F3', 'customer': 2, 'cost': 205}, {'facility': 'F3', 'customer': 3, 'cost': 570}, {'facility': 'F3', 'customer': 4, 'cost': 386}, {'facility': 'F3', 'customer': 5, 'cost': 763}, {'facility': 'F3', 'customer': 6, 'cost': 618}, {'facility': 'F3', 'customer': 7, 'cost': 214}, {'facility': 'F3', 'customer': 8, 'cost': 130}, {'facility': 'F3', 'customer': 9, 'cost': 739}, {'facility': 'F3', 'customer': 10, 'cost': 278}, {'facility': 'F3', 'customer': 11, 'cost': 379}, {'facility': 'F4', 'customer': 0, 'cost': 554}, {'facility': 'F4', 'customer': 1, 'cost': 989}, {'facility': 'F4', 'customer': 2, 'cost': 395}, {'facility': 'F4', 'customer': 3, 'cost': 869}, {'facility': 'F4', 'customer': 4, 'cost': 675}, {'facility': 'F4', 'customer': 5, 'cost': 523}, {'facility': 'F4', 'customer': 6, 'cost': 243}, {'facility': 'F4', 'customer': 7, 'cost': 228}, {'facility': 'F4', 'customer': 8, 'cost': 440}, {'facility': 'F4', 'customer': 9, 'cost': 867}, {'facility': 'F4', 'customer': 10, 'cost': 561}, {'facility': 'F4', 'customer': 11, 'cost': 344}, {'facility': 'F5', 'customer': 0, 'cost': 136}, {'facility': 'F5', 'customer': 1, 'cost': 825}, {'facility': 'F5', 'customer': 2, 'cost': 757}, {'facility': 'F5', 'customer': 3, 'cost': 734}, {'facility': 'F5', 'customer': 4, 'cost': 616}, {'facility': 'F5', 'customer': 5, 'cost': 892}, {'facility': 'F5', 'customer': 6, 'cost': 139}, {'facility': 'F5', 'customer': 7, 'cost': 345}, {'facility': 'F5', 'customer': 8, 'cost': 969}, {'facility': 'F5', 'customer': 9, 'cost': 910}, {'facility': 'F5', 'customer': 10, 'cost': 259}, {'facility': 'F5', 'customer': 11, 'cost': 665}], 'objective': 7087.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",36,csv,0
UFLP,UFLP,"Recently the team running a neighborhood art rental decided to rethink which pickup spots to offer and who should use each spot. The idea is to balance the cost of running each spot with how much it costs clients to get there — the plan that wins is the one with the lowest sum of the chosen spots’ operating fees plus all clients’ connection costs. It’s important that every client is assigned to one, and only one, open pickup point (no sharing and no leaving anyone out). The concrete details are provided below.
There are 5 candidate pickup points and 12 clients; pickup point operation fees are 1000, 1000, 1000, 1000, 1000.
Pickup point F1 has an operation fee of 1000.
Pickup point F2 has an operation fee of 1000.
Pickup point F3 has an operation fee of 1000.
Pickup point F4 has an operation fee of 1000.
Pickup point F5 has an operation fee of 1000.
For client A, the cost to use pickup point F1 is 559.
For client B, the cost to use pickup point F1 is 405.
For client C, the cost to use pickup point F1 is 403.
For client D, the cost to use pickup point F1 is 859.
For client E, the cost to use pickup point F1 is 522.
For client F, the cost to use pickup point F1 is 335.
For client G, the cost to use pickup point F1 is 90.
For client H, the cost to use pickup point F1 is 697.
For client I, the cost to use pickup point F1 is 223.
For client J, the cost to use pickup point F1 is 276.
For client K, the cost to use pickup point F1 is 372.
For client L, the cost to use pickup point F1 is 457.
For client A, the cost to use pickup point F2 is 202.
For client B, the cost to use pickup point F2 is 275.
For client C, the cost to use pickup point F2 is 302.
For client D, the cost to use pickup point F2 is 453.
For client E, the cost to use pickup point F2 is 700.
For client F, the cost to use pickup point F2 is 905.
For client G, the cost to use pickup point F2 is 638.
For client H, the cost to use pickup point F2 is 19.
For client I, the cost to use pickup point F2 is 536.
For client J, the cost to use pickup point F2 is 245.
For client K, the cost to use pickup point F2 is 867.
For client L, the cost to use pickup point F2 is 827.
For client A, the cost to use pickup point F3 is 371.
For client B, the cost to use pickup point F3 is 489.
For client C, the cost to use pickup point F3 is 495.
For client D, the cost to use pickup point F3 is 621.
For client E, the cost to use pickup point F3 is 146.
For client F, the cost to use pickup point F3 is 413.
For client G, the cost to use pickup point F3 is 939.
For client H, the cost to use pickup point F3 is 373.
For client I, the cost to use pickup point F3 is 375.
For client J, the cost to use pickup point F3 is 320.
For client K, the cost to use pickup point F3 is 709.
For client L, the cost to use pickup point F3 is 857.
For client A, the cost to use pickup point F4 is 457.
For client B, the cost to use pickup point F4 is 320.
For client C, the cost to use pickup point F4 is 353.
For client D, the cost to use pickup point F4 is 280.
For client E, the cost to use pickup point F4 is 225.
For client F, the cost to use pickup point F4 is 659.
For client G, the cost to use pickup point F4 is 747.
For client H, the cost to use pickup point F4 is 767.
For client I, the cost to use pickup point F4 is 870.
For client J, the cost to use pickup point F4 is 629.
For client K, the cost to use pickup point F4 is 2.
For client L, the cost to use pickup point F4 is 517.
For client A, the cost to use pickup point F5 is 487.
For client B, the cost to use pickup point F5 is 393.
For client C, the cost to use pickup point F5 is 588.
For client D, the cost to use pickup point F5 is 570.
For client E, the cost to use pickup point F5 is 447.
For client F, the cost to use pickup point F5 is 675.
For client G, the cost to use pickup point F5 is 876.
For client H, the cost to use pickup point F5 is 619.
For client I, the cost to use pickup point F5 is 38.
For client J, the cost to use pickup point F5 is 826.
For client K, the cost to use pickup point F5 is 423.
For client L, the cost to use pickup point F5 is 481.
Each following line names one pickup point or one client-to-point cost; together they define the inputs for selecting the lowest-cost plan.
Oh, and when you send the final pick of spots and who goes where, please use a simple JSON shape like this so I can read it automatically:
{
""solution"": {
""selected"": [<pickup_spot>, <pickup_spot>, ...],
""assignments"": [<assigned_spot>, <assigned_spot>, ...]
}
}
Pretty straightforward: ""selected"" is the list of pickup spots you choose to open, and ""assignments"" lists, in customer order, which open spot each customer will use. Think of it like filling out a quick form — this is just the expected shape, not the final content.
Important: use the exact identifiers from the instance input — do not rename or invent labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [1000, 1000, 1000, 1000, 1000], 'connection_costs': [[559, 405, 403, 859, 522, 335, 90, 697, 223, 276, 372, 457], [202, 275, 302, 453, 700, 905, 638, 19, 536, 245, 867, 827], [371, 489, 495, 621, 146, 413, 939, 373, 375, 320, 709, 857], [457, 320, 353, 280, 225, 659, 747, 767, 870, 629, 2, 517], [487, 393, 588, 570, 447, 675, 876, 619, 38, 826, 423, 481]], 'objective': 5495.0}","{'open_facilities': [0, 1], 'assignments': [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0]}",5495.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 12, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}, {'id': 'F5', 'opening_cost': 1000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}, {'id': 'L'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 559}, {'facility': 'F1', 'customer': 'B', 'cost': 405}, {'facility': 'F1', 'customer': 'C', 'cost': 403}, {'facility': 'F1', 'customer': 'D', 'cost': 859}, {'facility': 'F1', 'customer': 'E', 'cost': 522}, {'facility': 'F1', 'customer': 'F', 'cost': 335}, {'facility': 'F1', 'customer': 'G', 'cost': 90}, {'facility': 'F1', 'customer': 'H', 'cost': 697}, {'facility': 'F1', 'customer': 'I', 'cost': 223}, {'facility': 'F1', 'customer': 'J', 'cost': 276}, {'facility': 'F1', 'customer': 'K', 'cost': 372}, {'facility': 'F1', 'customer': 'L', 'cost': 457}, {'facility': 'F2', 'customer': 'A', 'cost': 202}, {'facility': 'F2', 'customer': 'B', 'cost': 275}, {'facility': 'F2', 'customer': 'C', 'cost': 302}, {'facility': 'F2', 'customer': 'D', 'cost': 453}, {'facility': 'F2', 'customer': 'E', 'cost': 700}, {'facility': 'F2', 'customer': 'F', 'cost': 905}, {'facility': 'F2', 'customer': 'G', 'cost': 638}, {'facility': 'F2', 'customer': 'H', 'cost': 19}, {'facility': 'F2', 'customer': 'I', 'cost': 536}, {'facility': 'F2', 'customer': 'J', 'cost': 245}, {'facility': 'F2', 'customer': 'K', 'cost': 867}, {'facility': 'F2', 'customer': 'L', 'cost': 827}, {'facility': 'F3', 'customer': 'A', 'cost': 371}, {'facility': 'F3', 'customer': 'B', 'cost': 489}, {'facility': 'F3', 'customer': 'C', 'cost': 495}, {'facility': 'F3', 'customer': 'D', 'cost': 621}, {'facility': 'F3', 'customer': 'E', 'cost': 146}, {'facility': 'F3', 'customer': 'F', 'cost': 413}, {'facility': 'F3', 'customer': 'G', 'cost': 939}, {'facility': 'F3', 'customer': 'H', 'cost': 373}, {'facility': 'F3', 'customer': 'I', 'cost': 375}, {'facility': 'F3', 'customer': 'J', 'cost': 320}, {'facility': 'F3', 'customer': 'K', 'cost': 709}, {'facility': 'F3', 'customer': 'L', 'cost': 857}, {'facility': 'F4', 'customer': 'A', 'cost': 457}, {'facility': 'F4', 'customer': 'B', 'cost': 320}, {'facility': 'F4', 'customer': 'C', 'cost': 353}, {'facility': 'F4', 'customer': 'D', 'cost': 280}, {'facility': 'F4', 'customer': 'E', 'cost': 225}, {'facility': 'F4', 'customer': 'F', 'cost': 659}, {'facility': 'F4', 'customer': 'G', 'cost': 747}, {'facility': 'F4', 'customer': 'H', 'cost': 767}, {'facility': 'F4', 'customer': 'I', 'cost': 870}, {'facility': 'F4', 'customer': 'J', 'cost': 629}, {'facility': 'F4', 'customer': 'K', 'cost': 2}, {'facility': 'F4', 'customer': 'L', 'cost': 517}, {'facility': 'F5', 'customer': 'A', 'cost': 487}, {'facility': 'F5', 'customer': 'B', 'cost': 393}, {'facility': 'F5', 'customer': 'C', 'cost': 588}, {'facility': 'F5', 'customer': 'D', 'cost': 570}, {'facility': 'F5', 'customer': 'E', 'cost': 447}, {'facility': 'F5', 'customer': 'F', 'cost': 675}, {'facility': 'F5', 'customer': 'G', 'cost': 876}, {'facility': 'F5', 'customer': 'H', 'cost': 619}, {'facility': 'F5', 'customer': 'I', 'cost': 38}, {'facility': 'F5', 'customer': 'J', 'cost': 826}, {'facility': 'F5', 'customer': 'K', 'cost': 423}, {'facility': 'F5', 'customer': 'L', 'cost': 481}], 'objective': 5495.0}","{'selected': ['F1', 'F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F1', 'F1', 'F1', 'F2', 'F1', 'F2', 'F1', 'F1']}",37,nl,names
UFLP,UFLP,"Many people in town use a subscription meal-kit, and the business needs to choose which packing locations to run and which location handles each order. Running a location costs a flat fee, and each order has a shipping cost depending on where it’s packed; the total cost to watch is simply the sum of the running fees for chosen locations plus the shipping costs for every assigned order. Every order has to be packed exactly once at an open location. The concrete instance info is below.
There are 6 candidate packing centers and 13 customer orders, and the list of opening fees is 9189, 5205, 5187, 3530, 9452, 9544.
Packing center F1 has an opening fee of 9189.
Packing center F2 has an opening fee of 5205.
Packing center F3 has an opening fee of 5187.
Packing center F4 has an opening fee of 3530.
Packing center F5 has an opening fee of 9452.
Packing center F6 has an opening fee of 9544.
If order 1 is packed at packing center F1, the shipping cost is 370.
If order 2 is packed at packing center F1, the shipping cost is 322.
If order 3 is packed at packing center F1, the shipping cost is 821.
If order 4 is packed at packing center F1, the shipping cost is 972.
If order 5 is packed at packing center F1, the shipping cost is 994.
If order 6 is packed at packing center F1, the shipping cost is 88.
If order 7 is packed at packing center F1, the shipping cost is 266.
If order 8 is packed at packing center F1, the shipping cost is 741.
If order 9 is packed at packing center F1, the shipping cost is 98.
If order 10 is packed at packing center F1, the shipping cost is 260.
If order 11 is packed at packing center F1, the shipping cost is 643.
If order 12 is packed at packing center F1, the shipping cost is 794.
If order 13 is packed at packing center F1, the shipping cost is 15.
If order 1 is packed at packing center F2, the shipping cost is 215.
If order 2 is packed at packing center F2, the shipping cost is 460.
If order 3 is packed at packing center F2, the shipping cost is 768.
If order 4 is packed at packing center F2, the shipping cost is 385.
If order 5 is packed at packing center F2, the shipping cost is 475.
If order 6 is packed at packing center F2, the shipping cost is 774.
If order 7 is packed at packing center F2, the shipping cost is 567.
If order 8 is packed at packing center F2, the shipping cost is 649.
If order 9 is packed at packing center F2, the shipping cost is 559.
If order 10 is packed at packing center F2, the shipping cost is 277.
If order 11 is packed at packing center F2, the shipping cost is 300.
If order 12 is packed at packing center F2, the shipping cost is 972.
If order 13 is packed at packing center F2, the shipping cost is 656.
If order 1 is packed at packing center F3, the shipping cost is 0.
If order 2 is packed at packing center F3, the shipping cost is 736.
If order 3 is packed at packing center F3, the shipping cost is 477.
If order 4 is packed at packing center F3, the shipping cost is 596.
If order 5 is packed at packing center F3, the shipping cost is 639.
If order 6 is packed at packing center F3, the shipping cost is 330.
If order 7 is packed at packing center F3, the shipping cost is 730.
If order 8 is packed at packing center F3, the shipping cost is 792.
If order 9 is packed at packing center F3, the shipping cost is 697.
If order 10 is packed at packing center F3, the shipping cost is 532.
If order 11 is packed at packing center F3, the shipping cost is 393.
If order 12 is packed at packing center F3, the shipping cost is 654.
If order 13 is packed at packing center F3, the shipping cost is 494.
If order 1 is packed at packing center F4, the shipping cost is 590.
If order 2 is packed at packing center F4, the shipping cost is 166.
If order 3 is packed at packing center F4, the shipping cost is 17.
If order 4 is packed at packing center F4, the shipping cost is 39.
If order 5 is packed at packing center F4, the shipping cost is 655.
If order 6 is packed at packing center F4, the shipping cost is 713.
If order 7 is packed at packing center F4, the shipping cost is 599.
If order 8 is packed at packing center F4, the shipping cost is 524.
If order 9 is packed at packing center F4, the shipping cost is 793.
If order 10 is packed at packing center F4, the shipping cost is 431.
If order 11 is packed at packing center F4, the shipping cost is 313.
If order 12 is packed at packing center F4, the shipping cost is 550.
If order 13 is packed at packing center F4, the shipping cost is 277.
If order 1 is packed at packing center F5, the shipping cost is 979.
If order 2 is packed at packing center F5, the shipping cost is 886.
If order 3 is packed at packing center F5, the shipping cost is 626.
If order 4 is packed at packing center F5, the shipping cost is 330.
If order 5 is packed at packing center F5, the shipping cost is 321.
If order 6 is packed at packing center F5, the shipping cost is 409.
If order 7 is packed at packing center F5, the shipping cost is 197.
If order 8 is packed at packing center F5, the shipping cost is 581.
If order 9 is packed at packing center F5, the shipping cost is 989.
If order 10 is packed at packing center F5, the shipping cost is 170.
If order 11 is packed at packing center F5, the shipping cost is 974.
If order 12 is packed at packing center F5, the shipping cost is 273.
If order 13 is packed at packing center F5, the shipping cost is 94.
If order 1 is packed at packing center F6, the shipping cost is 732.
If order 2 is packed at packing center F6, the shipping cost is 660.
If order 3 is packed at packing center F6, the shipping cost is 927.
