UFLP/UFLP_S_context.csv

task_name,problem_type,instruction,instance,solution,obj,instance_variant,solution_variant,context_index,input_format,input_index_base
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.

# num_candidate_libraries=2
# num_readers_total=5
# LIBRARYS
library_id,opening_fee
F1,1035
F2,1123
# READERS
reader_id
1
2
3
4
5
# TRAVELS
library_id,reader_id,travel_cost
F1,1,907
F1,2,615
F1,3,966
F1,4,376
F1,5,783
F2,1,46
F2,2,206
F2,3,401
F2,4,644
F2,5,478

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': [1035, 1123], 'connection_costs': [[907, 615, 966, 376, 783], [46, 206, 401, 644, 478]], 'objective': 2898.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1]}",2898.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 1035}, {'id': 'F2', 'opening_cost': 1123}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 907}, {'facility': 'F1', 'customer': 2, 'cost': 615}, {'facility': 'F1', 'customer': 3, 'cost': 966}, {'facility': 'F1', 'customer': 4, 'cost': 376}, {'facility': 'F1', 'customer': 5, 'cost': 783}, {'facility': 'F2', 'customer': 1, 'cost': 46}, {'facility': 'F2', 'customer': 2, 'cost': 206}, {'facility': 'F2', 'customer': 3, 'cost': 401}, {'facility': 'F2', 'customer': 4, 'cost': 644}, {'facility': 'F2', 'customer': 5, 'cost': 478}], 'objective': 2898.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2']}",1,csv,1
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.

{
  ""num_kitchens"": 2,
  ""num_orders"": 5,
  ""kitchens"": [
    {
      ""kitchen_id"": ""F1"",
      ""activation_fee"": 6266
    },
    {
      ""kitchen_id"": ""F2"",
      ""activation_fee"": 2140
    }
  ],
  ""orders"": [
    {
      ""order_id"": 0
    },
    {
      ""order_id"": 1
    },
    {
      ""order_id"": 2
    },
    {
      ""order_id"": 3
    },
    {
      ""order_id"": 4
    }
  ],
  ""delivery_distances"": [
    {
      ""kitchen_id"": ""F1"",
      ""order_id"": 0,
      ""delivery_distance"": 954
    },
    {
      ""kitchen_id"": ""F1"",
      ""order_id"": 1,
      ""delivery_distance"": 354
    },
    {
      ""kitchen_id"": ""F1"",
      ""order_id"": 2,
      ""delivery_distance"": 145
    },
    {
      ""kitchen_id"": ""F1"",
      ""order_id"": 3,
      ""delivery_distance"": 408
    },
    {
      ""kitchen_id"": ""F1"",
      ""order_id"": 4,
      ""delivery_distance"": 207
    },
    {
      ""kitchen_id"": ""F2"",
      ""order_id"": 0,
      ""delivery_distance"": 665
    },
    {
      ""kitchen_id"": ""F2"",
      ""order_id"": 1,
      ""delivery_distance"": 93
    },
    {
      ""kitchen_id"": ""F2"",
      ""order_id"": 2,
      ""delivery_distance"": 569
    },
    {
      ""kitchen_id"": ""F2"",
      ""order_id"": 3,
      ""delivery_distance"": 616
    },
    {
      ""kitchen_id"": ""F2"",
      ""order_id"": 4,
      ""delivery_distance"": 549
    }
  ]
}

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': [6266, 2140], 'connection_costs': [[954, 354, 145, 408, 207], [665, 93, 569, 616, 549]], 'objective': 4632.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1]}",4632.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 6266}, {'id': 'F2', 'opening_cost': 2140}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 954}, {'facility': 'F1', 'customer': 1, 'cost': 354}, {'facility': 'F1', 'customer': 2, 'cost': 145}, {'facility': 'F1', 'customer': 3, 'cost': 408}, {'facility': 'F1', 'customer': 4, 'cost': 207}, {'facility': 'F2', 'customer': 0, 'cost': 665}, {'facility': 'F2', 'customer': 1, 'cost': 93}, {'facility': 'F2', 'customer': 2, 'cost': 569}, {'facility': 'F2', 'customer': 3, 'cost': 616}, {'facility': 'F2', 'customer': 4, 'cost': 549}], 'objective': 4632.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2']}",2,json,0
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=2
# num_resident_cars=6
# CHARGERS
charger_id,installation_cost
F1,2000
F2,2000
# RESIDENT_CARS
resident_car_id
A
B
C
D
E
F
# WALKING_DISTANCES
charger_id,resident_car_id,walking_distance
F1,A,456
F1,B,345
F1,C,235
F1,D,796
F1,E,527
F1,F,823
F2,A,924
F2,B,363
F2,C,638
F2,D,112
F2,E,986
F2,F,432

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], 'connection_costs': [[456, 345, 235, 796, 527, 823], [924, 363, 638, 112, 986, 432]], 'objective': 5182.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0]}",5182.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 456}, {'facility': 'F1', 'customer': 'B', 'cost': 345}, {'facility': 'F1', 'customer': 'C', 'cost': 235}, {'facility': 'F1', 'customer': 'D', 'cost': 796}, {'facility': 'F1', 'customer': 'E', 'cost': 527}, {'facility': 'F1', 'customer': 'F', 'cost': 823}, {'facility': 'F2', 'customer': 'A', 'cost': 924}, {'facility': 'F2', 'customer': 'B', 'cost': 363}, {'facility': 'F2', 'customer': 'C', 'cost': 638}, {'facility': 'F2', 'customer': 'D', 'cost': 112}, {'facility': 'F2', 'customer': 'E', 'cost': 986}, {'facility': 'F2', 'customer': 'F', 'cost': 432}], 'objective': 5182.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",3,csv,names
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=7
# STALLS
stall_id,stall_rent
F1,1244
F2,1295
F3,1434
# SHOPPERS
shopper_id
A
B
C
D
E
F
G
# SHOPPER_WALKS
stall_id,shopper_id,shopper_walk_cost
F1,A,475
F1,B,251
F1,C,838
F1,D,367
F1,E,765
F1,F,254
F1,G,950
F2,A,527
F2,B,573
F2,C,300
F2,D,315
F2,E,798
F2,F,648
F2,G,927
F3,A,78
F3,B,217
F3,C,691
F3,D,609
F3,E,73
F3,F,808
F3,G,798

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': [1244, 1295, 1434], 'connection_costs': [[475, 251, 838, 367, 765, 254, 950], [527, 573, 300, 315, 798, 648, 927], [78, 217, 691, 609, 73, 808, 798]], 'objective': 4708.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2]}",4708.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 1244}, {'id': 'F2', 'opening_cost': 1295}, {'id': 'F3', 'opening_cost': 1434}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 475}, {'facility': 'F1', 'customer': 'B', 'cost': 251}, {'facility': 'F1', 'customer': 'C', 'cost': 838}, {'facility': 'F1', 'customer': 'D', 'cost': 367}, {'facility': 'F1', 'customer': 'E', 'cost': 765}, {'facility': 'F1', 'customer': 'F', 'cost': 254}, {'facility': 'F1', 'customer': 'G', 'cost': 950}, {'facility': 'F2', 'customer': 'A', 'cost': 527}, {'facility': 'F2', 'customer': 'B', 'cost': 573}, {'facility': 'F2', 'customer': 'C', 'cost': 300}, {'facility': 'F2', 'customer': 'D', 'cost': 315}, {'facility': 'F2', 'customer': 'E', 'cost': 798}, {'facility': 'F2', 'customer': 'F', 'cost': 648}, {'facility': 'F2', 'customer': 'G', 'cost': 927}, {'facility': 'F3', 'customer': 'A', 'cost': 78}, {'facility': 'F3', 'customer': 'B', 'cost': 217}, {'facility': 'F3', 'customer': 'C', 'cost': 691}, {'facility': 'F3', 'customer': 'D', 'cost': 609}, {'facility': 'F3', 'customer': 'E', 'cost': 73}, {'facility': 'F3', 'customer': 'F', 'cost': 808}, {'facility': 'F3', 'customer': 'G', 'cost': 798}], 'objective': 4708.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",4,csv,names
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.