If order 4 is packed at packing center F6, the shipping cost is 848.
If order 5 is packed at packing center F6, the shipping cost is 74.
If order 6 is packed at packing center F6, the shipping cost is 778.
If order 7 is packed at packing center F6, the shipping cost is 976.
If order 8 is packed at packing center F6, the shipping cost is 612.
If order 9 is packed at packing center F6, the shipping cost is 718.
If order 10 is packed at packing center F6, the shipping cost is 639.
If order 11 is packed at packing center F6, the shipping cost is 250.
If order 12 is packed at packing center F6, the shipping cost is 662.
If order 13 is packed at packing center F6, the shipping cost is 198.
Decisions should minimize the total of chosen opening fees plus the shipping costs for all assigned orders.
Also, when you send back your answer, please follow this simple JSON layout so I can read it easily:
{
""solution"": {
""selected"": [<packing_site_to_open>, <packing_site_to_open>, ...],
""assignments"": [<chosen_packing_location>, <chosen_packing_location>, ...]
}
}
This little sketch is just the shape I need: the selected list is where you say which packing locations we’ll run, and the assignments list says, for each order in the instance, which open packing location handles it. Think of it like a short form: ""selected"" = which sites we turn on, ""assignments"" = which site packs each order.
This is only a template of the expected shape — not the final answer itself.
Please be sure to use the identifiers exactly as they appear in the instance input — do not rename them or introduce new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [9189, 5205, 5187, 3530, 9452, 9544], 'connection_costs': [[370, 322, 821, 972, 994, 88, 266, 741, 98, 260, 643, 794, 15], [215, 460, 768, 385, 475, 774, 567, 649, 559, 277, 300, 972, 656], [0, 736, 477, 596, 639, 330, 730, 792, 697, 532, 393, 654, 494], [590, 166, 17, 39, 655, 713, 599, 524, 793, 431, 313, 550, 277], [979, 886, 626, 330, 321, 409, 197, 581, 989, 170, 974, 273, 94], [732, 660, 927, 848, 74, 778, 976, 612, 718, 639, 250, 662, 198]], 'objective': 9197.0}","{'open_facilities': [3], 'assignments': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]}",9197.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 13, 'facilities': [{'id': 'F1', 'opening_cost': 9189}, {'id': 'F2', 'opening_cost': 5205}, {'id': 'F3', 'opening_cost': 5187}, {'id': 'F4', 'opening_cost': 3530}, {'id': 'F5', 'opening_cost': 9452}, {'id': 'F6', 'opening_cost': 9544}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}, {'id': 12}, {'id': 13}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 370}, {'facility': 'F1', 'customer': 2, 'cost': 322}, {'facility': 'F1', 'customer': 3, 'cost': 821}, {'facility': 'F1', 'customer': 4, 'cost': 972}, {'facility': 'F1', 'customer': 5, 'cost': 994}, {'facility': 'F1', 'customer': 6, 'cost': 88}, {'facility': 'F1', 'customer': 7, 'cost': 266}, {'facility': 'F1', 'customer': 8, 'cost': 741}, {'facility': 'F1', 'customer': 9, 'cost': 98}, {'facility': 'F1', 'customer': 10, 'cost': 260}, {'facility': 'F1', 'customer': 11, 'cost': 643}, {'facility': 'F1', 'customer': 12, 'cost': 794}, {'facility': 'F1', 'customer': 13, 'cost': 15}, {'facility': 'F2', 'customer': 1, 'cost': 215}, {'facility': 'F2', 'customer': 2, 'cost': 460}, {'facility': 'F2', 'customer': 3, 'cost': 768}, {'facility': 'F2', 'customer': 4, 'cost': 385}, {'facility': 'F2', 'customer': 5, 'cost': 475}, {'facility': 'F2', 'customer': 6, 'cost': 774}, {'facility': 'F2', 'customer': 7, 'cost': 567}, {'facility': 'F2', 'customer': 8, 'cost': 649}, {'facility': 'F2', 'customer': 9, 'cost': 559}, {'facility': 'F2', 'customer': 10, 'cost': 277}, {'facility': 'F2', 'customer': 11, 'cost': 300}, {'facility': 'F2', 'customer': 12, 'cost': 972}, {'facility': 'F2', 'customer': 13, 'cost': 656}, {'facility': 'F3', 'customer': 1, 'cost': 0}, {'facility': 'F3', 'customer': 2, 'cost': 736}, {'facility': 'F3', 'customer': 3, 'cost': 477}, {'facility': 'F3', 'customer': 4, 'cost': 596}, {'facility': 'F3', 'customer': 5, 'cost': 639}, {'facility': 'F3', 'customer': 6, 'cost': 330}, {'facility': 'F3', 'customer': 7, 'cost': 730}, {'facility': 'F3', 'customer': 8, 'cost': 792}, {'facility': 'F3', 'customer': 9, 'cost': 697}, {'facility': 'F3', 'customer': 10, 'cost': 532}, {'facility': 'F3', 'customer': 11, 'cost': 393}, {'facility': 'F3', 'customer': 12, 'cost': 654}, {'facility': 'F3', 'customer': 13, 'cost': 494}, {'facility': 'F4', 'customer': 1, 'cost': 590}, {'facility': 'F4', 'customer': 2, 'cost': 166}, {'facility': 'F4', 'customer': 3, 'cost': 17}, {'facility': 'F4', 'customer': 4, 'cost': 39}, {'facility': 'F4', 'customer': 5, 'cost': 655}, {'facility': 'F4', 'customer': 6, 'cost': 713}, {'facility': 'F4', 'customer': 7, 'cost': 599}, {'facility': 'F4', 'customer': 8, 'cost': 524}, {'facility': 'F4', 'customer': 9, 'cost': 793}, {'facility': 'F4', 'customer': 10, 'cost': 431}, {'facility': 'F4', 'customer': 11, 'cost': 313}, {'facility': 'F4', 'customer': 12, 'cost': 550}, {'facility': 'F4', 'customer': 13, 'cost': 277}, {'facility': 'F5', 'customer': 1, 'cost': 979}, {'facility': 'F5', 'customer': 2, 'cost': 886}, {'facility': 'F5', 'customer': 3, 'cost': 626}, {'facility': 'F5', 'customer': 4, 'cost': 330}, {'facility': 'F5', 'customer': 5, 'cost': 321}, {'facility': 'F5', 'customer': 6, 'cost': 409}, {'facility': 'F5', 'customer': 7, 'cost': 197}, {'facility': 'F5', 'customer': 8, 'cost': 581}, {'facility': 'F5', 'customer': 9, 'cost': 989}, {'facility': 'F5', 'customer': 10, 'cost': 170}, {'facility': 'F5', 'customer': 11, 'cost': 974}, {'facility': 'F5', 'customer': 12, 'cost': 273}, {'facility': 'F5', 'customer': 13, 'cost': 94}, {'facility': 'F6', 'customer': 1, 'cost': 732}, {'facility': 'F6', 'customer': 2, 'cost': 660}, {'facility': 'F6', 'customer': 3, 'cost': 927}, {'facility': 'F6', 'customer': 4, 'cost': 848}, {'facility': 'F6', 'customer': 5, 'cost': 74}, {'facility': 'F6', 'customer': 6, 'cost': 778}, {'facility': 'F6', 'customer': 7, 'cost': 976}, {'facility': 'F6', 'customer': 8, 'cost': 612}, {'facility': 'F6', 'customer': 9, 'cost': 718}, {'facility': 'F6', 'customer': 10, 'cost': 639}, {'facility': 'F6', 'customer': 11, 'cost': 250}, {'facility': 'F6', 'customer': 12, 'cost': 662}, {'facility': 'F6', 'customer': 13, 'cost': 198}], 'objective': 9197.0}","{'selected': ['F4'], 'assignments': ['F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4']}",38,nl,1
UFLP,UFLP,"There’s a town shuttle plan on my desk: a list of possible stops with activation prices and a list of commuters with how far they’d have to travel to each stop. The trick is to decide which stops to switch on and then pair every commuter with one of the switched-on stops so the combined bill — paying for the stops we turned on plus the travel cost for everyone — ends up as small as it can be. Everyone must be assigned to a single active stop (no one gets skipped or sent to multiple stops), and active stops can handle unlimited riders. The concrete data appear below.
There are 6 stops and 13 commuters in this instance.
**Stops**
| stop_id | activation_cost |
|---|---|
| F1 | 1985 |
| F2 | 1494 |
| F3 | 1648 |
| F4 | 1484 |
| F5 | 1992 |
| F6 | 1189 |
**Commuters**
| commuter_id |
|---|
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| 7 |
| 8 |
| 9 |
| 10 |
| 11 |
| 12 |
| 13 |
**Travel Cost**
| stop_id | commuter_id | travel_cost |
|---|---|---|
| F1 | 1 | 451 |
| F1 | 2 | 727 |
| F1 | 3 | 543 |
| F1 | 4 | 561 |
| F1 | 5 | 435 |
| F1 | 6 | 439 |
| F1 | 7 | 720 |
| F1 | 8 | 852 |
| F1 | 9 | 967 |
| F1 | 10 | 843 |
| F1 | 11 | 132 |
| F1 | 12 | 355 |
| F1 | 13 | 643 |
| F2 | 1 | 139 |
| F2 | 2 | 398 |
| F2 | 3 | 561 |
| F2 | 4 | 162 |
| F2 | 5 | 438 |
| F2 | 6 | 627 |
| F2 | 7 | 700 |
| F2 | 8 | 820 |
| F2 | 9 | 288 |
| F2 | 10 | 316 |
| F2 | 11 | 583 |
| F2 | 12 | 9 |
| F2 | 13 | 691 |
| F3 | 1 | 803 |
| F3 | 2 | 409 |
| F3 | 3 | 211 |
| F3 | 4 | 292 |
| F3 | 5 | 619 |
| F3 | 6 | 406 |
| F3 | 7 | 129 |
| F3 | 8 | 256 |
| F3 | 9 | 592 |
| F3 | 10 | 674 |
| F3 | 11 | 215 |
| F3 | 12 | 27 |
| F3 | 13 | 34 |
| F4 | 1 | 452 |
| F4 | 2 | 951 |
| F4 | 3 | 776 |
| F4 | 4 | 235 |
| F4 | 5 | 623 |
| F4 | 6 | 158 |
| F4 | 7 | 384 |
| F4 | 8 | 557 |
| F4 | 9 | 800 |
| F4 | 10 | 449 |
| F4 | 11 | 841 |
| F4 | 12 | 701 |
| F4 | 13 | 445 |
| F5 | 1 | 939 |
| F5 | 2 | 770 |
| F5 | 3 | 321 |
| F5 | 4 | 462 |
| F5 | 5 | 933 |
| F5 | 6 | 842 |
| F5 | 7 | 624 |
| F5 | 8 | 186 |
| F5 | 9 | 690 |
| F5 | 10 | 495 |
| F5 | 11 | 56 |
| F5 | 12 | 516 |
| F5 | 13 | 678 |
| F6 | 1 | 824 |
| F6 | 2 | 251 |
| F6 | 3 | 938 |
| F6 | 4 | 823 |
| F6 | 5 | 100 |
| F6 | 6 | 960 |
| F6 | 7 | 264 |
| F6 | 8 | 160 |
| F6 | 9 | 373 |
| F6 | 10 | 209 |
| F6 | 11 | 780 |
| F6 | 12 | 610 |
| F6 | 13 | 490 |
I'll give the result in a small, predictable JSON shape so it's easy to read — nothing fancy, just the two things we need to report.
{
""solution"": {
""selected"": [<stop_to_open>, <stop_to_open>, ...],
""assignments"": [<chosen_open_stop>, <chosen_open_stop>, ...]
}
}
Pretty straightforward: ""selected"" is the list of stops we switch on (the activation purchases), and ""assignments"" tells which active stop each commuter uses, in the same order the commuters appear in the input. This is just the sketch of the expected shape, not the actual answer.
Please use identifiers exactly as they appear in the instance input — no renaming and no new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1985, 1494, 1648, 1484, 1992, 1189], 'connection_costs': [[451, 727, 543, 561, 435, 439, 720, 852, 967, 843, 132, 355, 643], [139, 398, 561, 162, 438, 627, 700, 820, 288, 316, 583, 9, 691], [803, 409, 211, 292, 619, 406, 129, 256, 592, 674, 215, 27, 34], [452, 951, 776, 235, 623, 158, 384, 557, 800, 449, 841, 701, 445], [939, 770, 321, 462, 933, 842, 624, 186, 690, 495, 56, 516, 678], [824, 251, 938, 823, 100, 960, 264, 160, 373, 209, 780, 610, 490]], 'objective': 6047.0}","{'open_facilities': [2, 5], 'assignments': [2, 5, 2, 2, 5, 2, 2, 5, 5, 5, 2, 2, 2]}",6047.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 13, 'facilities': [{'id': 'F1', 'opening_cost': 1985}, {'id': 'F2', 'opening_cost': 1494}, {'id': 'F3', 'opening_cost': 1648}, {'id': 'F4', 'opening_cost': 1484}, {'id': 'F5', 'opening_cost': 1992}, {'id': 'F6', 'opening_cost': 1189}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}, {'id': 12}, {'id': 13}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 451}, {'facility': 'F1', 'customer': 2, 'cost': 727}, {'facility': 'F1', 'customer': 3, 'cost': 543}, {'facility': 'F1', 'customer': 4, 'cost': 561}, {'facility': 'F1', 'customer': 5, 'cost': 435}, {'facility': 'F1', 'customer': 6, 'cost': 439}, {'facility': 'F1', 'customer': 7, 'cost': 720}, {'facility': 'F1', 'customer': 8, 'cost': 852}, {'facility': 'F1', 'customer': 9, 'cost': 967}, {'facility': 'F1', 'customer': 10, 'cost': 843}, {'facility': 'F1', 'customer': 11, 'cost': 132}, {'facility': 'F1', 'customer': 12, 'cost': 355}, {'facility': 'F1', 'customer': 13, 'cost': 643}, {'facility': 'F2', 'customer': 1, 'cost': 139}, {'facility': 'F2', 'customer': 2, 'cost': 398}, {'facility': 'F2', 'customer': 3, 'cost': 561}, {'facility': 'F2', 'customer': 4, 'cost': 162}, {'facility': 'F2', 'customer': 5, 'cost': 438}, {'facility': 'F2', 'customer': 6, 'cost': 627}, {'facility': 'F2', 'customer': 7, 'cost': 700}, {'facility': 'F2', 'customer': 8, 'cost': 820}, {'facility': 'F2', 'customer': 9, 'cost': 288}, {'facility': 'F2', 'customer': 10, 'cost': 316}, {'facility': 'F2', 'customer': 11, 'cost': 583}, {'facility': 'F2', 'customer': 12, 'cost': 9}, {'facility': 'F2', 'customer': 13, 'cost': 691}, {'facility': 'F3', 'customer': 1, 'cost': 803}, {'facility': 'F3', 'customer': 2, 'cost': 409}, {'facility': 'F3', 'customer': 3, 'cost': 211}, {'facility': 'F3', 'customer': 4, 'cost': 292}, {'facility': 'F3', 'customer': 5, 'cost': 619}, {'facility': 'F3', 'customer': 6, 'cost': 406}, {'facility': 'F3', 'customer': 7, 'cost': 129}, {'facility': 'F3', 'customer': 8, 'cost': 256}, {'facility': 'F3', 'customer': 9, 'cost': 592}, {'facility': 'F3', 'customer': 10, 'cost': 674}, {'facility': 'F3', 'customer': 11, 'cost': 215}, {'facility': 'F3', 'customer': 12, 'cost': 27}, {'facility': 'F3', 'customer': 13, 'cost': 34}, {'facility': 'F4', 'customer': 1, 'cost': 452}, {'facility': 'F4', 'customer': 2, 'cost': 951}, {'facility': 'F4', 'customer': 3, 'cost': 776}, {'facility': 'F4', 'customer': 4, 'cost': 235}, {'facility': 'F4', 'customer': 5, 'cost': 623}, {'facility': 'F4', 'customer': 6, 'cost': 158}, {'facility': 'F4', 'customer': 7, 'cost': 384}, {'facility': 'F4', 'customer': 8, 'cost': 557}, {'facility': 'F4', 'customer': 9, 'cost': 800}, {'facility': 'F4', 'customer': 10, 'cost': 449}, {'facility': 'F4', 'customer': 11, 'cost': 841}, {'facility': 'F4', 'customer': 12, 'cost': 701}, {'facility': 'F4', 'customer': 13, 'cost': 445}, {'facility': 'F5', 'customer': 1, 'cost': 939}, {'facility': 'F5', 'customer': 2, 'cost': 770}, {'facility': 'F5', 'customer': 3, 'cost': 321}, {'facility': 'F5', 'customer': 4, 'cost': 462}, {'facility': 'F5', 'customer': 5, 'cost': 933}, {'facility': 'F5', 'customer': 6, 'cost': 842}, {'facility': 'F5', 'customer': 7, 'cost': 624}, {'facility': 'F5', 'customer': 8, 'cost': 186}, {'facility': 'F5', 'customer': 9, 'cost': 690}, {'facility': 'F5', 'customer': 10, 'cost': 495}, {'facility': 'F5', 'customer': 11, 'cost': 56}, {'facility': 'F5', 'customer': 12, 'cost': 516}, {'facility': 'F5', 'customer': 13, 'cost': 678}, {'facility': 'F6', 'customer': 1, 'cost': 824}, {'facility': 'F6', 'customer': 2, 'cost': 251}, {'facility': 'F6', 'customer': 3, 'cost': 938}, {'facility': 'F6', 'customer': 4, 'cost': 823}, {'facility': 'F6', 'customer': 5, 'cost': 100}, {'facility': 'F6', 'customer': 6, 'cost': 960}, {'facility': 'F6', 'customer': 7, 'cost': 264}, {'facility': 'F6', 'customer': 8, 'cost': 160}, {'facility': 'F6', 'customer': 9, 'cost': 373}, {'facility': 'F6', 'customer': 10, 'cost': 209}, {'facility': 'F6', 'customer': 11, 'cost': 780}, {'facility': 'F6', 'customer': 12, 'cost': 610}, {'facility': 'F6', 'customer': 13, 'cost': 490}], 'objective': 6047.0}","{'selected': ['F3', 'F6'], 'assignments': ['F3', 'F6', 'F3', 'F3', 'F6', 'F3', 'F3', 'F6', 'F6', 'F6', 'F3', 'F3', 'F3']}",39,markdown_table,1
UFLP,UFLP,"Many people on the planning team are debating which neighborhood outlets to start and how to attach each block to a single open outlet. The choice is which outlets to pay to open (each has a setup price) and then making sure each block is linked to exactly one of those opened outlets — no block left unassigned and no double assignments — with each link costing a delivery or customer-travel amount. The best option is the one with the lowest combined expense: add up the setup costs for opened outlets and the travel/delivery costs for every block’s assignment. The instance details are presented below.
There are 4 candidate outlets and 9 blocks; the outlet setup costs are 1000, 1000, 1000, 1000.
Candidate outlet F1 has a setup cost of 1000.
Candidate outlet F2 has a setup cost of 1000.
Candidate outlet F3 has a setup cost of 1000.
Candidate outlet F4 has a setup cost of 1000.
Block 1 can be served by outlet F1 at delivery/travel cost 186.
Block 2 can be served by outlet F1 at delivery/travel cost 604.
Block 3 can be served by outlet F1 at delivery/travel cost 890.
Block 4 can be served by outlet F1 at delivery/travel cost 352.
Block 5 can be served by outlet F1 at delivery/travel cost 680.
Block 6 can be served by outlet F1 at delivery/travel cost 928.
Block 7 can be served by outlet F1 at delivery/travel cost 839.
Block 8 can be served by outlet F1 at delivery/travel cost 768.
Block 9 can be served by outlet F1 at delivery/travel cost 853.
Block 1 can be served by outlet F2 at delivery/travel cost 823.
Block 2 can be served by outlet F2 at delivery/travel cost 775.
Block 3 can be served by outlet F2 at delivery/travel cost 290.
Block 4 can be served by outlet F2 at delivery/travel cost 614.
Block 5 can be served by outlet F2 at delivery/travel cost 652.
Block 6 can be served by outlet F2 at delivery/travel cost 632.
Block 7 can be served by outlet F2 at delivery/travel cost 636.
Block 8 can be served by outlet F2 at delivery/travel cost 572.
Block 9 can be served by outlet F2 at delivery/travel cost 686.
Block 1 can be served by outlet F3 at delivery/travel cost 479.
Block 2 can be served by outlet F3 at delivery/travel cost 745.
Block 3 can be served by outlet F3 at delivery/travel cost 17.
Block 4 can be served by outlet F3 at delivery/travel cost 167.
Block 5 can be served by outlet F3 at delivery/travel cost 851.
Block 6 can be served by outlet F3 at delivery/travel cost 86.
Block 7 can be served by outlet F3 at delivery/travel cost 723.
Block 8 can be served by outlet F3 at delivery/travel cost 593.
Block 9 can be served by outlet F3 at delivery/travel cost 133.
Block 1 can be served by outlet F4 at delivery/travel cost 637.
Block 2 can be served by outlet F4 at delivery/travel cost 348.
Block 3 can be served by outlet F4 at delivery/travel cost 450.
Block 4 can be served by outlet F4 at delivery/travel cost 348.
Block 5 can be served by outlet F4 at delivery/travel cost 815.
Block 6 can be served by outlet F4 at delivery/travel cost 981.
Block 7 can be served by outlet F4 at delivery/travel cost 43.
Block 8 can be served by outlet F4 at delivery/travel cost 261.
Block 9 can be served by outlet F4 at delivery/travel cost 194.
The planning team will use these figures to decide which outlets to open and how to assign each block so the total of setup fees plus delivery/travel costs is minimized.
Just so we're all on the same page about how to give the final pick-and-link info, please use this simple JSON layout when you reply. It's just the shape I need — nothing fancy.
{
""solution"": {
""selected"": [<outlet_to_open>, <outlet_to_open>, ...],
""assignments"": [<assigned_outlet>, <assigned_outlet>, ...]
}
}
""selected"" is where you list the outlets you decide to open. ""assignments"" is a list, one entry per block, saying which opened outlet that block is attached to. Think of it like filling out a form: the first part names the open outlets, the second part maps every block to one of those outlets.
This JSON is only a sketch of the expected shape, not the actual solution. And please use the exact identifiers from the instance input — do not rename or invent labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [1000, 1000, 1000, 1000], 'connection_costs': [[186, 604, 890, 352, 680, 928, 839, 768, 853], [823, 775, 290, 614, 652, 632, 636, 572, 686], [479, 745, 17, 167, 851, 86, 723, 593, 133], [637, 348, 450, 348, 815, 981, 43, 261, 194]], 'objective': 4349.0}","{'open_facilities': [2, 3], 'assignments': [2, 3, 2, 2, 3, 2, 3, 3, 2]}",4349.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 9, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 186}, {'facility': 'F1', 'customer': 2, 'cost': 604}, {'facility': 'F1', 'customer': 3, 'cost': 890}, {'facility': 'F1', 'customer': 4, 'cost': 352}, {'facility': 'F1', 'customer': 5, 'cost': 680}, {'facility': 'F1', 'customer': 6, 'cost': 928}, {'facility': 'F1', 'customer': 7, 'cost': 839}, {'facility': 'F1', 'customer': 8, 'cost': 768}, {'facility': 'F1', 'customer': 9, 'cost': 853}, {'facility': 'F2', 'customer': 1, 'cost': 823}, {'facility': 'F2', 'customer': 2, 'cost': 775}, {'facility': 'F2', 'customer': 3, 'cost': 290}, {'facility': 'F2', 'customer': 4, 'cost': 614}, {'facility': 'F2', 'customer': 5, 'cost': 652}, {'facility': 'F2', 'customer': 6, 'cost': 632}, {'facility': 'F2', 'customer': 7, 'cost': 636}, {'facility': 'F2', 'customer': 8, 'cost': 572}, {'facility': 'F2', 'customer': 9, 'cost': 686}, {'facility': 'F3', 'customer': 1, 'cost': 479}, {'facility': 'F3', 'customer': 2, 'cost': 745}, {'facility': 'F3', 'customer': 3, 'cost': 17}, {'facility': 'F3', 'customer': 4, 'cost': 167}, {'facility': 'F3', 'customer': 5, 'cost': 851}, {'facility': 'F3', 'customer': 6, 'cost': 86}, {'facility': 'F3', 'customer': 7, 'cost': 723}, {'facility': 'F3', 'customer': 8, 'cost': 593}, {'facility': 'F3', 'customer': 9, 'cost': 133}, {'facility': 'F4', 'customer': 1, 'cost': 637}, {'facility': 'F4', 'customer': 2, 'cost': 348}, {'facility': 'F4', 'customer': 3, 'cost': 450}, {'facility': 'F4', 'customer': 4, 'cost': 348}, {'facility': 'F4', 'customer': 5, 'cost': 815}, {'facility': 'F4', 'customer': 6, 'cost': 981}, {'facility': 'F4', 'customer': 7, 'cost': 43}, {'facility': 'F4', 'customer': 8, 'cost': 261}, {'facility': 'F4', 'customer': 9, 'cost': 194}], 'objective': 4349.0}","{'selected': ['F3', 'F4'], 'assignments': ['F3', 'F4', 'F3', 'F3', 'F4', 'F3', 'F4', 'F4', 'F3']}",40,nl,1
UFLP,UFLP,"Many people will be at the block party, and the organizers must choose which food truck locations to pay for and tell each attendee area which staffed location to use. Every staffed spot requires a rental fee, and every area adds up walking distance depending on which spot it’s sent to, so the combined total—stall fees plus total walking distance—is what the team wants to keep low. Each area needs exactly one assignment; no area can be unassigned or assigned to multiple spots. The specific data for spots, fees, and attendee areas are listed below.
# num_spots=6
# num_attendee_areas=12
# SPOTS
spot_id,rental_fee
F1,2000
F2,2000
F3,2000
F4,2000
F5,2000
F6,2000
# AREAS
area_id
0
1
2
3
4
5
6
7
8
9
10
11
# WALKING_DISTANCES
spot_id,area_id,walking_distance
F1,0,327
F1,1,551
F1,2,814
F1,3,252
F1,4,749
F1,5,679
F1,6,411
F1,7,328
F1,8,968
F1,9,720
F1,10,300
F1,11,485
F2,0,120
F2,1,584
F2,2,499
F2,3,699
F2,4,843
F2,5,241
F2,6,223
F2,7,497
F2,8,113
F2,9,606
F2,10,617
F2,11,627
F3,0,613
F3,1,366
F3,2,282
F3,3,812
F3,4,4
F3,5,448
F3,6,588
F3,7,627
F3,8,673
F3,9,336
F3,10,236
F3,11,439
F4,0,467
F4,1,293
F4,2,162
F4,3,61
F4,4,50
F4,5,187
F4,6,600
F4,7,903
F4,8,972
F4,9,111
F4,10,530
F4,11,749
F5,0,676
F5,1,442
F5,2,458
F5,3,437
F5,4,147
F5,5,834
F5,6,510
F5,7,46
F5,8,534
F5,9,877
F5,10,473
F5,11,506
F6,0,155
F6,1,140
F6,2,148
F6,3,305
F6,4,960
F6,5,935
F6,6,340
F6,7,940
F6,8,215
F6,9,823
F6,10,122
F6,11,93
You can just send the final choices in a small JSON snippet like this so it's easy to read and parse. Here's the shape I expect:
{
""solution"": {
""selected"": [<stall_to_rent>, <stall_to_rent>, ...],
""assignments"": [<assigned_spot>, <assigned_spot>, ...]
}
}
""selected"" is the list of staffed spots you decide to pay for (the rental fees). ""assignments"" is, for each attendee area in the same order as the input, which staffed spot that area should use. Super casual: think of ""selected"" as the stalls you're booking, and ""assignments"" as the directions you'd hand out to each group.
This JSON is just a sketch of the expected shape — not the actual answer. Please make sure to use the exact identifiers from the instance input (do not rename them and don’t invent new labels).
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000, 2000, 2000], 'connection_costs': [[327, 551, 814, 252, 749, 679, 411, 328, 968, 720, 300, 485], [120, 584, 499, 699, 843, 241, 223, 497, 113, 606, 617, 627], [613, 366, 282, 812, 4, 448, 588, 627, 673, 336, 236, 439], [467, 293, 162, 61, 50, 187, 600, 903, 972, 111, 530, 749], [676, 442, 458, 437, 147, 834, 510, 46, 534, 877, 473, 506], [155, 140, 148, 305, 960, 935, 340, 940, 215, 823, 122, 93]], 'objective': 6525.0}","{'open_facilities': [3, 5], 'assignments': [5, 5, 5, 3, 3, 3, 5, 3, 5, 3, 5, 5]}",6525.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 12, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}, {'id': 'F6', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 327}, {'facility': 'F1', 'customer': 1, 'cost': 551}, {'facility': 'F1', 'customer': 2, 'cost': 814}, {'facility': 'F1', 'customer': 3, 'cost': 252}, {'facility': 'F1', 'customer': 4, 'cost': 749}, {'facility': 'F1', 'customer': 5, 'cost': 679}, {'facility': 'F1', 'customer': 6, 'cost': 411}, {'facility': 'F1', 'customer': 7, 'cost': 328}, {'facility': 'F1', 'customer': 8, 'cost': 968}, {'facility': 'F1', 'customer': 9, 'cost': 720}, {'facility': 'F1', 'customer': 10, 'cost': 300}, {'facility': 'F1', 'customer': 11, 'cost': 485}, {'facility': 'F2', 'customer': 0, 'cost': 120}, {'facility': 'F2', 'customer': 1, 'cost': 584}, {'facility': 'F2', 'customer': 2, 'cost': 499}, {'facility': 'F2', 'customer': 3, 'cost': 699}, {'facility': 'F2', 'customer': 4, 'cost': 843}, {'facility': 'F2', 'customer': 5, 'cost': 241}, {'facility': 'F2', 'customer': 6, 'cost': 223}, {'facility': 'F2', 'customer': 7, 'cost': 497}, {'facility': 'F2', 'customer': 8, 'cost': 113}, {'facility': 'F2', 'customer': 9, 'cost': 606}, {'facility': 'F2', 'customer': 10, 'cost': 617}, {'facility': 'F2', 'customer': 11, 'cost': 627}, {'facility': 'F3', 'customer': 0, 'cost': 613}, {'facility': 'F3', 'customer': 1, 'cost': 366}, {'facility': 'F3', 'customer': 2, 'cost': 282}, {'facility': 'F3', 'customer': 3, 'cost': 812}, {'facility': 'F3', 'customer': 4, 'cost': 4}, {'facility': 'F3', 'customer': 5, 'cost': 448}, {'facility': 'F3', 'customer': 6, 'cost': 588}, {'facility': 'F3', 'customer': 7, 'cost': 627}, {'facility': 'F3', 'customer': 8, 'cost': 673}, {'facility': 'F3', 'customer': 9, 'cost': 336}, {'facility': 'F3', 'customer': 10, 'cost': 236}, {'facility': 'F3', 'customer': 11, 'cost': 439}, {'facility': 'F4', 'customer': 0, 'cost': 467}, {'facility': 'F4', 'customer': 1, 'cost': 293}, {'facility': 'F4', 'customer': 2, 'cost': 162}, {'facility': 'F4', 'customer': 3, 'cost': 61}, {'facility': 'F4', 'customer': 4, 'cost': 50}, {'facility': 'F4', 'customer': 5, 'cost': 187}, {'facility': 'F4', 'customer': 6, 'cost': 600}, {'facility': 'F4', 'customer': 7, 'cost': 903}, {'facility': 'F4', 'customer': 8, 'cost': 972}, {'facility': 'F4', 'customer': 9, 'cost': 111}, {'facility': 'F4', 'customer': 10, 'cost': 530}, {'facility': 'F4', 'customer': 11, 'cost': 749}, {'facility': 'F5', 'customer': 0, 'cost': 676}, {'facility': 'F5', 'customer': 1, 'cost': 442}, {'facility': 'F5', 'customer': 2, 'cost': 458}, {'facility': 'F5', 'customer': 3, 'cost': 437}, {'facility': 'F5', 'customer': 4, 'cost': 147}, {'facility': 'F5', 'customer': 5, 'cost': 834}, {'facility': 'F5', 'customer': 6, 'cost': 510}, {'facility': 'F5', 'customer': 7, 'cost': 46}, {'facility': 'F5', 'customer': 8, 'cost': 534}, {'facility': 'F5', 'customer': 9, 'cost': 877}, {'facility': 'F5', 'customer': 10, 'cost': 473}, {'facility': 'F5', 'customer': 11, 'cost': 506}, {'facility': 'F6', 'customer': 0, 'cost': 155}, {'facility': 'F6', 'customer': 1, 'cost': 140}, {'facility': 'F6', 'customer': 2, 'cost': 148}, {'facility': 'F6', 'customer': 3, 'cost': 305}, {'facility': 'F6', 'customer': 4, 'cost': 960}, {'facility': 'F6', 'customer': 5, 'cost': 935}, {'facility': 'F6', 'customer': 6, 'cost': 340}, {'facility': 'F6', 'customer': 7, 'cost': 940}, {'facility': 'F6', 'customer': 8, 'cost': 215}, {'facility': 'F6', 'customer': 9, 'cost': 823}, {'facility': 'F6', 'customer': 10, 'cost': 122}, {'facility': 'F6', 'customer': 11, 'cost': 93}], 'objective': 6525.0}","{'selected': ['F4', 'F6'], 'assignments': ['F6', 'F6', 'F6', 'F4', 'F4', 'F4', 'F6', 'F4', 'F6', 'F4', 'F6', 'F6']}",41,csv,0
UFLP,UFLP,"Someone on the logistics team has to choose which cold depots to open and then point each clinic to exactly one of those open depots so vaccines and supplies can be sent. Every clinic must be tied to a single operating depot — no clinic gets left out and none is linked to a depot that’s closed. The way to tell which choice is preferable is to add the operating fees for the depots that are open and the transport cost for each clinic to its depot; the lower that sum, the better. The concrete numbers follow below.