There are 2 candidate sheds, 5 households, and the shed maintenance costs are 2000, 2000.
Shed F1 has maintenance cost 2000.
Shed F2 has maintenance cost 2000.
Household A would incur travel cost 192 to reach shed F1.
Household B would incur travel cost 355 to reach shed F1.
Household C would incur travel cost 448 to reach shed F1.
Household D would incur travel cost 826 to reach shed F1.
Household E would incur travel cost 593 to reach shed F1.
Household A would incur travel cost 476 to reach shed F2.
Household B would incur travel cost 647 to reach shed F2.
Household C would incur travel cost 363 to reach shed F2.
Household D would incur travel cost 979 to reach shed F2.
Household E would incur travel cost 417 to reach shed F2.
Use these entries to pick which sheds to keep and to assign every household so the combined maintenance plus travel cost is minimized.

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], 'connection_costs': [[192, 355, 448, 826, 593], [476, 647, 363, 979, 417]], 'objective': 4414.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0]}",4414.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 192}, {'facility': 'F1', 'customer': 'B', 'cost': 355}, {'facility': 'F1', 'customer': 'C', 'cost': 448}, {'facility': 'F1', 'customer': 'D', 'cost': 826}, {'facility': 'F1', 'customer': 'E', 'cost': 593}, {'facility': 'F2', 'customer': 'A', 'cost': 476}, {'facility': 'F2', 'customer': 'B', 'cost': 647}, {'facility': 'F2', 'customer': 'C', 'cost': 363}, {'facility': 'F2', 'customer': 'D', 'cost': 979}, {'facility': 'F2', 'customer': 'E', 'cost': 417}], 'objective': 4414.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1']}",5,nl,names
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.

# num_candidate_vans=3
# num_appointments=7
# VANS
van_id,deployment_cost
F1,7637
F2,9350
F3,1987
# APPOINTMENTS
appointment_id
1
2
3
4
5
6
7
# TRAVELS
van_id,appointment_id,travel_cost
F1,1,272
F1,2,443
F1,3,443
F1,4,314
F1,5,602
F1,6,286
F1,7,306
F2,1,813
F2,2,963
F2,3,689
F2,4,509
F2,5,802
F2,6,839
F2,7,102
F3,1,489
F3,2,727
F3,3,90
F3,4,529
F3,5,224
F3,6,200
F3,7,143

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': [7637, 9350, 1987], 'connection_costs': [[272, 443, 443, 314, 602, 286, 306], [813, 963, 689, 509, 802, 839, 102], [489, 727, 90, 529, 224, 200, 143]], 'objective': 4389.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2]}",4389.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 7637}, {'id': 'F2', 'opening_cost': 9350}, {'id': 'F3', 'opening_cost': 1987}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 272}, {'facility': 'F1', 'customer': 2, 'cost': 443}, {'facility': 'F1', 'customer': 3, 'cost': 443}, {'facility': 'F1', 'customer': 4, 'cost': 314}, {'facility': 'F1', 'customer': 5, 'cost': 602}, {'facility': 'F1', 'customer': 6, 'cost': 286}, {'facility': 'F1', 'customer': 7, 'cost': 306}, {'facility': 'F2', 'customer': 1, 'cost': 813}, {'facility': 'F2', 'customer': 2, 'cost': 963}, {'facility': 'F2', 'customer': 3, 'cost': 689}, {'facility': 'F2', 'customer': 4, 'cost': 509}, {'facility': 'F2', 'customer': 5, 'cost': 802}, {'facility': 'F2', 'customer': 6, 'cost': 839}, {'facility': 'F2', 'customer': 7, 'cost': 102}, {'facility': 'F3', 'customer': 1, 'cost': 489}, {'facility': 'F3', 'customer': 2, 'cost': 727}, {'facility': 'F3', 'customer': 3, 'cost': 90}, {'facility': 'F3', 'customer': 4, 'cost': 529}, {'facility': 'F3', 'customer': 5, 'cost': 224}, {'facility': 'F3', 'customer': 6, 'cost': 200}, {'facility': 'F3', 'customer': 7, 'cost': 143}], 'objective': 4389.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",6,csv,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.

{
  ""num_candidate_hubs"": 3,
  ""num_registered_customers"": 8,
  ""hubs"": [
    {
      ""hub_id"": ""F1"",
      ""hub_opening_fee"": 1000
    },
    {
      ""hub_id"": ""F2"",
      ""hub_opening_fee"": 1000
    },
    {
      ""hub_id"": ""F3"",
      ""hub_opening_fee"": 1000
    }
  ],
  ""customers"": [
    {
      ""customer_id"": 0
    },
    {
      ""customer_id"": 1
    },
    {
      ""customer_id"": 2
    },
    {
      ""customer_id"": 3
    },
    {
      ""customer_id"": 4
    },
    {
      ""customer_id"": 5
    },
    {
      ""customer_id"": 6
    },
    {
      ""customer_id"": 7
    }
  ],
  ""travel_cost_to_hubs"": [
    {
      ""hub_id"": ""F1"",
      ""customer_id"": 0,
      ""travel_cost_to_hub"": 996
    },
    {
      ""hub_id"": ""F1"",
      ""customer_id"": 1,
      ""travel_cost_to_hub"": 548
    },
    {
      ""hub_id"": ""F1"",
      ""customer_id"": 2,
      ""travel_cost_to_hub"": 363
    },
    {
      ""hub_id"": ""F1"",
      ""customer_id"": 3,
      ""travel_cost_to_hub"": 859
    },
    {
      ""hub_id"": ""F1"",
      ""customer_id"": 4,
      ""travel_cost_to_hub"": 857
    },
    {
      ""hub_id"": ""F1"",
      ""customer_id"": 5,
      ""travel_cost_to_hub"": 132
    },
    {
      ""hub_id"": ""F1"",
      ""customer_id"": 6,
      ""travel_cost_to_hub"": 353
    },
    {
      ""hub_id"": ""F1"",
      ""customer_id"": 7,
      ""travel_cost_to_hub"": 718
    },
    {
      ""hub_id"": ""F2"",
      ""customer_id"": 0,
      ""travel_cost_to_hub"": 235
    },
    {
      ""hub_id"": ""F2"",
      ""customer_id"": 1,
      ""travel_cost_to_hub"": 831
    },
    {
      ""hub_id"": ""F2"",
      ""customer_id"": 2,
      ""travel_cost_to_hub"": 627
    },
    {
      ""hub_id"": ""F2"",
      ""customer_id"": 3,
      ""travel_cost_to_hub"": 763
    },
    {
      ""hub_id"": ""F2"",
      ""customer_id"": 4,
      ""travel_cost_to_hub"": 211
    },
    {
      ""hub_id"": ""F2"",
      ""customer_id"": 5,
      ""travel_cost_to_hub"": 260
    },
    {
      ""hub_id"": ""F2"",
      ""customer_id"": 6,
      ""travel_cost_to_hub"": 498
    },
    {
      ""hub_id"": ""F2"",
      ""customer_id"": 7,
      ""travel_cost_to_hub"": 373
    },
    {
      ""hub_id"": ""F3"",
      ""customer_id"": 0,
      ""travel_cost_to_hub"": 42
    },
    {
      ""hub_id"": ""F3"",
      ""customer_id"": 1,
      ""travel_cost_to_hub"": 117
    },
    {
      ""hub_id"": ""F3"",
      ""customer_id"": 2,
      ""travel_cost_to_hub"": 984
    },
    {
      ""hub_id"": ""F3"",
      ""customer_id"": 3,
      ""travel_cost_to_hub"": 943
    },
    {
      ""hub_id"": ""F3"",
      ""customer_id"": 4,
      ""travel_cost_to_hub"": 102
    },
    {
      ""hub_id"": ""F3"",
      ""customer_id"": 5,
      ""travel_cost_to_hub"": 453
    },
    {
      ""hub_id"": ""F3"",
      ""customer_id"": 6,
      ""travel_cost_to_hub"": 648
    },
    {
      ""hub_id"": ""F3"",
      ""customer_id"": 7,
      ""travel_cost_to_hub"": 921
    }
  ]
}