Someone on the logistics team sees 5 candidate depots, 13 clinics, and the depot operating fees are 1000, 1000, 1000, 1000, 1000.
Someone on the logistics team can open depot F1 at a fixed operating fee of 1000.
Someone on the logistics team can open depot F2 at a fixed operating fee of 1000.
Someone on the logistics team can open depot F3 at a fixed operating fee of 1000.
Someone on the logistics team can open depot F4 at a fixed operating fee of 1000.
Someone on the logistics team can open depot F5 at a fixed operating fee of 1000.
Someone on the logistics team would assign clinic A to depot F1 with a transport cost of 930.
Someone on the logistics team would assign clinic B to depot F1 with a transport cost of 809.
Someone on the logistics team would assign clinic C to depot F1 with a transport cost of 127.
Someone on the logistics team would assign clinic D to depot F1 with a transport cost of 509.
Someone on the logistics team would assign clinic E to depot F1 with a transport cost of 82.
Someone on the logistics team would assign clinic F to depot F1 with a transport cost of 847.
Someone on the logistics team would assign clinic G to depot F1 with a transport cost of 156.
Someone on the logistics team would assign clinic H to depot F1 with a transport cost of 482.
Someone on the logistics team would assign clinic I to depot F1 with a transport cost of 565.
Someone on the logistics team would assign clinic J to depot F1 with a transport cost of 274.
Someone on the logistics team would assign clinic K to depot F1 with a transport cost of 251.
Someone on the logistics team would assign clinic L to depot F1 with a transport cost of 407.
Someone on the logistics team would assign clinic M to depot F1 with a transport cost of 627.
Someone on the logistics team would assign clinic A to depot F2 with a transport cost of 928.
Someone on the logistics team would assign clinic B to depot F2 with a transport cost of 334.
Someone on the logistics team would assign clinic C to depot F2 with a transport cost of 884.
Someone on the logistics team would assign clinic D to depot F2 with a transport cost of 462.
Someone on the logistics team would assign clinic E to depot F2 with a transport cost of 461.
Someone on the logistics team would assign clinic F to depot F2 with a transport cost of 259.
Someone on the logistics team would assign clinic G to depot F2 with a transport cost of 286.
Someone on the logistics team would assign clinic H to depot F2 with a transport cost of 781.
Someone on the logistics team would assign clinic I to depot F2 with a transport cost of 770.
Someone on the logistics team would assign clinic J to depot F2 with a transport cost of 369.
Someone on the logistics team would assign clinic K to depot F2 with a transport cost of 875.
Someone on the logistics team would assign clinic L to depot F2 with a transport cost of 486.
Someone on the logistics team would assign clinic M to depot F2 with a transport cost of 709.
Someone on the logistics team would assign clinic A to depot F3 with a transport cost of 502.
Someone on the logistics team would assign clinic B to depot F3 with a transport cost of 405.
Someone on the logistics team would assign clinic C to depot F3 with a transport cost of 758.
Someone on the logistics team would assign clinic D to depot F3 with a transport cost of 397.
Someone on the logistics team would assign clinic E to depot F3 with a transport cost of 159.
Someone on the logistics team would assign clinic F to depot F3 with a transport cost of 431.
Someone on the logistics team would assign clinic G to depot F3 with a transport cost of 426.
Someone on the logistics team would assign clinic H to depot F3 with a transport cost of 497.
Someone on the logistics team would assign clinic I to depot F3 with a transport cost of 923.
Someone on the logistics team would assign clinic J to depot F3 with a transport cost of 570.
Someone on the logistics team would assign clinic K to depot F3 with a transport cost of 79.
Someone on the logistics team would assign clinic L to depot F3 with a transport cost of 39.
Someone on the logistics team would assign clinic M to depot F3 with a transport cost of 125.
Someone on the logistics team would assign clinic A to depot F4 with a transport cost of 794.
Someone on the logistics team would assign clinic B to depot F4 with a transport cost of 79.
Someone on the logistics team would assign clinic C to depot F4 with a transport cost of 26.
Someone on the logistics team would assign clinic D to depot F4 with a transport cost of 346.
Someone on the logistics team would assign clinic E to depot F4 with a transport cost of 298.
Someone on the logistics team would assign clinic F to depot F4 with a transport cost of 439.
Someone on the logistics team would assign clinic G to depot F4 with a transport cost of 322.
Someone on the logistics team would assign clinic H to depot F4 with a transport cost of 51.
Someone on the logistics team would assign clinic I to depot F4 with a transport cost of 418.
Someone on the logistics team would assign clinic J to depot F4 with a transport cost of 76.
Someone on the logistics team would assign clinic K to depot F4 with a transport cost of 520.
Someone on the logistics team would assign clinic L to depot F4 with a transport cost of 306.
Someone on the logistics team would assign clinic M to depot F4 with a transport cost of 708.
Someone on the logistics team would assign clinic A to depot F5 with a transport cost of 124.
Someone on the logistics team would assign clinic B to depot F5 with a transport cost of 479.
Someone on the logistics team would assign clinic C to depot F5 with a transport cost of 263.
Someone on the logistics team would assign clinic D to depot F5 with a transport cost of 545.
Someone on the logistics team would assign clinic E to depot F5 with a transport cost of 397.
Someone on the logistics team would assign clinic F to depot F5 with a transport cost of 612.
Someone on the logistics team would assign clinic G to depot F5 with a transport cost of 127.
Someone on the logistics team would assign clinic H to depot F5 with a transport cost of 14.
Someone on the logistics team would assign clinic I to depot F5 with a transport cost of 789.
Someone on the logistics team would assign clinic J to depot F5 with a transport cost of 231.
Someone on the logistics team would assign clinic K to depot F5 with a transport cost of 54.
Someone on the logistics team would assign clinic L to depot F5 with a transport cost of 183.
Someone on the logistics team would assign clinic M to depot F5 with a transport cost of 802.
Someone on the logistics team will use these numbers to sum opened depots' operating fees and assigned transport costs and choose the lowest total.
Also, when you send back the actual choices, please use this simple JSON layout so it’s easy to read and plug into our tools — here’s the shape we expect:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
Quick note on what those fields mean in plain terms: selected is the list of depot ids you decide to open; assignments lists, for each clinic (in the same order as the instance), the id of the open depot that clinic will use. Think of it like a short form: which depots open, and who goes where.
This JSON is just a sketch of the expected shape — not the actual answer. Please make sure all identifiers are used exactly as they appear in the instance input — no renaming and no new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1000, 1000, 1000, 1000, 1000], 'connection_costs': [[930, 809, 127, 509, 82, 847, 156, 482, 565, 274, 251, 407, 627], [928, 334, 884, 462, 461, 259, 286, 781, 770, 369, 875, 486, 709], [502, 405, 758, 397, 159, 431, 426, 497, 923, 570, 79, 39, 125], [794, 79, 26, 346, 298, 439, 322, 51, 418, 76, 520, 306, 708], [124, 479, 263, 545, 397, 612, 127, 14, 789, 231, 54, 183, 802]], 'objective': 4653.0}","{'open_facilities': [2, 3], 'assignments': [2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2]}",4653.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 13, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}, {'id': 'F5', 'opening_cost': 1000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}, {'id': 'L'}, {'id': 'M'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 930}, {'facility': 'F1', 'customer': 'B', 'cost': 809}, {'facility': 'F1', 'customer': 'C', 'cost': 127}, {'facility': 'F1', 'customer': 'D', 'cost': 509}, {'facility': 'F1', 'customer': 'E', 'cost': 82}, {'facility': 'F1', 'customer': 'F', 'cost': 847}, {'facility': 'F1', 'customer': 'G', 'cost': 156}, {'facility': 'F1', 'customer': 'H', 'cost': 482}, {'facility': 'F1', 'customer': 'I', 'cost': 565}, {'facility': 'F1', 'customer': 'J', 'cost': 274}, {'facility': 'F1', 'customer': 'K', 'cost': 251}, {'facility': 'F1', 'customer': 'L', 'cost': 407}, {'facility': 'F1', 'customer': 'M', 'cost': 627}, {'facility': 'F2', 'customer': 'A', 'cost': 928}, {'facility': 'F2', 'customer': 'B', 'cost': 334}, {'facility': 'F2', 'customer': 'C', 'cost': 884}, {'facility': 'F2', 'customer': 'D', 'cost': 462}, {'facility': 'F2', 'customer': 'E', 'cost': 461}, {'facility': 'F2', 'customer': 'F', 'cost': 259}, {'facility': 'F2', 'customer': 'G', 'cost': 286}, {'facility': 'F2', 'customer': 'H', 'cost': 781}, {'facility': 'F2', 'customer': 'I', 'cost': 770}, {'facility': 'F2', 'customer': 'J', 'cost': 369}, {'facility': 'F2', 'customer': 'K', 'cost': 875}, {'facility': 'F2', 'customer': 'L', 'cost': 486}, {'facility': 'F2', 'customer': 'M', 'cost': 709}, {'facility': 'F3', 'customer': 'A', 'cost': 502}, {'facility': 'F3', 'customer': 'B', 'cost': 405}, {'facility': 'F3', 'customer': 'C', 'cost': 758}, {'facility': 'F3', 'customer': 'D', 'cost': 397}, {'facility': 'F3', 'customer': 'E', 'cost': 159}, {'facility': 'F3', 'customer': 'F', 'cost': 431}, {'facility': 'F3', 'customer': 'G', 'cost': 426}, {'facility': 'F3', 'customer': 'H', 'cost': 497}, {'facility': 'F3', 'customer': 'I', 'cost': 923}, {'facility': 'F3', 'customer': 'J', 'cost': 570}, {'facility': 'F3', 'customer': 'K', 'cost': 79}, {'facility': 'F3', 'customer': 'L', 'cost': 39}, {'facility': 'F3', 'customer': 'M', 'cost': 125}, {'facility': 'F4', 'customer': 'A', 'cost': 794}, {'facility': 'F4', 'customer': 'B', 'cost': 79}, {'facility': 'F4', 'customer': 'C', 'cost': 26}, {'facility': 'F4', 'customer': 'D', 'cost': 346}, {'facility': 'F4', 'customer': 'E', 'cost': 298}, {'facility': 'F4', 'customer': 'F', 'cost': 439}, {'facility': 'F4', 'customer': 'G', 'cost': 322}, {'facility': 'F4', 'customer': 'H', 'cost': 51}, {'facility': 'F4', 'customer': 'I', 'cost': 418}, {'facility': 'F4', 'customer': 'J', 'cost': 76}, {'facility': 'F4', 'customer': 'K', 'cost': 520}, {'facility': 'F4', 'customer': 'L', 'cost': 306}, {'facility': 'F4', 'customer': 'M', 'cost': 708}, {'facility': 'F5', 'customer': 'A', 'cost': 124}, {'facility': 'F5', 'customer': 'B', 'cost': 479}, {'facility': 'F5', 'customer': 'C', 'cost': 263}, {'facility': 'F5', 'customer': 'D', 'cost': 545}, {'facility': 'F5', 'customer': 'E', 'cost': 397}, {'facility': 'F5', 'customer': 'F', 'cost': 612}, {'facility': 'F5', 'customer': 'G', 'cost': 127}, {'facility': 'F5', 'customer': 'H', 'cost': 14}, {'facility': 'F5', 'customer': 'I', 'cost': 789}, {'facility': 'F5', 'customer': 'J', 'cost': 231}, {'facility': 'F5', 'customer': 'K', 'cost': 54}, {'facility': 'F5', 'customer': 'L', 'cost': 183}, {'facility': 'F5', 'customer': 'M', 'cost': 802}], 'objective': 4653.0}","{'selected': ['F3', 'F4'], 'assignments': ['F3', 'F4', 'F4', 'F4', 'F3', 'F3', 'F4', 'F4', 'F4', 'F4', 'F3', 'F3', 'F3']}",42,nl,names
UFLP,UFLP,"I run the distribution side of a retail network and need to pick which micro-warehouses to switch on and which hub will serve each shop. The idea is simple: every shop has to be tied to one—and only one—open hub, and the total bill is the sum of the opening fees for the hubs chosen plus all the shipment costs from hubs to shops. A plan is better when that combined bill is smaller, so the challenge is to turn on a smart set of hubs and link each shop to one of them without leaving any shop out or giving any shop two homes. The concrete details (locations, fees and shipping costs) are shown below.
# total_candidate_hubs=6
# total_shops=14
# HUBS
hub_id,activation_fee
F1,2000
F2,2000
F3,2000
F4,2000
F5,2000
F6,2000
# SHOPS
shop_id
0
1
2
3
4
5
6
7
8
9
10
11
12
13
# SHIPMENTS
hub_id,shop_id,shipment_cost
F1,0,108
F1,1,33
F1,2,158
F1,3,52
F1,4,49
F1,5,199
F1,6,658
F1,7,280
F1,8,876
F1,9,859
F1,10,747
F1,11,388
F1,12,173
F1,13,319
F2,0,921
F2,1,372
F2,2,559
F2,3,9
F2,4,906
F2,5,799
F2,6,891
F2,7,915
F2,8,222
F2,9,361
F2,10,77
F2,11,223
F2,12,877
F2,13,691
F3,0,981
F3,1,337
F3,2,829
F3,3,874
F3,4,337
F3,5,925
F3,6,580
F3,7,128
F3,8,239
F3,9,201
F3,10,329
F3,11,668
F3,12,239
F3,13,655
F4,0,967
F4,1,185
F4,2,395
F4,3,517
F4,4,981
F4,5,823
F4,6,485
F4,7,979
F4,8,164
F4,9,611
F4,10,363
F4,11,659
F4,12,621
F4,13,919
F5,0,615
F5,1,618
F5,2,516
F5,3,75
F5,4,79
F5,5,925
F5,6,557
F5,7,86
F5,8,279
F5,9,942
F5,10,984
F5,11,764
F5,12,396
F5,13,394
F6,0,450
F6,1,845
F6,2,998
F6,3,443
F6,4,100
F6,5,749
F6,6,881
F6,7,631
F6,8,180
F6,9,182
F6,10,775
F6,11,499
F6,12,585
F6,13,536
Also, when you hand back the plan, please use this little JSON layout so I can read it automatically — nothing fancy, just two lists: which micro-warehouses you flip on, and which open micro-warehouse serves each shop.
{
""solution"": {
""selected"": [<microwarehouse_to_open>, <microwarehouse_to_open>, ...],
""assignments"": [<chosen_open_microwarehouse>, <chosen_open_microwarehouse>, ...]
}
}
Think of ""selected"" as the checklist of micro-warehouses you plan to switch on (their IDs), and ""assignments"" as a one-to-one list that says, in the same order as the shops in the instance, which open micro-warehouse will serve that shop. This JSON is just a sketch of the shape I need — not the actual answer.
Please make sure you use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [2000, 2000, 2000, 2000, 2000, 2000], 'connection_costs': [[108, 33, 158, 52, 49, 199, 658, 280, 876, 859, 747, 388, 173, 319], [921, 372, 559, 9, 906, 799, 891, 915, 222, 361, 77, 223, 877, 691], [981, 337, 829, 874, 337, 925, 580, 128, 239, 201, 329, 668, 239, 655], [967, 185, 395, 517, 981, 823, 485, 979, 164, 611, 363, 659, 621, 919], [615, 618, 516, 75, 79, 925, 557, 86, 279, 942, 984, 764, 396, 394], [450, 845, 998, 443, 100, 749, 881, 631, 180, 182, 775, 499, 585, 536]], 'objective': 6869.0}","{'open_facilities': [0, 1], 'assignments': [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]}",6869.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 14, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}, {'id': 'F6', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}, {'id': 11}, {'id': 12}, {'id': 13}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 108}, {'facility': 'F1', 'customer': 1, 'cost': 33}, {'facility': 'F1', 'customer': 2, 'cost': 158}, {'facility': 'F1', 'customer': 3, 'cost': 52}, {'facility': 'F1', 'customer': 4, 'cost': 49}, {'facility': 'F1', 'customer': 5, 'cost': 199}, {'facility': 'F1', 'customer': 6, 'cost': 658}, {'facility': 'F1', 'customer': 7, 'cost': 280}, {'facility': 'F1', 'customer': 8, 'cost': 876}, {'facility': 'F1', 'customer': 9, 'cost': 859}, {'facility': 'F1', 'customer': 10, 'cost': 747}, {'facility': 'F1', 'customer': 11, 'cost': 388}, {'facility': 'F1', 'customer': 12, 'cost': 173}, {'facility': 'F1', 'customer': 13, 'cost': 319}, {'facility': 'F2', 'customer': 0, 'cost': 921}, {'facility': 'F2', 'customer': 1, 'cost': 372}, {'facility': 'F2', 'customer': 2, 'cost': 559}, {'facility': 'F2', 'customer': 3, 'cost': 9}, {'facility': 'F2', 'customer': 4, 'cost': 906}, {'facility': 'F2', 'customer': 5, 'cost': 799}, {'facility': 'F2', 'customer': 6, 'cost': 891}, {'facility': 'F2', 'customer': 7, 'cost': 915}, {'facility': 'F2', 'customer': 8, 'cost': 222}, {'facility': 'F2', 'customer': 9, 'cost': 361}, {'facility': 'F2', 'customer': 10, 'cost': 77}, {'facility': 'F2', 'customer': 11, 'cost': 223}, {'facility': 'F2', 'customer': 12, 'cost': 877}, {'facility': 'F2', 'customer': 13, 'cost': 691}, {'facility': 'F3', 'customer': 0, 'cost': 981}, {'facility': 'F3', 'customer': 1, 'cost': 337}, {'facility': 'F3', 'customer': 2, 'cost': 829}, {'facility': 'F3', 'customer': 3, 'cost': 874}, {'facility': 'F3', 'customer': 4, 'cost': 337}, {'facility': 'F3', 'customer': 5, 'cost': 925}, {'facility': 'F3', 'customer': 6, 'cost': 580}, {'facility': 'F3', 'customer': 7, 'cost': 128}, {'facility': 'F3', 'customer': 8, 'cost': 239}, {'facility': 'F3', 'customer': 9, 'cost': 201}, {'facility': 'F3', 'customer': 10, 'cost': 329}, {'facility': 'F3', 'customer': 11, 'cost': 668}, {'facility': 'F3', 'customer': 12, 'cost': 239}, {'facility': 'F3', 'customer': 13, 'cost': 655}, {'facility': 'F4', 'customer': 0, 'cost': 967}, {'facility': 'F4', 'customer': 1, 'cost': 185}, {'facility': 'F4', 'customer': 2, 'cost': 395}, {'facility': 'F4', 'customer': 3, 'cost': 517}, {'facility': 'F4', 'customer': 4, 'cost': 981}, {'facility': 'F4', 'customer': 5, 'cost': 823}, {'facility': 'F4', 'customer': 6, 'cost': 485}, {'facility': 'F4', 'customer': 7, 'cost': 979}, {'facility': 'F4', 'customer': 8, 'cost': 164}, {'facility': 'F4', 'customer': 9, 'cost': 611}, {'facility': 'F4', 'customer': 10, 'cost': 363}, {'facility': 'F4', 'customer': 11, 'cost': 659}, {'facility': 'F4', 'customer': 12, 'cost': 621}, {'facility': 'F4', 'customer': 13, 'cost': 919}, {'facility': 'F5', 'customer': 0, 'cost': 615}, {'facility': 'F5', 'customer': 1, 'cost': 618}, {'facility': 'F5', 'customer': 2, 'cost': 516}, {'facility': 'F5', 'customer': 3, 'cost': 75}, {'facility': 'F5', 'customer': 4, 'cost': 79}, {'facility': 'F5', 'customer': 5, 'cost': 925}, {'facility': 'F5', 'customer': 6, 'cost': 557}, {'facility': 'F5', 'customer': 7, 'cost': 86}, {'facility': 'F5', 'customer': 8, 'cost': 279}, {'facility': 'F5', 'customer': 9, 'cost': 942}, {'facility': 'F5', 'customer': 10, 'cost': 984}, {'facility': 'F5', 'customer': 11, 'cost': 764}, {'facility': 'F5', 'customer': 12, 'cost': 396}, {'facility': 'F5', 'customer': 13, 'cost': 394}, {'facility': 'F6', 'customer': 0, 'cost': 450}, {'facility': 'F6', 'customer': 1, 'cost': 845}, {'facility': 'F6', 'customer': 2, 'cost': 998}, {'facility': 'F6', 'customer': 3, 'cost': 443}, {'facility': 'F6', 'customer': 4, 'cost': 100}, {'facility': 'F6', 'customer': 5, 'cost': 749}, {'facility': 'F6', 'customer': 6, 'cost': 881}, {'facility': 'F6', 'customer': 7, 'cost': 631}, {'facility': 'F6', 'customer': 8, 'cost': 180}, {'facility': 'F6', 'customer': 9, 'cost': 182}, {'facility': 'F6', 'customer': 10, 'cost': 775}, {'facility': 'F6', 'customer': 11, 'cost': 499}, {'facility': 'F6', 'customer': 12, 'cost': 585}, {'facility': 'F6', 'customer': 13, 'cost': 536}], 'objective': 6869.0}","{'selected': ['F1', 'F2'], 'assignments': ['F1', 'F1', 'F1', 'F2', 'F1', 'F1', 'F1', 'F1', 'F2', 'F2', 'F2', 'F2', 'F1', 'F1']}",43,csv,0
UFLP,UFLP,"I’m lining up which library-style book branches the district should actually open and then signing each neighborhood school up with one of those open branches. The idea is simple: every branch costs money to start, and each school has a delivery or pickup cost to be served from a particular branch, so the total bill is the sum of the branch opening fees plus all the delivery/pickup charges. The job is to pick which branches to open and make sure every school is assigned to exactly one open branch (no school left unassigned and no school registered to two branches), while keeping that total bill as small as possible. The concrete entries—branch options, opening fees, and school delivery costs—are listed below.
There are 6 branchs and 14 schools in this instance.
**Branchs**
| branch_id | branch_opening_fee |
|---|---|
| F1 | 1000 |
| F2 | 1000 |
| F3 | 1000 |
| F4 | 1000 |
| F5 | 1000 |
| F6 | 1000 |
**Schools**
| school_id |
|---|
| A |
| B |
| C |
| D |
| E |
| F |
| G |
| H |
| I |
| J |
| K |
| L |
| M |
| N |
**Delivery Cost**
| branch_id | school_id | delivery_cost |
|---|---|---|
| F1 | A | 292 |
| F1 | B | 880 |
| F1 | C | 546 |
| F1 | D | 62 |
| F1 | E | 429 |
| F1 | F | 692 |
| F1 | G | 596 |
| F1 | H | 126 |
| F1 | I | 424 |
| F1 | J | 254 |
| F1 | K | 378 |
| F1 | L | 152 |
| F1 | M | 732 |
| F1 | N | 848 |
| F2 | A | 449 |
| F2 | B | 869 |
| F2 | C | 355 |
| F2 | D | 12 |
| F2 | E | 579 |
| F2 | F | 786 |
| F2 | G | 404 |
| F2 | H | 710 |
| F2 | I | 262 |
| F2 | J | 383 |
| F2 | K | 308 |
| F2 | L | 404 |
| F2 | M | 583 |
| F2 | N | 354 |
| F3 | A | 79 |
| F3 | B | 996 |
| F3 | C | 217 |
| F3 | D | 52 |
| F3 | E | 905 |
| F3 | F | 608 |
| F3 | G | 729 |
| F3 | H | 396 |
| F3 | I | 144 |
| F3 | J | 408 |
| F3 | K | 838 |
| F3 | L | 927 |
| F3 | M | 85 |
| F3 | N | 148 |
| F4 | A | 729 |
| F4 | B | 486 |
| F4 | C | 535 |
| F4 | D | 913 |
| F4 | E | 4 |
| F4 | F | 120 |
| F4 | G | 63 |
| F4 | H | 64 |
| F4 | I | 203 |
| F4 | J | 299 |
| F4 | K | 839 |
| F4 | L | 27 |
| F4 | M | 293 |
| F4 | N | 799 |
| F5 | A | 966 |
| F5 | B | 422 |
| F5 | C | 404 |
| F5 | D | 868 |
| F5 | E | 899 |
| F5 | F | 744 |
| F5 | G | 527 |
| F5 | H | 250 |
| F5 | I | 913 |
| F5 | J | 978 |
| F5 | K | 498 |
| F5 | L | 453 |
| F5 | M | 60 |
| F5 | N | 338 |
| F6 | A | 115 |
| F6 | B | 887 |
| F6 | C | 294 |
| F6 | D | 513 |
| F6 | E | 969 |
| F6 | F | 322 |
| F6 | G | 681 |
| F6 | H | 542 |
| F6 | I | 711 |
| F6 | J | 843 |
| F6 | K | 874 |
| F6 | L | 718 |
| F6 | M | 704 |
| F6 | N | 966 |
Also, when you send the solution back, just stick to this little JSON shape so it’s easy to read and parse:
{
""solution"": {
""selected"": [<branch_to_open>, <branch_to_open>, ...],
""assignments"": [<chosen_open_branch>, <chosen_open_branch>, ...]
}
}
This is just a sketch of the shape I’m expecting — nothing filled in yet. ""selected"" is the list of branches the district will open, and ""assignments"" is a list (in the same order as the schools were given in the instance) saying which opened branch each school signs up with.
Please note: all identifiers in your actual answer must match the instance input exactly — don’t rename them and don’t invent new labels. For example: Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'opening_costs': [1000, 1000, 1000, 1000, 1000, 1000], 'connection_costs': [[292, 880, 546, 62, 429, 692, 596, 126, 424, 254, 378, 152, 732, 848], [449, 869, 355, 12, 579, 786, 404, 710, 262, 383, 308, 404, 583, 354], [79, 996, 217, 52, 905, 608, 729, 396, 144, 408, 838, 927, 85, 148], [729, 486, 535, 913, 4, 120, 63, 64, 203, 299, 839, 27, 293, 799], [966, 422, 404, 868, 899, 744, 527, 250, 913, 978, 498, 453, 60, 338], [115, 887, 294, 513, 969, 322, 681, 542, 711, 843, 874, 718, 704, 966]], 'objective': 4626.0}","{'open_facilities': [2, 3], 'assignments': [2, 3, 2, 2, 3, 3, 3, 3, 2, 3, 2, 3, 2, 2]}",4626.0,"{'problem_type': 'UFLP', 'num_facilities': 6, 'num_customers': 14, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}, {'id': 'F4', 'opening_cost': 1000}, {'id': 'F5', 'opening_cost': 1000}, {'id': 'F6', 'opening_cost': 1000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}, {'id': 'L'}, {'id': 'M'}, {'id': 'N'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 292}, {'facility': 'F1', 'customer': 'B', 'cost': 880}, {'facility': 'F1', 'customer': 'C', 'cost': 546}, {'facility': 'F1', 'customer': 'D', 'cost': 62}, {'facility': 'F1', 'customer': 'E', 'cost': 429}, {'facility': 'F1', 'customer': 'F', 'cost': 692}, {'facility': 'F1', 'customer': 'G', 'cost': 596}, {'facility': 'F1', 'customer': 'H', 'cost': 126}, {'facility': 'F1', 'customer': 'I', 'cost': 424}, {'facility': 'F1', 'customer': 'J', 'cost': 254}, {'facility': 'F1', 'customer': 'K', 'cost': 378}, {'facility': 'F1', 'customer': 'L', 'cost': 152}, {'facility': 'F1', 'customer': 'M', 'cost': 732}, {'facility': 'F1', 'customer': 'N', 'cost': 848}, {'facility': 'F2', 'customer': 'A', 'cost': 449}, {'facility': 'F2', 'customer': 'B', 'cost': 869}, {'facility': 'F2', 'customer': 'C', 'cost': 355}, {'facility': 'F2', 'customer': 'D', 'cost': 12}, {'facility': 'F2', 'customer': 'E', 'cost': 579}, {'facility': 'F2', 'customer': 'F', 'cost': 786}, {'facility': 'F2', 'customer': 'G', 'cost': 404}, {'facility': 'F2', 'customer': 'H', 'cost': 710}, {'facility': 'F2', 'customer': 'I', 'cost': 262}, {'facility': 'F2', 'customer': 'J', 'cost': 383}, {'facility': 'F2', 'customer': 'K', 'cost': 308}, {'facility': 'F2', 'customer': 'L', 'cost': 404}, {'facility': 'F2', 'customer': 'M', 'cost': 583}, {'facility': 'F2', 'customer': 'N', 'cost': 354}, {'facility': 'F3', 'customer': 'A', 'cost': 79}, {'facility': 'F3', 'customer': 'B', 'cost': 996}, {'facility': 'F3', 'customer': 'C', 'cost': 217}, {'facility': 'F3', 'customer': 'D', 'cost': 52}, {'facility': 'F3', 'customer': 'E', 'cost': 905}, {'facility': 'F3', 'customer': 'F', 'cost': 608}, {'facility': 'F3', 'customer': 'G', 'cost': 729}, {'facility': 'F3', 'customer': 'H', 'cost': 396}, {'facility': 'F3', 'customer': 'I', 'cost': 144}, {'facility': 'F3', 'customer': 'J', 'cost': 408}, {'facility': 'F3', 'customer': 'K', 'cost': 838}, {'facility': 'F3', 'customer': 'L', 'cost': 927}, {'facility': 'F3', 'customer': 'M', 'cost': 85}, {'facility': 'F3', 'customer': 'N', 'cost': 148}, {'facility': 'F4', 'customer': 'A', 'cost': 729}, {'facility': 'F4', 'customer': 'B', 'cost': 486}, {'facility': 'F4', 'customer': 'C', 'cost': 535}, {'facility': 'F4', 'customer': 'D', 'cost': 913}, {'facility': 'F4', 'customer': 'E', 'cost': 4}, {'facility': 'F4', 'customer': 'F', 'cost': 120}, {'facility': 'F4', 'customer': 'G', 'cost': 63}, {'facility': 'F4', 'customer': 'H', 'cost': 64}, {'facility': 'F4', 'customer': 'I', 'cost': 203}, {'facility': 'F4', 'customer': 'J', 'cost': 299}, {'facility': 'F4', 'customer': 'K', 'cost': 839}, {'facility': 'F4', 'customer': 'L', 'cost': 27}, {'facility': 'F4', 'customer': 'M', 'cost': 293}, {'facility': 'F4', 'customer': 'N', 'cost': 799}, {'facility': 'F5', 'customer': 'A', 'cost': 966}, {'facility': 'F5', 'customer': 'B', 'cost': 422}, {'facility': 'F5', 'customer': 'C', 'cost': 404}, {'facility': 'F5', 'customer': 'D', 'cost': 868}, {'facility': 'F5', 'customer': 'E', 'cost': 899}, {'facility': 'F5', 'customer': 'F', 'cost': 744}, {'facility': 'F5', 'customer': 'G', 'cost': 527}, {'facility': 'F5', 'customer': 'H', 'cost': 250}, {'facility': 'F5', 'customer': 'I', 'cost': 913}, {'facility': 'F5', 'customer': 'J', 'cost': 978}, {'facility': 'F5', 'customer': 'K', 'cost': 498}, {'facility': 'F5', 'customer': 'L', 'cost': 453}, {'facility': 'F5', 'customer': 'M', 'cost': 60}, {'facility': 'F5', 'customer': 'N', 'cost': 338}, {'facility': 'F6', 'customer': 'A', 'cost': 115}, {'facility': 'F6', 'customer': 'B', 'cost': 887}, {'facility': 'F6', 'customer': 'C', 'cost': 294}, {'facility': 'F6', 'customer': 'D', 'cost': 513}, {'facility': 'F6', 'customer': 'E', 'cost': 969}, {'facility': 'F6', 'customer': 'F', 'cost': 322}, {'facility': 'F6', 'customer': 'G', 'cost': 681}, {'facility': 'F6', 'customer': 'H', 'cost': 542}, {'facility': 'F6', 'customer': 'I', 'cost': 711}, {'facility': 'F6', 'customer': 'J', 'cost': 843}, {'facility': 'F6', 'customer': 'K', 'cost': 874}, {'facility': 'F6', 'customer': 'L', 'cost': 718}, {'facility': 'F6', 'customer': 'M', 'cost': 704}, {'facility': 'F6', 'customer': 'N', 'cost': 966}], 'objective': 4626.0}","{'selected': ['F3', 'F4'], 'assignments': ['F3', 'F4', 'F3', 'F3', 'F4', 'F4', 'F4', 'F4', 'F3', 'F4', 'F3', 'F4', 'F3', 'F3']}",44,markdown_table,names
UFLP,UFLP,"Recently the food bank had to tighten the budget, so the director needed to decide which distribution points to keep open. Each candidate point has a running fee, and getting food to a community group from a point costs volunteer time or transport money. The task is to pick the set of points to operate and assign each group to exactly one of those points so that the total expense — the sum of the operating fees plus every group’s delivery cost — is as small as possible; every group must be assigned once and sites can serve any number of groups. The detailed list of sites, their operating costs, and group-by-group delivery costs is shown below.