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': [1000, 1000, 1000], 'connection_costs': [[996, 548, 363, 859, 857, 132, 353, 718], [235, 831, 627, 763, 211, 260, 498, 373], [42, 117, 984, 943, 102, 453, 648, 921]], 'objective': 4686.0}","{'open_facilities': [0, 2], 'assignments': [2, 2, 0, 0, 2, 0, 0, 0]}",4686.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 8, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 996}, {'facility': 'F1', 'customer': 1, 'cost': 548}, {'facility': 'F1', 'customer': 2, 'cost': 363}, {'facility': 'F1', 'customer': 3, 'cost': 859}, {'facility': 'F1', 'customer': 4, 'cost': 857}, {'facility': 'F1', 'customer': 5, 'cost': 132}, {'facility': 'F1', 'customer': 6, 'cost': 353}, {'facility': 'F1', 'customer': 7, 'cost': 718}, {'facility': 'F2', 'customer': 0, 'cost': 235}, {'facility': 'F2', 'customer': 1, 'cost': 831}, {'facility': 'F2', 'customer': 2, 'cost': 627}, {'facility': 'F2', 'customer': 3, 'cost': 763}, {'facility': 'F2', 'customer': 4, 'cost': 211}, {'facility': 'F2', 'customer': 5, 'cost': 260}, {'facility': 'F2', 'customer': 6, 'cost': 498}, {'facility': 'F2', 'customer': 7, 'cost': 373}, {'facility': 'F3', 'customer': 0, 'cost': 42}, {'facility': 'F3', 'customer': 1, 'cost': 117}, {'facility': 'F3', 'customer': 2, 'cost': 984}, {'facility': 'F3', 'customer': 3, 'cost': 943}, {'facility': 'F3', 'customer': 4, 'cost': 102}, {'facility': 'F3', 'customer': 5, 'cost': 453}, {'facility': 'F3', 'customer': 6, 'cost': 648}, {'facility': 'F3', 'customer': 7, 'cost': 921}], 'objective': 4686.0}","{'selected': ['F1', 'F3'], 'assignments': ['F3', 'F3', 'F1', 'F1', 'F3', 'F1', 'F1', 'F1']}",7,json,0
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.

Here are the 4 candidate plots, the 8 families, and the setup costs 2000, 2000, 2000, 2000.
Plot F1 costs 2000 to prepare.
Plot F2 costs 2000 to prepare.
Plot F3 costs 2000 to prepare.
Plot F4 costs 2000 to prepare.
Family 1 has travel cost 369 to plot F1.
Family 2 has travel cost 941 to plot F1.
Family 3 has travel cost 524 to plot F1.
Family 4 has travel cost 324 to plot F1.
Family 5 has travel cost 597 to plot F1.
Family 6 has travel cost 415 to plot F1.
Family 7 has travel cost 427 to plot F1.
Family 8 has travel cost 876 to plot F1.
Family 1 has travel cost 69 to plot F2.
Family 2 has travel cost 730 to plot F2.
Family 3 has travel cost 135 to plot F2.
Family 4 has travel cost 162 to plot F2.
Family 5 has travel cost 714 to plot F2.
Family 6 has travel cost 835 to plot F2.
Family 7 has travel cost 193 to plot F2.
Family 8 has travel cost 495 to plot F2.
Family 1 has travel cost 622 to plot F3.
Family 2 has travel cost 625 to plot F3.
Family 3 has travel cost 798 to plot F3.
Family 4 has travel cost 829 to plot F3.
Family 5 has travel cost 696 to plot F3.
Family 6 has travel cost 416 to plot F3.
Family 7 has travel cost 98 to plot F3.
Family 8 has travel cost 993 to plot F3.
Family 1 has travel cost 59 to plot F4.
Family 2 has travel cost 124 to plot F4.
Family 3 has travel cost 619 to plot F4.
Family 4 has travel cost 247 to plot F4.
Family 5 has travel cost 26 to plot F4.
Family 6 has travel cost 9 to plot F4.
Family 7 has travel cost 881 to plot F4.
Family 8 has travel cost 866 to plot F4.
I'll use these details to pick which plots to prepare and assign every family so the total bill is as small as possible.

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': [2000, 2000, 2000, 2000], 'connection_costs': [[369, 941, 524, 324, 597, 415, 427, 876], [69, 730, 135, 162, 714, 835, 193, 495], [622, 625, 798, 829, 696, 416, 98, 993], [59, 124, 619, 247, 26, 9, 881, 866]], 'objective': 4831.0}","{'open_facilities': [3], 'assignments': [3, 3, 3, 3, 3, 3, 3, 3]}",4831.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 8, '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}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 369}, {'facility': 'F1', 'customer': 2, 'cost': 941}, {'facility': 'F1', 'customer': 3, 'cost': 524}, {'facility': 'F1', 'customer': 4, 'cost': 324}, {'facility': 'F1', 'customer': 5, 'cost': 597}, {'facility': 'F1', 'customer': 6, 'cost': 415}, {'facility': 'F1', 'customer': 7, 'cost': 427}, {'facility': 'F1', 'customer': 8, 'cost': 876}, {'facility': 'F2', 'customer': 1, 'cost': 69}, {'facility': 'F2', 'customer': 2, 'cost': 730}, {'facility': 'F2', 'customer': 3, 'cost': 135}, {'facility': 'F2', 'customer': 4, 'cost': 162}, {'facility': 'F2', 'customer': 5, 'cost': 714}, {'facility': 'F2', 'customer': 6, 'cost': 835}, {'facility': 'F2', 'customer': 7, 'cost': 193}, {'facility': 'F2', 'customer': 8, 'cost': 495}, {'facility': 'F3', 'customer': 1, 'cost': 622}, {'facility': 'F3', 'customer': 2, 'cost': 625}, {'facility': 'F3', 'customer': 3, 'cost': 798}, {'facility': 'F3', 'customer': 4, 'cost': 829}, {'facility': 'F3', 'customer': 5, 'cost': 696}, {'facility': 'F3', 'customer': 6, 'cost': 416}, {'facility': 'F3', 'customer': 7, 'cost': 98}, {'facility': 'F3', 'customer': 8, 'cost': 993}, {'facility': 'F4', 'customer': 1, 'cost': 59}, {'facility': 'F4', 'customer': 2, 'cost': 124}, {'facility': 'F4', 'customer': 3, 'cost': 619}, {'facility': 'F4', 'customer': 4, 'cost': 247}, {'facility': 'F4', 'customer': 5, 'cost': 26}, {'facility': 'F4', 'customer': 6, 'cost': 9}, {'facility': 'F4', 'customer': 7, 'cost': 881}, {'facility': 'F4', 'customer': 8, 'cost': 866}], 'objective': 4831.0}","{'selected': ['F4'], 'assignments': ['F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4', 'F4']}",8,nl,1
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.

{
  ""num_candidate_centers"": 3,
  ""num_students"": 7,
  ""centers"": [
    {
      ""center_id"": ""F1"",
      ""launch_cost"": 2000
    },
    {
      ""center_id"": ""F2"",
      ""launch_cost"": 2000
    },
    {
      ""center_id"": ""F3"",
      ""launch_cost"": 2000
    }
  ],
  ""students"": [
    {
      ""student_id"": 1
    },
    {
      ""student_id"": 2
    },
    {
      ""student_id"": 3
    },
    {
      ""student_id"": 4
    },
    {
      ""student_id"": 5
    },
    {
      ""student_id"": 6
    },
    {
      ""student_id"": 7
    }
  ],
  ""commutes"": [
    {
      ""center_id"": ""F1"",
      ""student_id"": 1,
      ""commute_cost"": 326
    },
    {
      ""center_id"": ""F1"",
      ""student_id"": 2,
      ""commute_cost"": 74
    },
    {
      ""center_id"": ""F1"",
      ""student_id"": 3,
      ""commute_cost"": 123
    },
    {
      ""center_id"": ""F1"",
      ""student_id"": 4,
      ""commute_cost"": 675
    },
    {
      ""center_id"": ""F1"",
      ""student_id"": 5,
      ""commute_cost"": 451
    },
    {
      ""center_id"": ""F1"",
      ""student_id"": 6,
      ""commute_cost"": 738
    },
    {
      ""center_id"": ""F1"",
      ""student_id"": 7,
      ""commute_cost"": 704
    },
    {
      ""center_id"": ""F2"",
      ""student_id"": 1,
      ""commute_cost"": 340
    },
    {
      ""center_id"": ""F2"",
      ""student_id"": 2,
      ""commute_cost"": 165
    },
    {
      ""center_id"": ""F2"",
      ""student_id"": 3,
      ""commute_cost"": 797
    },
    {
      ""center_id"": ""F2"",
      ""student_id"": 4,
      ""commute_cost"": 199
    },
    {
      ""center_id"": ""F2"",
      ""student_id"": 5,
      ""commute_cost"": 577
    },
    {
      ""center_id"": ""F2"",
      ""student_id"": 6,
      ""commute_cost"": 944
    },
    {
      ""center_id"": ""F2"",
      ""student_id"": 7,
      ""commute_cost"": 636
    },
    {
      ""center_id"": ""F3"",
      ""student_id"": 1,
      ""commute_cost"": 343
    },
    {
      ""center_id"": ""F3"",
      ""student_id"": 2,
      ""commute_cost"": 864
    },
    {
      ""center_id"": ""F3"",
      ""student_id"": 3,
      ""commute_cost"": 58
    },
    {
      ""center_id"": ""F3"",
      ""student_id"": 4,
      ""commute_cost"": 86
    },
    {
      ""center_id"": ""F3"",
      ""student_id"": 5,
      ""commute_cost"": 579
    },
    {
      ""center_id"": ""F3"",
      ""student_id"": 6,
      ""commute_cost"": 335
    },
    {
      ""center_id"": ""F3"",
      ""student_id"": 7,
      ""commute_cost"": 545
    }
  ]
}

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], 'connection_costs': [[326, 74, 123, 675, 451, 738, 704], [340, 165, 797, 199, 577, 944, 636], [343, 864, 58, 86, 579, 335, 545]], 'objective': 4810.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2]}",4810.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 326}, {'facility': 'F1', 'customer': 2, 'cost': 74}, {'facility': 'F1', 'customer': 3, 'cost': 123}, {'facility': 'F1', 'customer': 4, 'cost': 675}, {'facility': 'F1', 'customer': 5, 'cost': 451}, {'facility': 'F1', 'customer': 6, 'cost': 738}, {'facility': 'F1', 'customer': 7, 'cost': 704}, {'facility': 'F2', 'customer': 1, 'cost': 340}, {'facility': 'F2', 'customer': 2, 'cost': 165}, {'facility': 'F2', 'customer': 3, 'cost': 797}, {'facility': 'F2', 'customer': 4, 'cost': 199}, {'facility': 'F2', 'customer': 5, 'cost': 577}, {'facility': 'F2', 'customer': 6, 'cost': 944}, {'facility': 'F2', 'customer': 7, 'cost': 636}, {'facility': 'F3', 'customer': 1, 'cost': 343}, {'facility': 'F3', 'customer': 2, 'cost': 864}, {'facility': 'F3', 'customer': 3, 'cost': 58}, {'facility': 'F3', 'customer': 4, 'cost': 86}, {'facility': 'F3', 'customer': 5, 'cost': 579}, {'facility': 'F3', 'customer': 6, 'cost': 335}, {'facility': 'F3', 'customer': 7, 'cost': 545}], 'objective': 4810.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",9,json,1
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"": 3,
  ""num_riders"": 7,
  ""kiosks"": [
    {
      ""kiosk_id"": ""F1"",
      ""installation_cost"": 1000
    },
    {
      ""kiosk_id"": ""F2"",
      ""installation_cost"": 1000
    },
    {
      ""kiosk_id"": ""F3"",
      ""installation_cost"": 1000
    }
  ],
  ""riders"": [
    {
      ""rider_id"": ""A""
    },
    {
      ""rider_id"": ""B""
    },
    {
      ""rider_id"": ""C""
    },
    {
      ""rider_id"": ""D""
    },
    {
      ""rider_id"": ""E""
    },
    {
      ""rider_id"": ""F""
    },
    {
      ""rider_id"": ""G""
    }
  ],
  ""detour_distance_ors"": [
    {
      ""kiosk_id"": ""F1"",
      ""rider_id"": ""A"",
      ""detour_distance_or_cost"": 175
    },
    {
      ""kiosk_id"": ""F1"",
      ""rider_id"": ""B"",
      ""detour_distance_or_cost"": 707
    },
    {
      ""kiosk_id"": ""F1"",
      ""rider_id"": ""C"",
      ""detour_distance_or_cost"": 626
    },
    {
      ""kiosk_id"": ""F1"",
      ""rider_id"": ""D"",
      ""detour_distance_or_cost"": 410
    },
    {
      ""kiosk_id"": ""F1"",
      ""rider_id"": ""E"",
      ""detour_distance_or_cost"": 179
    },
    {
      ""kiosk_id"": ""F1"",
      ""rider_id"": ""F"",
      ""detour_distance_or_cost"": 963
    },
    {
      ""kiosk_id"": ""F1"",
      ""rider_id"": ""G"",
      ""detour_distance_or_cost"": 418
    },
    {
      ""kiosk_id"": ""F2"",
      ""rider_id"": ""A"",
      ""detour_distance_or_cost"": 964
    },
    {
      ""kiosk_id"": ""F2"",
      ""rider_id"": ""B"",
      ""detour_distance_or_cost"": 990
    },
    {
      ""kiosk_id"": ""F2"",
      ""rider_id"": ""C"",
      ""detour_distance_or_cost"": 334
    },
    {
      ""kiosk_id"": ""F2"",
      ""rider_id"": ""D"",
      ""detour_distance_or_cost"": 345
    },
    {
      ""kiosk_id"": ""F2"",
      ""rider_id"": ""E"",
      ""detour_distance_or_cost"": 612
    },
    {
      ""kiosk_id"": ""F2"",
      ""rider_id"": ""F"",
      ""detour_distance_or_cost"": 425
    },
    {
      ""kiosk_id"": ""F2"",
      ""rider_id"": ""G"",
      ""detour_distance_or_cost"": 304
    },
    {
      ""kiosk_id"": ""F3"",
      ""rider_id"": ""A"",
      ""detour_distance_or_cost"": 805
    },
    {
      ""kiosk_id"": ""F3"",
      ""rider_id"": ""B"",
      ""detour_distance_or_cost"": 62
    },
    {
      ""kiosk_id"": ""F3"",
      ""rider_id"": ""C"",
      ""detour_distance_or_cost"": 3
    },
    {
      ""kiosk_id"": ""F3"",
      ""rider_id"": ""D"",
      ""detour_distance_or_cost"": 983
    },
    {
      ""kiosk_id"": ""F3"",
      ""rider_id"": ""E"",
      ""detour_distance_or_cost"": 459
    },
    {
      ""kiosk_id"": ""F3"",
      ""rider_id"": ""F"",
      ""detour_distance_or_cost"": 313
    },
    {
      ""kiosk_id"": ""F3"",
      ""rider_id"": ""G"",
      ""detour_distance_or_cost"": 819
    }
  ]
}