There are 5 distribution points and 11 community groups in this instance.
**Distribution Points**
| distribution_point_id | running_fee |
|---|---|
| F1 | 1940 |
| F2 | 1747 |
| F3 | 1358 |
| F4 | 1881 |
| F5 | 1043 |
**Community Groups**
| community_group_id |
|---|
| 0 |
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| 7 |
| 8 |
| 9 |
| 10 |
**Delivery Cost**
| distribution_point_id | community_group_id | delivery_cost |
|---|---|---|
| F1 | 0 | 280 |
| F1 | 1 | 691 |
| F1 | 2 | 718 |
| F1 | 3 | 459 |
| F1 | 4 | 572 |
| F1 | 5 | 483 |
| F1 | 6 | 164 |
| F1 | 7 | 609 |
| F1 | 8 | 232 |
| F1 | 9 | 779 |
| F1 | 10 | 651 |
| F2 | 0 | 909 |
| F2 | 1 | 972 |
| F2 | 2 | 973 |
| F2 | 3 | 960 |
| F2 | 4 | 209 |
| F2 | 5 | 362 |
| F2 | 6 | 849 |
| F2 | 7 | 835 |
| F2 | 8 | 989 |
| F2 | 9 | 180 |
| F2 | 10 | 531 |
| F3 | 0 | 449 |
| F3 | 1 | 527 |
| F3 | 2 | 584 |
| F3 | 3 | 319 |
| F3 | 4 | 193 |
| F3 | 5 | 897 |
| F3 | 6 | 966 |
| F3 | 7 | 72 |
| F3 | 8 | 473 |
| F3 | 9 | 767 |
| F3 | 10 | 479 |
| F4 | 0 | 927 |
| F4 | 1 | 691 |
| F4 | 2 | 381 |
| F4 | 3 | 967 |
| F4 | 4 | 140 |
| F4 | 5 | 750 |
| F4 | 6 | 589 |
| F4 | 7 | 648 |
| F4 | 8 | 403 |
| F4 | 9 | 226 |
| F4 | 10 | 994 |
| F5 | 0 | 246 |
| F5 | 1 | 69 |
| F5 | 2 | 954 |
| F5 | 3 | 55 |
| F5 | 4 | 981 |
| F5 | 5 | 439 |
| F5 | 6 | 815 |
| F5 | 7 | 116 |
| F5 | 8 | 263 |
| F5 | 9 | 792 |
| F5 | 10 | 681 |
Oh, and when you send the decision back, please follow this little JSON layout so it's easy to read and process. For our story it might look like this:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<site_assigned>, <site_assigned>, ...]
}
}
""selected"" is where you list the site IDs you'll keep operating (those are the sites we pay the running fee for). ""assignments"" gives, in the same order as the community groups appear in the instance, which open site each group is assigned to. Think of it as a simple form — a list of open sites and then a list that points each group to one of those sites.
This JSON is just the sketch of the shape I expect, not the actual solution.
Please make sure to use the exact identifiers from the instance input — do not rename them or create new labels.
- for example: ""Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".""","{'opening_costs': [1940, 1747, 1358, 1881, 1043], 'connection_costs': [[280, 691, 718, 459, 572, 483, 164, 609, 232, 779, 651], [909, 972, 973, 960, 209, 362, 849, 835, 989, 180, 531], [449, 527, 584, 319, 193, 897, 966, 72, 473, 767, 479], [927, 691, 381, 967, 140, 750, 589, 648, 403, 226, 994], [246, 69, 954, 55, 981, 439, 815, 116, 263, 792, 681]], 'objective': 6129.0}","{'open_facilities': [3, 4], 'assignments': [4, 4, 3, 4, 3, 4, 3, 4, 4, 3, 4]}",6129.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 1940}, {'id': 'F2', 'opening_cost': 1747}, {'id': 'F3', 'opening_cost': 1358}, {'id': 'F4', 'opening_cost': 1881}, {'id': 'F5', 'opening_cost': 1043}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 280}, {'facility': 'F1', 'customer': 1, 'cost': 691}, {'facility': 'F1', 'customer': 2, 'cost': 718}, {'facility': 'F1', 'customer': 3, 'cost': 459}, {'facility': 'F1', 'customer': 4, 'cost': 572}, {'facility': 'F1', 'customer': 5, 'cost': 483}, {'facility': 'F1', 'customer': 6, 'cost': 164}, {'facility': 'F1', 'customer': 7, 'cost': 609}, {'facility': 'F1', 'customer': 8, 'cost': 232}, {'facility': 'F1', 'customer': 9, 'cost': 779}, {'facility': 'F1', 'customer': 10, 'cost': 651}, {'facility': 'F2', 'customer': 0, 'cost': 909}, {'facility': 'F2', 'customer': 1, 'cost': 972}, {'facility': 'F2', 'customer': 2, 'cost': 973}, {'facility': 'F2', 'customer': 3, 'cost': 960}, {'facility': 'F2', 'customer': 4, 'cost': 209}, {'facility': 'F2', 'customer': 5, 'cost': 362}, {'facility': 'F2', 'customer': 6, 'cost': 849}, {'facility': 'F2', 'customer': 7, 'cost': 835}, {'facility': 'F2', 'customer': 8, 'cost': 989}, {'facility': 'F2', 'customer': 9, 'cost': 180}, {'facility': 'F2', 'customer': 10, 'cost': 531}, {'facility': 'F3', 'customer': 0, 'cost': 449}, {'facility': 'F3', 'customer': 1, 'cost': 527}, {'facility': 'F3', 'customer': 2, 'cost': 584}, {'facility': 'F3', 'customer': 3, 'cost': 319}, {'facility': 'F3', 'customer': 4, 'cost': 193}, {'facility': 'F3', 'customer': 5, 'cost': 897}, {'facility': 'F3', 'customer': 6, 'cost': 966}, {'facility': 'F3', 'customer': 7, 'cost': 72}, {'facility': 'F3', 'customer': 8, 'cost': 473}, {'facility': 'F3', 'customer': 9, 'cost': 767}, {'facility': 'F3', 'customer': 10, 'cost': 479}, {'facility': 'F4', 'customer': 0, 'cost': 927}, {'facility': 'F4', 'customer': 1, 'cost': 691}, {'facility': 'F4', 'customer': 2, 'cost': 381}, {'facility': 'F4', 'customer': 3, 'cost': 967}, {'facility': 'F4', 'customer': 4, 'cost': 140}, {'facility': 'F4', 'customer': 5, 'cost': 750}, {'facility': 'F4', 'customer': 6, 'cost': 589}, {'facility': 'F4', 'customer': 7, 'cost': 648}, {'facility': 'F4', 'customer': 8, 'cost': 403}, {'facility': 'F4', 'customer': 9, 'cost': 226}, {'facility': 'F4', 'customer': 10, 'cost': 994}, {'facility': 'F5', 'customer': 0, 'cost': 246}, {'facility': 'F5', 'customer': 1, 'cost': 69}, {'facility': 'F5', 'customer': 2, 'cost': 954}, {'facility': 'F5', 'customer': 3, 'cost': 55}, {'facility': 'F5', 'customer': 4, 'cost': 981}, {'facility': 'F5', 'customer': 5, 'cost': 439}, {'facility': 'F5', 'customer': 6, 'cost': 815}, {'facility': 'F5', 'customer': 7, 'cost': 116}, {'facility': 'F5', 'customer': 8, 'cost': 263}, {'facility': 'F5', 'customer': 9, 'cost': 792}, {'facility': 'F5', 'customer': 10, 'cost': 681}], 'objective': 6129.0}","{'selected': ['F4', 'F5'], 'assignments': ['F5', 'F5', 'F4', 'F5', 'F4', 'F5', 'F4', 'F5', 'F5', 'F4', 'F5']}",45,markdown_table,0
UFLP,UFLP,"Many neighborhoods are waiting for pop-up clinic visits, so the coordinator has to decide which health posts to staff and which staffed post each residential cluster will use. The rule is straightforward: each cluster must go to exactly one staffed post (not zero, not two), and any staffed post can take unlimited clusters. The aim is to keep overall expenses as low as possible by adding up the staffing costs for the posts that are opened and the travel cost for all patients to reach their assigned post — lower total is better. The concrete details and numbers are provided below.
There are 4 posts and 9 clusters in this instance.
**Posts**
| post_id | staffing_cost |
|---|---|
| F1 | 2000 |
| F2 | 2000 |
| F3 | 2000 |
| F4 | 2000 |
**Clusters**
| cluster_id |
|---|
| A |
| B |
| C |
| D |
| E |
| F |
| G |
| H |
| I |
**Travel Cost**
| post_id | cluster_id | travel_cost |
|---|---|---|
| F1 | A | 69 |
| F1 | B | 961 |
| F1 | C | 185 |
| F1 | D | 624 |
| F1 | E | 117 |
| F1 | F | 927 |
| F1 | G | 947 |
| F1 | H | 39 |
| F1 | I | 449 |
| F2 | A | 702 |
| F2 | B | 345 |
| F2 | C | 968 |
| F2 | D | 960 |
| F2 | E | 0 |
| F2 | F | 754 |
| F2 | G | 194 |
| F2 | H | 811 |
| F2 | I | 839 |
| F3 | A | 890 |
| F3 | B | 607 |
| F3 | C | 741 |
| F3 | D | 817 |
| F3 | E | 151 |
| F3 | F | 104 |
| F3 | G | 74 |
| F3 | H | 532 |
| F3 | I | 625 |
| F4 | A | 374 |
| F4 | B | 281 |
| F4 | C | 3 |
| F4 | D | 696 |
| F4 | E | 436 |
| F4 | F | 217 |
| F4 | G | 245 |
| F4 | H | 265 |
| F4 | I | 152 |
Oh, and when you send the actual plan back, please stick to this JSON layout so it's easy to parse:
{
""solution"": {
""selected"": [<post_to_staff>, <post_to_staff>, ...],
""assignments"": [<chosen_staffed_post>, <chosen_staffed_post>, ...]
}
}
Think of ""selected"" as the list of posts you'll staff, and ""assignments"" as which staffed post each residential cluster will use (one entry per cluster, in the same order as the instance's cluster list). This JSON is just a sketch of the shape I expect, not the final answer.
Please also be sure to use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".","{'opening_costs': [2000, 2000, 2000, 2000], 'connection_costs': [[69, 961, 185, 624, 117, 927, 947, 39, 449], [702, 345, 968, 960, 0, 754, 194, 811, 839], [890, 607, 741, 817, 151, 104, 74, 532, 625], [374, 281, 3, 696, 436, 217, 245, 265, 152]], 'objective': 4669.0}","{'open_facilities': [3], 'assignments': [3, 3, 3, 3, 3, 3, 3, 3, 3]}",4669.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 9, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 69}, {'facility': 'F1', 'customer': 'B', 'cost': 961}, {'facility': 'F1', 'customer': 'C', 'cost': 185}, {'facility': 'F1', 'customer': 'D', 'cost': 624}, {'facility': 'F1', 'customer': 'E', 'cost': 117}, {'facility': 'F1', 'customer': 'F', 'cost': 927}, {'facility': 'F1', 'customer': 'G', 'cost': 947}, {'facility': 'F1', 'customer': 'H', 'cost': 39}, {'facility': 'F1', 'customer': 'I', 'cost': 449}, {'facility': 'F2', 'customer': 'A', 'cost': 702}, {'facility': 'F2', 'customer': 'B', 'cost': 345}, {'facility': 'F2', 'customer': 'C', 'cost': 968}, {'facility': 'F2', 'customer': 'D', 'cost': 960}, {'facility': 'F2', 'customer': 'E', 'cost': 0}, {'facility': 'F2', 'customer': 'F', 'cost': 754}, {'facility': 'F2', 'customer': 'G', 'cost': 194}, {'facility': 'F2', 'customer': 'H', 'cost': 811}, {'facility': 'F2', 'customer': 'I', 'cost': 839}, {'facility': 'F3', 'customer': 'A', 'cost': 890}, {'facility': 'F3', 'customer': 'B', 'cost': 607}, {'facility': 'F3', 'customer': 'C', 'cost': 741}, {'facility': 'F3', 'customer': 'D', 'cost': 817}, {'facility': 'F3', 'customer': 'E', 'cost': 151}, {'facility': 'F3', 'customer': 'F', 'cost': 104}, {'facility': 'F3', 'customer': 'G', 'cost': 74}, {'facility': 'F3', 'customer': 'H', 'cost': 532}, {'facility': 'F3', 'customer': 'I', 'cost': 625}, {'facility': 'F4', 'customer': 'A', 'cost': 374}, {'facility': 'F4', 'customer': 'B', 'cost': 281}, {'facility': 'F4', 'customer': 'C', 'cost': 3}, {'facility': 'F4', 'customer': 'D', 'cost': 696}, {'facility': 'F4', 'customer': 'E', 'cost': 436}, {'facility': 'F4', 'customer': 'F', 'cost': 217}, {'facility': 'F4', 'customer': 'G', 'cost': 245}, {'facility': 'F4', 'customer': 'H', 'cost': 265}, {'facility': 'F4', 'customer': 'I', 'cost': 152}], 'objective': 4669.0}","{'selected': ['F4'], 'assignments': ['F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4']}",46,markdown_table,names
UFLP,UFLP,"There’s a practical problem at the co-op: some central pickup sites could stay active while others could be shut down, and each decision affects how far farmers have to travel. The task is to pick a set of sites to keep running (each incurs its own upkeep cost) and then attach each farm to one of those running sites. The measure of a good plan is the total spending — the sum of the maintenance bills for the active sites plus all farmers’ delivery costs to their chosen site — and that total should be as small as possible. Each farm must be tied to exactly one active site, no exceptions or duplicates. The concrete setup and numbers follow below.
# num_pickup_sites=5
# num_farms=10
# SITES
site_id,site_upkeep_cost
F1,2000
F2,2000
F3,2000
F4,2000
F5,2000
# FARMS
farm_id
A
B
C
D
E
F
G
H
I
J
# DELIVERYS
site_id,farm_id,delivery_cost
F1,A,134
F1,B,688
F1,C,43
F1,D,940
F1,E,348
F1,F,766
F1,G,427
F1,H,82
F1,I,472
F1,J,127
F2,A,873
F2,B,441
F2,C,168
F2,D,323
F2,E,702
F2,F,625
F2,G,397
F2,H,899
F2,I,28
F2,J,78
F3,A,427
F3,B,431
F3,C,85
F3,D,370
F3,E,83
F3,F,16
F3,G,706
F3,H,669
F3,I,692
F3,J,846
F4,A,394
F4,B,373
F4,C,45
F4,D,920
F4,E,662
F4,F,819
F4,G,957
F4,H,440
F4,I,819
F4,J,287
F5,A,498
F5,B,308
F5,C,940
F5,D,946
F5,E,558
F5,F,165
F5,G,35
F5,H,618
F5,I,410
F5,J,697
Also, to keep things simple, please give the final plan in a tiny JSON sketch like this:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
Here ""selected"" is the list of sites you choose to keep running, and ""assignments"" lists, for each farm, the site it's assigned to (use the same order the instance uses for farms). Think of it like filling out a form: first pick which sites stay active, then say which active site each farm goes to.
This is just the expected shape — a sketch to show the layout, not the filled-in answer.