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': [1000, 1000, 1000], 'connection_costs': [[175, 707, 626, 410, 179, 963, 418], [964, 990, 334, 345, 612, 425, 304], [805, 62, 3, 983, 459, 313, 819]], 'objective': 3560.0}","{'open_facilities': [0, 2], 'assignments': [0, 2, 2, 0, 0, 2, 0]}",3560.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 175}, {'facility': 'F1', 'customer': 'B', 'cost': 707}, {'facility': 'F1', 'customer': 'C', 'cost': 626}, {'facility': 'F1', 'customer': 'D', 'cost': 410}, {'facility': 'F1', 'customer': 'E', 'cost': 179}, {'facility': 'F1', 'customer': 'F', 'cost': 963}, {'facility': 'F1', 'customer': 'G', 'cost': 418}, {'facility': 'F2', 'customer': 'A', 'cost': 964}, {'facility': 'F2', 'customer': 'B', 'cost': 990}, {'facility': 'F2', 'customer': 'C', 'cost': 334}, {'facility': 'F2', 'customer': 'D', 'cost': 345}, {'facility': 'F2', 'customer': 'E', 'cost': 612}, {'facility': 'F2', 'customer': 'F', 'cost': 425}, {'facility': 'F2', 'customer': 'G', 'cost': 304}, {'facility': 'F3', 'customer': 'A', 'cost': 805}, {'facility': 'F3', 'customer': 'B', 'cost': 62}, {'facility': 'F3', 'customer': 'C', 'cost': 3}, {'facility': 'F3', 'customer': 'D', 'cost': 983}, {'facility': 'F3', 'customer': 'E', 'cost': 459}, {'facility': 'F3', 'customer': 'F', 'cost': 313}, {'facility': 'F3', 'customer': 'G', 'cost': 819}], 'objective': 3560.0}","{'selected': ['F1', 'F3'], 'assignments': ['F1', 'F3', 'F3', 'F1', 'F1', 'F3', 'F1']}",10,json,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 2 candidate caches, 5 households, and stocking costs 1499, 1348.
Cache F1 costs 1499 to stock.
Cache F2 costs 1348 to stock.
If we serve household A from cache F1, the travel cost is 716.
If we serve household B from cache F1, the travel cost is 683.
If we serve household C from cache F1, the travel cost is 637.
If we serve household D from cache F1, the travel cost is 519.
If we serve household E from cache F1, the travel cost is 62.
If we serve household A from cache F2, the travel cost is 332.
If we serve household B from cache F2, the travel cost is 350.
If we serve household C from cache F2, the travel cost is 394.
If we serve household D from cache F2, the travel cost is 806.
If we serve household E from cache F2, the travel cost is 884.
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': [1499, 1348], 'connection_costs': [[716, 683, 637, 519, 62], [332, 350, 394, 806, 884]], 'objective': 4114.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1]}",4114.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 1499}, {'id': 'F2', 'opening_cost': 1348}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 716}, {'facility': 'F1', 'customer': 'B', 'cost': 683}, {'facility': 'F1', 'customer': 'C', 'cost': 637}, {'facility': 'F1', 'customer': 'D', 'cost': 519}, {'facility': 'F1', 'customer': 'E', 'cost': 62}, {'facility': 'F2', 'customer': 'A', 'cost': 332}, {'facility': 'F2', 'customer': 'B', 'cost': 350}, {'facility': 'F2', 'customer': 'C', 'cost': 394}, {'facility': 'F2', 'customer': 'D', 'cost': 806}, {'facility': 'F2', 'customer': 'E', 'cost': 884}], 'objective': 4114.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2']}",11,nl,names
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.