Please make sure to use the exact identifiers from the instance input with no renaming or invented labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000, 2000], 'connection_costs': [[134, 688, 43, 940, 348, 766, 427, 82, 472, 127], [873, 441, 168, 323, 702, 625, 397, 899, 28, 78], [427, 431, 85, 370, 83, 16, 706, 669, 692, 846], [394, 373, 45, 920, 662, 819, 957, 440, 819, 287], [498, 308, 940, 946, 558, 165, 35, 618, 410, 697]], 'objective': 6027.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}",6027.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 10, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 134}, {'facility': 'F1', 'customer': 'B', 'cost': 688}, {'facility': 'F1', 'customer': 'C', 'cost': 43}, {'facility': 'F1', 'customer': 'D', 'cost': 940}, {'facility': 'F1', 'customer': 'E', 'cost': 348}, {'facility': 'F1', 'customer': 'F', 'cost': 766}, {'facility': 'F1', 'customer': 'G', 'cost': 427}, {'facility': 'F1', 'customer': 'H', 'cost': 82}, {'facility': 'F1', 'customer': 'I', 'cost': 472}, {'facility': 'F1', 'customer': 'J', 'cost': 127}, {'facility': 'F2', 'customer': 'A', 'cost': 873}, {'facility': 'F2', 'customer': 'B', 'cost': 441}, {'facility': 'F2', 'customer': 'C', 'cost': 168}, {'facility': 'F2', 'customer': 'D', 'cost': 323}, {'facility': 'F2', 'customer': 'E', 'cost': 702}, {'facility': 'F2', 'customer': 'F', 'cost': 625}, {'facility': 'F2', 'customer': 'G', 'cost': 397}, {'facility': 'F2', 'customer': 'H', 'cost': 899}, {'facility': 'F2', 'customer': 'I', 'cost': 28}, {'facility': 'F2', 'customer': 'J', 'cost': 78}, {'facility': 'F3', 'customer': 'A', 'cost': 427}, {'facility': 'F3', 'customer': 'B', 'cost': 431}, {'facility': 'F3', 'customer': 'C', 'cost': 85}, {'facility': 'F3', 'customer': 'D', 'cost': 370}, {'facility': 'F3', 'customer': 'E', 'cost': 83}, {'facility': 'F3', 'customer': 'F', 'cost': 16}, {'facility': 'F3', 'customer': 'G', 'cost': 706}, {'facility': 'F3', 'customer': 'H', 'cost': 669}, {'facility': 'F3', 'customer': 'I', 'cost': 692}, {'facility': 'F3', 'customer': 'J', 'cost': 846}, {'facility': 'F4', 'customer': 'A', 'cost': 394}, {'facility': 'F4', 'customer': 'B', 'cost': 373}, {'facility': 'F4', 'customer': 'C', 'cost': 45}, {'facility': 'F4', 'customer': 'D', 'cost': 920}, {'facility': 'F4', 'customer': 'E', 'cost': 662}, {'facility': 'F4', 'customer': 'F', 'cost': 819}, {'facility': 'F4', 'customer': 'G', 'cost': 957}, {'facility': 'F4', 'customer': 'H', 'cost': 440}, {'facility': 'F4', 'customer': 'I', 'cost': 819}, {'facility': 'F4', 'customer': 'J', 'cost': 287}, {'facility': 'F5', 'customer': 'A', 'cost': 498}, {'facility': 'F5', 'customer': 'B', 'cost': 308}, {'facility': 'F5', 'customer': 'C', 'cost': 940}, {'facility': 'F5', 'customer': 'D', 'cost': 946}, {'facility': 'F5', 'customer': 'E', 'cost': 558}, {'facility': 'F5', 'customer': 'F', 'cost': 165}, {'facility': 'F5', 'customer': 'G', 'cost': 35}, {'facility': 'F5', 'customer': 'H', 'cost': 618}, {'facility': 'F5', 'customer': 'I', 'cost': 410}, {'facility': 'F5', 'customer': 'J', 'cost': 697}], 'objective': 6027.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",47,csv,names
UFLP,UFLP,"There’s a fleet logistics puzzle: the company needs to decide which charging sites to enable and then send each parking zone’s vehicles to a single enabled site. Enabling a site isn’t free, and drivers spend time and fuel getting cars from their zones to the assigned site, so the total expense is the sum of the enabling fees plus all those repositioning costs — the aim is to keep that combined expense as low as possible. Each zone needs one and only one destination hub, and a hub can accept unlimited zones. The concrete instance details are listed below.
# num_candidate_hubs=5
# num_parking_zones=11
# HUBS
hub_id,enabling_fee
F1,6567
F2,2396
F3,7987
F4,6976
F5,9616
# ZONES
zone_id
0
1
2
3
4
5
6
7
8
9
10
# REPOSITIONINGS
hub_id,zone_id,repositioning_cost
F1,0,179
F1,1,458
F1,2,253
F1,3,660
F1,4,965
F1,5,878
F1,6,932
F1,7,190
F1,8,48
F1,9,234
F1,10,995
F2,0,886
F2,1,599
F2,2,78
F2,3,354
F2,4,664
F2,5,839
F2,6,500
F2,7,782
F2,8,451
F2,9,784
F2,10,743
F3,0,160
F3,1,339
F3,2,90
F3,3,206
F3,4,795
F3,5,628
F3,6,975
F3,7,686
F3,8,915
F3,9,803
F3,10,614
F4,0,960
F4,1,680
F4,2,41
F4,3,678
F4,4,226
F4,5,969
F4,6,2
F4,7,112
F4,8,794
F4,9,855
F4,10,408
F5,0,375
F5,1,890
F5,2,317
F5,3,413
F5,4,692
F5,5,914
F5,6,370
F5,7,149
F5,8,139
F5,9,670
F5,10,247
Oh, and when you send the answer back, just follow this simple JSON shape so I can read it easily:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<assigned_site>, <assigned_site>, ...]
}
}
This only sketches the format I'm expecting: ""selected"" is where you list the sites you decide to enable, and ""assignments"" is a list (one entry per parking zone, in the same order as the instance) saying which enabled site that zone uses. Pretty informal — think of it like filling out a short form, not a full report.
Please use the exact identifiers from the instance input when you fill those placeholders — do not rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [6567, 2396, 7987, 6976, 9616], 'connection_costs': [[179, 458, 253, 660, 965, 878, 932, 190, 48, 234, 995], [886, 599, 78, 354, 664, 839, 500, 782, 451, 784, 743], [160, 339, 90, 206, 795, 628, 975, 686, 915, 803, 614], [960, 680, 41, 678, 226, 969, 2, 112, 794, 855, 408], [375, 890, 317, 413, 692, 914, 370, 149, 139, 670, 247]], 'objective': 9076.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}",9076.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 11, 'facilities': [{'id': 'F1', 'opening_cost': 6567}, {'id': 'F2', 'opening_cost': 2396}, {'id': 'F3', 'opening_cost': 7987}, {'id': 'F4', 'opening_cost': 6976}, {'id': 'F5', 'opening_cost': 9616}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 179}, {'facility': 'F1', 'customer': 1, 'cost': 458}, {'facility': 'F1', 'customer': 2, 'cost': 253}, {'facility': 'F1', 'customer': 3, 'cost': 660}, {'facility': 'F1', 'customer': 4, 'cost': 965}, {'facility': 'F1', 'customer': 5, 'cost': 878}, {'facility': 'F1', 'customer': 6, 'cost': 932}, {'facility': 'F1', 'customer': 7, 'cost': 190}, {'facility': 'F1', 'customer': 8, 'cost': 48}, {'facility': 'F1', 'customer': 9, 'cost': 234}, {'facility': 'F1', 'customer': 10, 'cost': 995}, {'facility': 'F2', 'customer': 0, 'cost': 886}, {'facility': 'F2', 'customer': 1, 'cost': 599}, {'facility': 'F2', 'customer': 2, 'cost': 78}, {'facility': 'F2', 'customer': 3, 'cost': 354}, {'facility': 'F2', 'customer': 4, 'cost': 664}, {'facility': 'F2', 'customer': 5, 'cost': 839}, {'facility': 'F2', 'customer': 6, 'cost': 500}, {'facility': 'F2', 'customer': 7, 'cost': 782}, {'facility': 'F2', 'customer': 8, 'cost': 451}, {'facility': 'F2', 'customer': 9, 'cost': 784}, {'facility': 'F2', 'customer': 10, 'cost': 743}, {'facility': 'F3', 'customer': 0, 'cost': 160}, {'facility': 'F3', 'customer': 1, 'cost': 339}, {'facility': 'F3', 'customer': 2, 'cost': 90}, {'facility': 'F3', 'customer': 3, 'cost': 206}, {'facility': 'F3', 'customer': 4, 'cost': 795}, {'facility': 'F3', 'customer': 5, 'cost': 628}, {'facility': 'F3', 'customer': 6, 'cost': 975}, {'facility': 'F3', 'customer': 7, 'cost': 686}, {'facility': 'F3', 'customer': 8, 'cost': 915}, {'facility': 'F3', 'customer': 9, 'cost': 803}, {'facility': 'F3', 'customer': 10, 'cost': 614}, {'facility': 'F4', 'customer': 0, 'cost': 960}, {'facility': 'F4', 'customer': 1, 'cost': 680}, {'facility': 'F4', 'customer': 2, 'cost': 41}, {'facility': 'F4', 'customer': 3, 'cost': 678}, {'facility': 'F4', 'customer': 4, 'cost': 226}, {'facility': 'F4', 'customer': 5, 'cost': 969}, {'facility': 'F4', 'customer': 6, 'cost': 2}, {'facility': 'F4', 'customer': 7, 'cost': 112}, {'facility': 'F4', 'customer': 8, 'cost': 794}, {'facility': 'F4', 'customer': 9, 'cost': 855}, {'facility': 'F4', 'customer': 10, 'cost': 408}, {'facility': 'F5', 'customer': 0, 'cost': 375}, {'facility': 'F5', 'customer': 1, 'cost': 890}, {'facility': 'F5', 'customer': 2, 'cost': 317}, {'facility': 'F5', 'customer': 3, 'cost': 413}, {'facility': 'F5', 'customer': 4, 'cost': 692}, {'facility': 'F5', 'customer': 5, 'cost': 914}, {'facility': 'F5', 'customer': 6, 'cost': 370}, {'facility': 'F5', 'customer': 7, 'cost': 149}, {'facility': 'F5', 'customer': 8, 'cost': 139}, {'facility': 'F5', 'customer': 9, 'cost': 670}, {'facility': 'F5', 'customer': 10, 'cost': 247}], 'objective': 9076.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",48,csv,0
UFLP,UFLP,"In our town’s relief planning, the team will choose which clothing distribution centers to activate and then allocate each shelter to one of those active centers. It’s important that every shelter is assigned to exactly one open center — no shelter can be left out or be assigned to multiple centers. The goal is to minimize the total outlay: sum the opening costs of the centers that are opened and the transportation costs for all shelter assignments. The concrete numbers and locations are listed below.
{
""num_centers"": 5,
""num_shelters"": 12,
""centers"": [
{
""center_id"": ""F1"",
""center_opening_cost"": 2000
},
{
""center_id"": ""F2"",
""center_opening_cost"": 2000
},
{
""center_id"": ""F3"",
""center_opening_cost"": 2000
},
{
""center_id"": ""F4"",
""center_opening_cost"": 2000
},
{
""center_id"": ""F5"",
""center_opening_cost"": 2000
}
],
""shelters"": [
{
""shelter_id"": ""A""
},
{
""shelter_id"": ""B""
},
{
""shelter_id"": ""C""
},
{
""shelter_id"": ""D""
},
{
""shelter_id"": ""E""
},
{
""shelter_id"": ""F""
},
{
""shelter_id"": ""G""
},
{
""shelter_id"": ""H""
},
{
""shelter_id"": ""I""
},
{
""shelter_id"": ""J""
},
{
""shelter_id"": ""K""
},
{
""shelter_id"": ""L""
}
],
""transportations"": [
{
""center_id"": ""F1"",
""shelter_id"": ""A"",
""transportation_cost"": 203
},
{
""center_id"": ""F1"",
""shelter_id"": ""B"",
""transportation_cost"": 487
},
{
""center_id"": ""F1"",
""shelter_id"": ""C"",
""transportation_cost"": 312
},
{
""center_id"": ""F1"",
""shelter_id"": ""D"",
""transportation_cost"": 596
},
{
""center_id"": ""F1"",
""shelter_id"": ""E"",
""transportation_cost"": 559
},
{
""center_id"": ""F1"",
""shelter_id"": ""F"",
""transportation_cost"": 730
},
{
""center_id"": ""F1"",
""shelter_id"": ""G"",
""transportation_cost"": 990
},
{
""center_id"": ""F1"",
""shelter_id"": ""H"",
""transportation_cost"": 810
},
{
""center_id"": ""F1"",
""shelter_id"": ""I"",
""transportation_cost"": 188
},
{
""center_id"": ""F1"",
""shelter_id"": ""J"",
""transportation_cost"": 216
},
{
""center_id"": ""F1"",
""shelter_id"": ""K"",
""transportation_cost"": 895
},
{
""center_id"": ""F1"",
""shelter_id"": ""L"",
""transportation_cost"": 334
},
{
""center_id"": ""F2"",
""shelter_id"": ""A"",
""transportation_cost"": 731
},
{
""center_id"": ""F2"",
""shelter_id"": ""B"",
""transportation_cost"": 439
},
{
""center_id"": ""F2"",
""shelter_id"": ""C"",
""transportation_cost"": 387
},
{
""center_id"": ""F2"",
""shelter_id"": ""D"",
""transportation_cost"": 669
},
{
""center_id"": ""F2"",
""shelter_id"": ""E"",
""transportation_cost"": 828
},
{
""center_id"": ""F2"",
""shelter_id"": ""F"",
""transportation_cost"": 449
},
{
""center_id"": ""F2"",
""shelter_id"": ""G"",
""transportation_cost"": 814
},
{
""center_id"": ""F2"",
""shelter_id"": ""H"",
""transportation_cost"": 765
},
{
""center_id"": ""F2"",
""shelter_id"": ""I"",
""transportation_cost"": 901
},
{
""center_id"": ""F2"",
""shelter_id"": ""J"",
""transportation_cost"": 633
},
{
""center_id"": ""F2"",
""shelter_id"": ""K"",
""transportation_cost"": 687
},
{
""center_id"": ""F2"",
""shelter_id"": ""L"",
""transportation_cost"": 15
},
{
""center_id"": ""F3"",
""shelter_id"": ""A"",
""transportation_cost"": 509
},
{
""center_id"": ""F3"",
""shelter_id"": ""B"",
""transportation_cost"": 891
},
{
""center_id"": ""F3"",
""shelter_id"": ""C"",
""transportation_cost"": 254
},
{
""center_id"": ""F3"",
""shelter_id"": ""D"",
""transportation_cost"": 149
},
{
""center_id"": ""F3"",
""shelter_id"": ""E"",
""transportation_cost"": 21
},
{
""center_id"": ""F3"",
""shelter_id"": ""F"",
""transportation_cost"": 160
},
{
""center_id"": ""F3"",
""shelter_id"": ""G"",
""transportation_cost"": 841
},
{
""center_id"": ""F3"",
""shelter_id"": ""H"",
""transportation_cost"": 924
},
{
""center_id"": ""F3"",
""shelter_id"": ""I"",
""transportation_cost"": 569
},
{
""center_id"": ""F3"",
""shelter_id"": ""J"",
""transportation_cost"": 77
},
{
""center_id"": ""F3"",
""shelter_id"": ""K"",
""transportation_cost"": 810
},
{
""center_id"": ""F3"",
""shelter_id"": ""L"",
""transportation_cost"": 513
},
{
""center_id"": ""F4"",
""shelter_id"": ""A"",
""transportation_cost"": 333
},
{
""center_id"": ""F4"",
""shelter_id"": ""B"",
""transportation_cost"": 257
},
{
""center_id"": ""F4"",
""shelter_id"": ""C"",
""transportation_cost"": 584
},
{
""center_id"": ""F4"",
""shelter_id"": ""D"",
""transportation_cost"": 544
},
{
""center_id"": ""F4"",
""shelter_id"": ""E"",
""transportation_cost"": 911
},
{
""center_id"": ""F4"",
""shelter_id"": ""F"",
""transportation_cost"": 83
},
{
""center_id"": ""F4"",
""shelter_id"": ""G"",
""transportation_cost"": 966
},
{
""center_id"": ""F4"",
""shelter_id"": ""H"",
""transportation_cost"": 951
},
{
""center_id"": ""F4"",
""shelter_id"": ""I"",
""transportation_cost"": 632
},
{
""center_id"": ""F4"",
""shelter_id"": ""J"",
""transportation_cost"": 881
},
{
""center_id"": ""F4"",
""shelter_id"": ""K"",
""transportation_cost"": 205
},
{
""center_id"": ""F4"",
""shelter_id"": ""L"",
""transportation_cost"": 463
},
{
""center_id"": ""F5"",
""shelter_id"": ""A"",
""transportation_cost"": 630
},
{
""center_id"": ""F5"",
""shelter_id"": ""B"",
""transportation_cost"": 562
},
{
""center_id"": ""F5"",
""shelter_id"": ""C"",
""transportation_cost"": 614
},
{
""center_id"": ""F5"",
""shelter_id"": ""D"",
""transportation_cost"": 767
},
{
""center_id"": ""F5"",
""shelter_id"": ""E"",
""transportation_cost"": 46
},
{
""center_id"": ""F5"",
""shelter_id"": ""F"",
""transportation_cost"": 734
},
{
""center_id"": ""F5"",
""shelter_id"": ""G"",
""transportation_cost"": 331
},
{
""center_id"": ""F5"",
""shelter_id"": ""H"",
""transportation_cost"": 580
},
{
""center_id"": ""F5"",
""shelter_id"": ""I"",
""transportation_cost"": 32
},
{
""center_id"": ""F5"",
""shelter_id"": ""J"",
""transportation_cost"": 833
},
{
""center_id"": ""F5"",
""shelter_id"": ""K"",
""transportation_cost"": 641
},
{
""center_id"": ""F5"",
""shelter_id"": ""L"",
""transportation_cost"": 516
}
]
}
Also, please send your answer using a simple JSON shape so it's easy to read and check. Here's the structure I expect:
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_open_site>, <chosen_open_site>, ...]