{
  ""num_candidate_stalls"": 3,
  ""num_attendees"": 7,
  ""stalls"": [
    {
      ""stall_id"": ""F1"",
      ""stall_rent"": 9182
    },
    {
      ""stall_id"": ""F2"",
      ""stall_rent"": 1373
    },
    {
      ""stall_id"": ""F3"",
      ""stall_rent"": 4548
    }
  ],
  ""attendees"": [
    {
      ""attendee_id"": 0
    },
    {
      ""attendee_id"": 1
    },
    {
      ""attendee_id"": 2
    },
    {
      ""attendee_id"": 3
    },
    {
      ""attendee_id"": 4
    },
    {
      ""attendee_id"": 5
    },
    {
      ""attendee_id"": 6
    }
  ],
  ""walking_distances"": [
    {
      ""stall_id"": ""F1"",
      ""attendee_id"": 0,
      ""walking_distance_cost"": 689
    },
    {
      ""stall_id"": ""F1"",
      ""attendee_id"": 1,
      ""walking_distance_cost"": 742
    },
    {
      ""stall_id"": ""F1"",
      ""attendee_id"": 2,
      ""walking_distance_cost"": 898
    },
    {
      ""stall_id"": ""F1"",
      ""attendee_id"": 3,
      ""walking_distance_cost"": 681
    },
    {
      ""stall_id"": ""F1"",
      ""attendee_id"": 4,
      ""walking_distance_cost"": 661
    },
    {
      ""stall_id"": ""F1"",
      ""attendee_id"": 5,
      ""walking_distance_cost"": 438
    },
    {
      ""stall_id"": ""F1"",
      ""attendee_id"": 6,
      ""walking_distance_cost"": 210
    },
    {
      ""stall_id"": ""F2"",
      ""attendee_id"": 0,
      ""walking_distance_cost"": 465
    },
    {
      ""stall_id"": ""F2"",
      ""attendee_id"": 1,
      ""walking_distance_cost"": 317
    },
    {
      ""stall_id"": ""F2"",
      ""attendee_id"": 2,
      ""walking_distance_cost"": 669
    },
    {
      ""stall_id"": ""F2"",
      ""attendee_id"": 3,
      ""walking_distance_cost"": 727
    },
    {
      ""stall_id"": ""F2"",
      ""attendee_id"": 4,
      ""walking_distance_cost"": 907
    },
    {
      ""stall_id"": ""F2"",
      ""attendee_id"": 5,
      ""walking_distance_cost"": 973
    },
    {
      ""stall_id"": ""F2"",
      ""attendee_id"": 6,
      ""walking_distance_cost"": 206
    },
    {
      ""stall_id"": ""F3"",
      ""attendee_id"": 0,
      ""walking_distance_cost"": 1
    },
    {
      ""stall_id"": ""F3"",
      ""attendee_id"": 1,
      ""walking_distance_cost"": 280
    },
    {
      ""stall_id"": ""F3"",
      ""attendee_id"": 2,
      ""walking_distance_cost"": 6
    },
    {
      ""stall_id"": ""F3"",
      ""attendee_id"": 3,
      ""walking_distance_cost"": 324
    },
    {
      ""stall_id"": ""F3"",
      ""attendee_id"": 4,
      ""walking_distance_cost"": 131
    },
    {
      ""stall_id"": ""F3"",
      ""attendee_id"": 5,
      ""walking_distance_cost"": 698
    },
    {
      ""stall_id"": ""F3"",
      ""attendee_id"": 6,
      ""walking_distance_cost"": 691
    }
  ]
}

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': [9182, 1373, 4548], 'connection_costs': [[689, 742, 898, 681, 661, 438, 210], [465, 317, 669, 727, 907, 973, 206], [1, 280, 6, 324, 131, 698, 691]], 'objective': 5637.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1, 1]}",5637.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 9182}, {'id': 'F2', 'opening_cost': 1373}, {'id': 'F3', 'opening_cost': 4548}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 689}, {'facility': 'F1', 'customer': 1, 'cost': 742}, {'facility': 'F1', 'customer': 2, 'cost': 898}, {'facility': 'F1', 'customer': 3, 'cost': 681}, {'facility': 'F1', 'customer': 4, 'cost': 661}, {'facility': 'F1', 'customer': 5, 'cost': 438}, {'facility': 'F1', 'customer': 6, 'cost': 210}, {'facility': 'F2', 'customer': 0, 'cost': 465}, {'facility': 'F2', 'customer': 1, 'cost': 317}, {'facility': 'F2', 'customer': 2, 'cost': 669}, {'facility': 'F2', 'customer': 3, 'cost': 727}, {'facility': 'F2', 'customer': 4, 'cost': 907}, {'facility': 'F2', 'customer': 5, 'cost': 973}, {'facility': 'F2', 'customer': 6, 'cost': 206}, {'facility': 'F3', 'customer': 0, 'cost': 1}, {'facility': 'F3', 'customer': 1, 'cost': 280}, {'facility': 'F3', 'customer': 2, 'cost': 6}, {'facility': 'F3', 'customer': 3, 'cost': 324}, {'facility': 'F3', 'customer': 4, 'cost': 131}, {'facility': 'F3', 'customer': 5, 'cost': 698}, {'facility': 'F3', 'customer': 6, 'cost': 691}], 'objective': 5637.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",12,json,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"": 2,
  ""num_freelancers"": 5,
  ""pods"": [
    {
      ""pod_id"": ""F1"",
      ""pod_setup_cost"": 1361
    },
    {
      ""pod_id"": ""F2"",
      ""pod_setup_cost"": 1833
    }
  ],
  ""freelancers"": [
    {
      ""freelancer_id"": 0
    },
    {
      ""freelancer_id"": 1
    },
    {
      ""freelancer_id"": 2
    },
    {
      ""freelancer_id"": 3
    },
    {
      ""freelancer_id"": 4
    }
  ],
  ""commute_inconveniences"": [
    {
      ""pod_id"": ""F1"",
      ""freelancer_id"": 0,
      ""commute_inconvenience_cost"": 900
    },
    {
      ""pod_id"": ""F1"",
      ""freelancer_id"": 1,
      ""commute_inconvenience_cost"": 420
    },
    {
      ""pod_id"": ""F1"",
      ""freelancer_id"": 2,
      ""commute_inconvenience_cost"": 851
    },
    {
      ""pod_id"": ""F1"",
      ""freelancer_id"": 3,
      ""commute_inconvenience_cost"": 528
    },
    {
      ""pod_id"": ""F1"",
      ""freelancer_id"": 4,
      ""commute_inconvenience_cost"": 892
    },
    {
      ""pod_id"": ""F2"",
      ""freelancer_id"": 0,
      ""commute_inconvenience_cost"": 364
    },
    {
      ""pod_id"": ""F2"",
      ""freelancer_id"": 1,
      ""commute_inconvenience_cost"": 81
    },
    {
      ""pod_id"": ""F2"",
      ""freelancer_id"": 2,
      ""commute_inconvenience_cost"": 709
    },
    {
      ""pod_id"": ""F2"",
      ""freelancer_id"": 3,
      ""commute_inconvenience_cost"": 840
    },
    {
      ""pod_id"": ""F2"",
      ""freelancer_id"": 4,
      ""commute_inconvenience_cost"": 186
    }
  ]
}

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': [1361, 1833], 'connection_costs': [[900, 420, 851, 528, 892], [364, 81, 709, 840, 186]], 'objective': 4013.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1]}",4013.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 1361}, {'id': 'F2', 'opening_cost': 1833}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 900}, {'facility': 'F1', 'customer': 1, 'cost': 420}, {'facility': 'F1', 'customer': 2, 'cost': 851}, {'facility': 'F1', 'customer': 3, 'cost': 528}, {'facility': 'F1', 'customer': 4, 'cost': 892}, {'facility': 'F2', 'customer': 0, 'cost': 364}, {'facility': 'F2', 'customer': 1, 'cost': 81}, {'facility': 'F2', 'customer': 2, 'cost': 709}, {'facility': 'F2', 'customer': 3, 'cost': 840}, {'facility': 'F2', 'customer': 4, 'cost': 186}], 'objective': 4013.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2']}",13,json,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"": 2,
  ""num_students"": 5,
  ""trailers"": [
    {
      ""trailer_id"": ""F1"",
      ""trailer_bring_cost"": 1731
    },
    {
      ""trailer_id"": ""F2"",
      ""trailer_bring_cost"": 1397
    }
  ],
  ""students"": [
    {
      ""student_id"": 1
    },
    {
      ""student_id"": 2
    },
    {
      ""student_id"": 3
    },
    {
      ""student_id"": 4
    },
    {
      ""student_id"": 5
    }
  ],
  ""student_travel_times"": [
    {
      ""trailer_id"": ""F1"",
      ""student_id"": 1,
      ""student_travel_time_cost"": 571
    },
    {
      ""trailer_id"": ""F1"",
      ""student_id"": 2,
      ""student_travel_time_cost"": 761
    },
    {
      ""trailer_id"": ""F1"",
      ""student_id"": 3,
      ""student_travel_time_cost"": 359
    },
    {
      ""trailer_id"": ""F1"",
      ""student_id"": 4,
      ""student_travel_time_cost"": 299
    },
    {
      ""trailer_id"": ""F1"",
      ""student_id"": 5,
      ""student_travel_time_cost"": 283
    },
    {
      ""trailer_id"": ""F2"",
      ""student_id"": 1,
      ""student_travel_time_cost"": 817
    },
    {
      ""trailer_id"": ""F2"",
      ""student_id"": 2,
      ""student_travel_time_cost"": 449
    },
    {
      ""trailer_id"": ""F2"",
      ""student_id"": 3,
      ""student_travel_time_cost"": 121
    },
    {
      ""trailer_id"": ""F2"",
      ""student_id"": 4,
      ""student_travel_time_cost"": 299
    },
    {
      ""trailer_id"": ""F2"",
      ""student_id"": 5,
      ""student_travel_time_cost"": 695
    }
  ]
}

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': [1731, 1397], 'connection_costs': [[571, 761, 359, 299, 283], [817, 449, 121, 299, 695]], 'objective': 3778.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1]}",3778.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 1731}, {'id': 'F2', 'opening_cost': 1397}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 571}, {'facility': 'F1', 'customer': 2, 'cost': 761}, {'facility': 'F1', 'customer': 3, 'cost': 359}, {'facility': 'F1', 'customer': 4, 'cost': 299}, {'facility': 'F1', 'customer': 5, 'cost': 283}, {'facility': 'F2', 'customer': 1, 'cost': 817}, {'facility': 'F2', 'customer': 2, 'cost': 449}, {'facility': 'F2', 'customer': 3, 'cost': 121}, {'facility': 'F2', 'customer': 4, 'cost': 299}, {'facility': 'F2', 'customer': 5, 'cost': 695}], 'objective': 3778.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2']}",14,json,1
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"": 3,
  ""total_blocks"": 6,
  ""sites"": [
    {
      ""site_id"": ""F1"",
      ""maintenance_fee"": 2000
    },
    {
      ""site_id"": ""F2"",
      ""maintenance_fee"": 2000
    },
    {
      ""site_id"": ""F3"",
      ""maintenance_fee"": 2000
    }
  ],
  ""blocks"": [
    {
      ""block_id"": ""A""
    },
    {
      ""block_id"": ""B""
    },
    {
      ""block_id"": ""C""
    },
    {
      ""block_id"": ""D""
    },
    {
      ""block_id"": ""E""
    },
    {
      ""block_id"": ""F""
    }
  ],
  ""walking_distances"": [
    {
      ""site_id"": ""F1"",
      ""block_id"": ""A"",
      ""walking_distance"": 817
    },
    {
      ""site_id"": ""F1"",
      ""block_id"": ""B"",
      ""walking_distance"": 926
    },
    {
      ""site_id"": ""F1"",
      ""block_id"": ""C"",
      ""walking_distance"": 361
    },
    {
      ""site_id"": ""F1"",
      ""block_id"": ""D"",
      ""walking_distance"": 608
    },
    {
      ""site_id"": ""F1"",
      ""block_id"": ""E"",
      ""walking_distance"": 924
    },
    {
      ""site_id"": ""F1"",
      ""block_id"": ""F"",
      ""walking_distance"": 783
    },
    {
      ""site_id"": ""F2"",
      ""block_id"": ""A"",
      ""walking_distance"": 191
    },
    {
      ""site_id"": ""F2"",
      ""block_id"": ""B"",
      ""walking_distance"": 371
    },
    {
      ""site_id"": ""F2"",
      ""block_id"": ""C"",
      ""walking_distance"": 200
    },
    {
      ""site_id"": ""F2"",
      ""block_id"": ""D"",
      ""walking_distance"": 4
    },
    {
      ""site_id"": ""F2"",
      ""block_id"": ""E"",
      ""walking_distance"": 855
    },
    {
      ""site_id"": ""F2"",
      ""block_id"": ""F"",
      ""walking_distance"": 463
    },
    {
      ""site_id"": ""F3"",
      ""block_id"": ""A"",
      ""walking_distance"": 86
    },
    {
      ""site_id"": ""F3"",
      ""block_id"": ""B"",
      ""walking_distance"": 563
    },
    {
      ""site_id"": ""F3"",
      ""block_id"": ""C"",
      ""walking_distance"": 146
    },
    {
      ""site_id"": ""F3"",
      ""block_id"": ""D"",
      ""walking_distance"": 499
    },
    {
      ""site_id"": ""F3"",
      ""block_id"": ""E"",
      ""walking_distance"": 814
    },
    {
      ""site_id"": ""F3"",
      ""block_id"": ""F"",
      ""walking_distance"": 648
    }
  ]
}

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': [2000, 2000, 2000], 'connection_costs': [[817, 926, 361, 608, 924, 783], [191, 371, 200, 4, 855, 463], [86, 563, 146, 499, 814, 648]], 'objective': 4084.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1]}",4084.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 817}, {'facility': 'F1', 'customer': 'B', 'cost': 926}, {'facility': 'F1', 'customer': 'C', 'cost': 361}, {'facility': 'F1', 'customer': 'D', 'cost': 608}, {'facility': 'F1', 'customer': 'E', 'cost': 924}, {'facility': 'F1', 'customer': 'F', 'cost': 783}, {'facility': 'F2', 'customer': 'A', 'cost': 191}, {'facility': 'F2', 'customer': 'B', 'cost': 371}, {'facility': 'F2', 'customer': 'C', 'cost': 200}, {'facility': 'F2', 'customer': 'D', 'cost': 4}, {'facility': 'F2', 'customer': 'E', 'cost': 855}, {'facility': 'F2', 'customer': 'F', 'cost': 463}, {'facility': 'F3', 'customer': 'A', 'cost': 86}, {'facility': 'F3', 'customer': 'B', 'cost': 563}, {'facility': 'F3', 'customer': 'C', 'cost': 146}, {'facility': 'F3', 'customer': 'D', 'cost': 499}, {'facility': 'F3', 'customer': 'E', 'cost': 814}, {'facility': 'F3', 'customer': 'F', 'cost': 648}], 'objective': 4084.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",15,json,names
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.