}
}
""selected"" is where you list which distribution centers you decide to activate. ""assignments"" is a list that, for each shelter in order, names the open center that shelter will use. Think of the JSON as a little form — a sketch of the expected shape, not the actual final choices.
One more thing: use the exact identifiers from the instance input — do not rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [2000, 2000, 2000, 2000, 2000], 'connection_costs': [[203, 487, 312, 596, 559, 730, 990, 810, 188, 216, 895, 334], [731, 439, 387, 669, 828, 449, 814, 765, 901, 633, 687, 15], [509, 891, 254, 149, 21, 160, 841, 924, 569, 77, 810, 513], [333, 257, 584, 544, 911, 83, 966, 951, 632, 881, 205, 463], [630, 562, 614, 767, 46, 734, 331, 580, 32, 833, 641, 516]], 'objective': 7718.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}",7718.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 12, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}, {'id': 'F4', 'opening_cost': 2000}, {'id': 'F5', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}, {'id': 'I'}, {'id': 'J'}, {'id': 'K'}, {'id': 'L'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 203}, {'facility': 'F1', 'customer': 'B', 'cost': 487}, {'facility': 'F1', 'customer': 'C', 'cost': 312}, {'facility': 'F1', 'customer': 'D', 'cost': 596}, {'facility': 'F1', 'customer': 'E', 'cost': 559}, {'facility': 'F1', 'customer': 'F', 'cost': 730}, {'facility': 'F1', 'customer': 'G', 'cost': 990}, {'facility': 'F1', 'customer': 'H', 'cost': 810}, {'facility': 'F1', 'customer': 'I', 'cost': 188}, {'facility': 'F1', 'customer': 'J', 'cost': 216}, {'facility': 'F1', 'customer': 'K', 'cost': 895}, {'facility': 'F1', 'customer': 'L', 'cost': 334}, {'facility': 'F2', 'customer': 'A', 'cost': 731}, {'facility': 'F2', 'customer': 'B', 'cost': 439}, {'facility': 'F2', 'customer': 'C', 'cost': 387}, {'facility': 'F2', 'customer': 'D', 'cost': 669}, {'facility': 'F2', 'customer': 'E', 'cost': 828}, {'facility': 'F2', 'customer': 'F', 'cost': 449}, {'facility': 'F2', 'customer': 'G', 'cost': 814}, {'facility': 'F2', 'customer': 'H', 'cost': 765}, {'facility': 'F2', 'customer': 'I', 'cost': 901}, {'facility': 'F2', 'customer': 'J', 'cost': 633}, {'facility': 'F2', 'customer': 'K', 'cost': 687}, {'facility': 'F2', 'customer': 'L', 'cost': 15}, {'facility': 'F3', 'customer': 'A', 'cost': 509}, {'facility': 'F3', 'customer': 'B', 'cost': 891}, {'facility': 'F3', 'customer': 'C', 'cost': 254}, {'facility': 'F3', 'customer': 'D', 'cost': 149}, {'facility': 'F3', 'customer': 'E', 'cost': 21}, {'facility': 'F3', 'customer': 'F', 'cost': 160}, {'facility': 'F3', 'customer': 'G', 'cost': 841}, {'facility': 'F3', 'customer': 'H', 'cost': 924}, {'facility': 'F3', 'customer': 'I', 'cost': 569}, {'facility': 'F3', 'customer': 'J', 'cost': 77}, {'facility': 'F3', 'customer': 'K', 'cost': 810}, {'facility': 'F3', 'customer': 'L', 'cost': 513}, {'facility': 'F4', 'customer': 'A', 'cost': 333}, {'facility': 'F4', 'customer': 'B', 'cost': 257}, {'facility': 'F4', 'customer': 'C', 'cost': 584}, {'facility': 'F4', 'customer': 'D', 'cost': 544}, {'facility': 'F4', 'customer': 'E', 'cost': 911}, {'facility': 'F4', 'customer': 'F', 'cost': 83}, {'facility': 'F4', 'customer': 'G', 'cost': 966}, {'facility': 'F4', 'customer': 'H', 'cost': 951}, {'facility': 'F4', 'customer': 'I', 'cost': 632}, {'facility': 'F4', 'customer': 'J', 'cost': 881}, {'facility': 'F4', 'customer': 'K', 'cost': 205}, {'facility': 'F4', 'customer': 'L', 'cost': 463}, {'facility': 'F5', 'customer': 'A', 'cost': 630}, {'facility': 'F5', 'customer': 'B', 'cost': 562}, {'facility': 'F5', 'customer': 'C', 'cost': 614}, {'facility': 'F5', 'customer': 'D', 'cost': 767}, {'facility': 'F5', 'customer': 'E', 'cost': 46}, {'facility': 'F5', 'customer': 'F', 'cost': 734}, {'facility': 'F5', 'customer': 'G', 'cost': 331}, {'facility': 'F5', 'customer': 'H', 'cost': 580}, {'facility': 'F5', 'customer': 'I', 'cost': 32}, {'facility': 'F5', 'customer': 'J', 'cost': 833}, {'facility': 'F5', 'customer': 'K', 'cost': 641}, {'facility': 'F5', 'customer': 'L', 'cost': 516}], 'objective': 7718.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",49,json,names
UFLP,UFLP,"I work with a city planner who's trying to figure out which public lockers to put around town and which neighborhood of commuters should use each installed locker. The idea is simple: every locker that gets installed costs money, and every commuter who has to detour to reach their assigned locker pays a little extra in time or distance. The planner needs to pick which lockers to install and then give each commuter catchment exactly one of those installed lockers to use — nothing left unassigned, and no catchment sent to more than one locker. In the end, the tally is the sum of the installation fees for the chosen lockers plus all the detour costs for commuters, and the plan that keeps that total as small as possible is the one they want. Concrete details about candidate locations, fees, and detour distances are shown below.
{
""num_lockers"": 5,
""num_catchments"": 10,
""lockers"": [
{
""locker_id"": ""F1"",
""installation_fee"": 1965
},
{
""locker_id"": ""F2"",
""installation_fee"": 1681
},
{
""locker_id"": ""F3"",
""installation_fee"": 1562
},
{
""locker_id"": ""F4"",
""installation_fee"": 1224
},
{
""locker_id"": ""F5"",
""installation_fee"": 1594
}
],
""catchments"": [
{
""catchment_id"": 1
},
{
""catchment_id"": 2
},
{
""catchment_id"": 3
},
{
""catchment_id"": 4
},
{
""catchment_id"": 5
},
{
""catchment_id"": 6
},
{
""catchment_id"": 7
},
{
""catchment_id"": 8
},
{
""catchment_id"": 9
},
{
""catchment_id"": 10
}
],
""detours"": [
{
""locker_id"": ""F1"",
""catchment_id"": 1,
""detour_cost"": 963
},
{
""locker_id"": ""F1"",
""catchment_id"": 2,
""detour_cost"": 371
},
{
""locker_id"": ""F1"",
""catchment_id"": 3,
""detour_cost"": 320
},
{
""locker_id"": ""F1"",
""catchment_id"": 4,
""detour_cost"": 547
},
{
""locker_id"": ""F1"",
""catchment_id"": 5,
""detour_cost"": 296
},
{
""locker_id"": ""F1"",
""catchment_id"": 6,
""detour_cost"": 41
},
{
""locker_id"": ""F1"",
""catchment_id"": 7,
""detour_cost"": 526
},
{
""locker_id"": ""F1"",
""catchment_id"": 8,
""detour_cost"": 134
},
{
""locker_id"": ""F1"",
""catchment_id"": 9,
""detour_cost"": 657
},
{
""locker_id"": ""F1"",
""catchment_id"": 10,
""detour_cost"": 810
},
{
""locker_id"": ""F2"",
""catchment_id"": 1,
""detour_cost"": 844
},
{
""locker_id"": ""F2"",
""catchment_id"": 2,
""detour_cost"": 100
},
{
""locker_id"": ""F2"",
""catchment_id"": 3,
""detour_cost"": 469
},
{
""locker_id"": ""F2"",
""catchment_id"": 4,
""detour_cost"": 792
},
{
""locker_id"": ""F2"",
""catchment_id"": 5,
""detour_cost"": 10
},
{
""locker_id"": ""F2"",
""catchment_id"": 6,
""detour_cost"": 354
},
{
""locker_id"": ""F2"",
""catchment_id"": 7,
""detour_cost"": 839
},
{
""locker_id"": ""F2"",
""catchment_id"": 8,
""detour_cost"": 814
},
{
""locker_id"": ""F2"",
""catchment_id"": 9,
""detour_cost"": 819
},
{
""locker_id"": ""F2"",
""catchment_id"": 10,
""detour_cost"": 191
},
{
""locker_id"": ""F3"",
""catchment_id"": 1,
""detour_cost"": 75
},
{
""locker_id"": ""F3"",
""catchment_id"": 2,
""detour_cost"": 844
},
{
""locker_id"": ""F3"",
""catchment_id"": 3,
""detour_cost"": 384
},
{
""locker_id"": ""F3"",
""catchment_id"": 4,
""detour_cost"": 31
},
{
""locker_id"": ""F3"",
""catchment_id"": 5,
""detour_cost"": 184
},
{
""locker_id"": ""F3"",
""catchment_id"": 6,
""detour_cost"": 44
},
{
""locker_id"": ""F3"",
""catchment_id"": 7,
""detour_cost"": 814
},
{
""locker_id"": ""F3"",
""catchment_id"": 8,
""detour_cost"": 354
},
{
""locker_id"": ""F3"",
""catchment_id"": 9,
""detour_cost"": 486
},
{
""locker_id"": ""F3"",
""catchment_id"": 10,
""detour_cost"": 474
},
{
""locker_id"": ""F4"",
""catchment_id"": 1,
""detour_cost"": 155
},
{
""locker_id"": ""F4"",
""catchment_id"": 2,
""detour_cost"": 756
},
{
""locker_id"": ""F4"",
""catchment_id"": 3,
""detour_cost"": 468
},
{
""locker_id"": ""F4"",
""catchment_id"": 4,
""detour_cost"": 521
},
{
""locker_id"": ""F4"",
""catchment_id"": 5,
""detour_cost"": 931
},
{
""locker_id"": ""F4"",
""catchment_id"": 6,
""detour_cost"": 159
},
{
""locker_id"": ""F4"",
""catchment_id"": 7,
""detour_cost"": 754
},
{
""locker_id"": ""F4"",
""catchment_id"": 8,
""detour_cost"": 837
},
{
""locker_id"": ""F4"",
""catchment_id"": 9,
""detour_cost"": 100
},
{
""locker_id"": ""F4"",
""catchment_id"": 10,
""detour_cost"": 408
},
{
""locker_id"": ""F5"",
""catchment_id"": 1,
""detour_cost"": 359
},
{
""locker_id"": ""F5"",
""catchment_id"": 2,
""detour_cost"": 762
},
{
""locker_id"": ""F5"",
""catchment_id"": 3,
""detour_cost"": 911
},
{
""locker_id"": ""F5"",
""catchment_id"": 4,
""detour_cost"": 907
},
{
""locker_id"": ""F5"",
""catchment_id"": 5,
""detour_cost"": 11
},
{
""locker_id"": ""F5"",
""catchment_id"": 6,
""detour_cost"": 27
},
{
""locker_id"": ""F5"",
""catchment_id"": 7,
""detour_cost"": 874
},
{
""locker_id"": ""F5"",
""catchment_id"": 8,
""detour_cost"": 554
},
{
""locker_id"": ""F5"",
""catchment_id"": 9,
""detour_cost"": 53
},
{
""locker_id"": ""F5"",
""catchment_id"": 10,
""detour_cost"": 809
}
]
}
Oh, and to make it easy for me to read your plan, please send the final pick and the commuter assignments in this little JSON shape — nothing fancy, just a consistent form I can parse.
{
""solution"": {
""selected"": [<site_to_open>, <site_to_open>, ...],
""assignments"": [<chosen_site>, <chosen_site>, ...]
}
}
Pretty simple: ""selected"" is the list of locker sites you want installed, and ""assignments"" lists, in the same order as the commuter catchments are given in the instance, which installed site each catchment should use. Think of it like a short form — not the real answer, just the shape I expect.
Please make sure to use the exact identifiers from the instance input — don't rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'opening_costs': [1965, 1681, 1562, 1224, 1594], 'connection_costs': [[963, 371, 320, 547, 296, 41, 526, 134, 657, 810], [844, 100, 469, 792, 10, 354, 839, 814, 819, 191], [75, 844, 384, 31, 184, 44, 814, 354, 486, 474], [155, 756, 468, 521, 931, 159, 754, 837, 100, 408], [359, 762, 911, 907, 11, 27, 874, 554, 53, 809]], 'objective': 5252.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}",5252.0,"{'problem_type': 'UFLP', 'num_facilities': 5, 'num_customers': 10, 'facilities': [{'id': 'F1', 'opening_cost': 1965}, {'id': 'F2', 'opening_cost': 1681}, {'id': 'F3', 'opening_cost': 1562}, {'id': 'F4', 'opening_cost': 1224}, {'id': 'F5', 'opening_cost': 1594}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}, {'id': 9}, {'id': 10}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 963}, {'facility': 'F1', 'customer': 2, 'cost': 371}, {'facility': 'F1', 'customer': 3, 'cost': 320}, {'facility': 'F1', 'customer': 4, 'cost': 547}, {'facility': 'F1', 'customer': 5, 'cost': 296}, {'facility': 'F1', 'customer': 6, 'cost': 41}, {'facility': 'F1', 'customer': 7, 'cost': 526}, {'facility': 'F1', 'customer': 8, 'cost': 134}, {'facility': 'F1', 'customer': 9, 'cost': 657}, {'facility': 'F1', 'customer': 10, 'cost': 810}, {'facility': 'F2', 'customer': 1, 'cost': 844}, {'facility': 'F2', 'customer': 2, 'cost': 100}, {'facility': 'F2', 'customer': 3, 'cost': 469}, {'facility': 'F2', 'customer': 4, 'cost': 792}, {'facility': 'F2', 'customer': 5, 'cost': 10}, {'facility': 'F2', 'customer': 6, 'cost': 354}, {'facility': 'F2', 'customer': 7, 'cost': 839}, {'facility': 'F2', 'customer': 8, 'cost': 814}, {'facility': 'F2', 'customer': 9, 'cost': 819}, {'facility': 'F2', 'customer': 10, 'cost': 191}, {'facility': 'F3', 'customer': 1, 'cost': 75}, {'facility': 'F3', 'customer': 2, 'cost': 844}, {'facility': 'F3', 'customer': 3, 'cost': 384}, {'facility': 'F3', 'customer': 4, 'cost': 31}, {'facility': 'F3', 'customer': 5, 'cost': 184}, {'facility': 'F3', 'customer': 6, 'cost': 44}, {'facility': 'F3', 'customer': 7, 'cost': 814}, {'facility': 'F3', 'customer': 8, 'cost': 354}, {'facility': 'F3', 'customer': 9, 'cost': 486}, {'facility': 'F3', 'customer': 10, 'cost': 474}, {'facility': 'F4', 'customer': 1, 'cost': 155}, {'facility': 'F4', 'customer': 2, 'cost': 756}, {'facility': 'F4', 'customer': 3, 'cost': 468}, {'facility': 'F4', 'customer': 4, 'cost': 521}, {'facility': 'F4', 'customer': 5, 'cost': 931}, {'facility': 'F4', 'customer': 6, 'cost': 159}, {'facility': 'F4', 'customer': 7, 'cost': 754}, {'facility': 'F4', 'customer': 8, 'cost': 837}, {'facility': 'F4', 'customer': 9, 'cost': 100}, {'facility': 'F4', 'customer': 10, 'cost': 408}, {'facility': 'F5', 'customer': 1, 'cost': 359}, {'facility': 'F5', 'customer': 2, 'cost': 762}, {'facility': 'F5', 'customer': 3, 'cost': 911}, {'facility': 'F5', 'customer': 4, 'cost': 907}, {'facility': 'F5', 'customer': 5, 'cost': 11}, {'facility': 'F5', 'customer': 6, 'cost': 27}, {'facility': 'F5', 'customer': 7, 'cost': 874}, {'facility': 'F5', 'customer': 8, 'cost': 554}, {'facility': 'F5', 'customer': 9, 'cost': 53}, {'facility': 'F5', 'customer': 10, 'cost': 809}], 'objective': 5252.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",50,json,1
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