# num_candidate_stands=3
# num_regular_customers=6
# STANDS
stand_id,stand_opening_cost
F1,2000
F2,2000
F3,2000
# BUYERS
buyer_id
A
B
C
D
E
F
# TRAVELS
stand_id,buyer_id,travel_cost
F1,A,508
F1,B,378
F1,C,287
F1,D,706
F1,E,544
F1,F,127
F2,A,461
F2,B,368
F2,C,654
F2,D,341
F2,E,205
F2,F,620
F3,A,363
F3,B,957
F3,C,148
F3,D,435
F3,E,702
F3,F,794

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': [2000, 2000, 2000], 'connection_costs': [[508, 378, 287, 706, 544, 127], [461, 368, 654, 341, 205, 620], [363, 957, 148, 435, 702, 794]], 'objective': 4550.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0]}",4550.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 508}, {'facility': 'F1', 'customer': 'B', 'cost': 378}, {'facility': 'F1', 'customer': 'C', 'cost': 287}, {'facility': 'F1', 'customer': 'D', 'cost': 706}, {'facility': 'F1', 'customer': 'E', 'cost': 544}, {'facility': 'F1', 'customer': 'F', 'cost': 127}, {'facility': 'F2', 'customer': 'A', 'cost': 461}, {'facility': 'F2', 'customer': 'B', 'cost': 368}, {'facility': 'F2', 'customer': 'C', 'cost': 654}, {'facility': 'F2', 'customer': 'D', 'cost': 341}, {'facility': 'F2', 'customer': 'E', 'cost': 205}, {'facility': 'F2', 'customer': 'F', 'cost': 620}, {'facility': 'F3', 'customer': 'A', 'cost': 363}, {'facility': 'F3', 'customer': 'B', 'cost': 957}, {'facility': 'F3', 'customer': 'C', 'cost': 148}, {'facility': 'F3', 'customer': 'D', 'cost': 435}, {'facility': 'F3', 'customer': 'E', 'cost': 702}, {'facility': 'F3', 'customer': 'F', 'cost': 794}], 'objective': 4550.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",16,csv,names
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.

There are 3 candidate rooms, 6 musicians, and the room upkeep costs are 2000, 2000, 2000.
Room F1 has upkeep cost 2000.
Room F2 has upkeep cost 2000.
Room F3 has upkeep cost 2000.
Musician 0 incurs walking time 875 to room F1.
Musician 1 incurs walking time 51 to room F1.
Musician 2 incurs walking time 711 to room F1.
Musician 3 incurs walking time 331 to room F1.
Musician 4 incurs walking time 38 to room F1.
Musician 5 incurs walking time 362 to room F1.
Musician 0 incurs walking time 859 to room F2.
Musician 1 incurs walking time 625 to room F2.
Musician 2 incurs walking time 127 to room F2.
Musician 3 incurs walking time 547 to room F2.
Musician 4 incurs walking time 991 to room F2.
Musician 5 incurs walking time 255 to room F2.
Musician 0 incurs walking time 520 to room F3.
Musician 1 incurs walking time 793 to room F3.
Musician 2 incurs walking time 623 to room F3.
Musician 3 incurs walking time 331 to room F3.
Musician 4 incurs walking time 353 to room F3.
Musician 5 incurs walking time 241 to room F3.
The director will choose the open rooms and assignments that minimize total room upkeep plus walking time.

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': [2000, 2000, 2000], 'connection_costs': [[875, 51, 711, 331, 38, 362], [859, 625, 127, 547, 991, 255], [520, 793, 623, 331, 353, 241]], 'objective': 4368.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0]}",4368.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 875}, {'facility': 'F1', 'customer': 1, 'cost': 51}, {'facility': 'F1', 'customer': 2, 'cost': 711}, {'facility': 'F1', 'customer': 3, 'cost': 331}, {'facility': 'F1', 'customer': 4, 'cost': 38}, {'facility': 'F1', 'customer': 5, 'cost': 362}, {'facility': 'F2', 'customer': 0, 'cost': 859}, {'facility': 'F2', 'customer': 1, 'cost': 625}, {'facility': 'F2', 'customer': 2, 'cost': 127}, {'facility': 'F2', 'customer': 3, 'cost': 547}, {'facility': 'F2', 'customer': 4, 'cost': 991}, {'facility': 'F2', 'customer': 5, 'cost': 255}, {'facility': 'F3', 'customer': 0, 'cost': 520}, {'facility': 'F3', 'customer': 1, 'cost': 793}, {'facility': 'F3', 'customer': 2, 'cost': 623}, {'facility': 'F3', 'customer': 3, 'cost': 331}, {'facility': 'F3', 'customer': 4, 'cost': 353}, {'facility': 'F3', 'customer': 5, 'cost': 241}], 'objective': 4368.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",17,nl,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=4
# total_donors=8
# BOXS
box_id,installation_fee
F1,1530
F2,1780
F3,1433
F4,1638
# DONORS
donor_id
A
B
C
D
E
F
G
H
# DONOR_DETOURS
box_id,donor_id,donor_detour_cost
F1,A,691
F1,B,899
F1,C,993
F1,D,62
F1,E,635
F1,F,265
F1,G,216
F1,H,628
F2,A,693
F2,B,866
F2,C,729
F2,D,426
F2,E,470
F2,F,435
F2,G,455
F2,H,721
F3,A,499
F3,B,376
F3,C,481
F3,D,290
F3,E,435
F3,F,966
F3,G,302
F3,H,503
F4,A,908
F4,B,933
F4,C,294
F4,D,328
F4,E,863
F4,F,224
F4,G,693
F4,H,312

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': [1530, 1780, 1433, 1638], 'connection_costs': [[691, 899, 993, 62, 635, 265, 216, 628], [693, 866, 729, 426, 470, 435, 455, 721], [499, 376, 481, 290, 435, 966, 302, 503], [908, 933, 294, 328, 863, 224, 693, 312]], 'objective': 5285.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2]}",5285.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 8, 'facilities': [{'id': 'F1', 'opening_cost': 1530}, {'id': 'F2', 'opening_cost': 1780}, {'id': 'F3', 'opening_cost': 1433}, {'id': 'F4', 'opening_cost': 1638}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 691}, {'facility': 'F1', 'customer': 'B', 'cost': 899}, {'facility': 'F1', 'customer': 'C', 'cost': 993}, {'facility': 'F1', 'customer': 'D', 'cost': 62}, {'facility': 'F1', 'customer': 'E', 'cost': 635}, {'facility': 'F1', 'customer': 'F', 'cost': 265}, {'facility': 'F1', 'customer': 'G', 'cost': 216}, {'facility': 'F1', 'customer': 'H', 'cost': 628}, {'facility': 'F2', 'customer': 'A', 'cost': 693}, {'facility': 'F2', 'customer': 'B', 'cost': 866}, {'facility': 'F2', 'customer': 'C', 'cost': 729}, {'facility': 'F2', 'customer': 'D', 'cost': 426}, {'facility': 'F2', 'customer': 'E', 'cost': 470}, {'facility': 'F2', 'customer': 'F', 'cost': 435}, {'facility': 'F2', 'customer': 'G', 'cost': 455}, {'facility': 'F2', 'customer': 'H', 'cost': 721}, {'facility': 'F3', 'customer': 'A', 'cost': 499}, {'facility': 'F3', 'customer': 'B', 'cost': 376}, {'facility': 'F3', 'customer': 'C', 'cost': 481}, {'facility': 'F3', 'customer': 'D', 'cost': 290}, {'facility': 'F3', 'customer': 'E', 'cost': 435}, {'facility': 'F3', 'customer': 'F', 'cost': 966}, {'facility': 'F3', 'customer': 'G', 'cost': 302}, {'facility': 'F3', 'customer': 'H', 'cost': 503}, {'facility': 'F4', 'customer': 'A', 'cost': 908}, {'facility': 'F4', 'customer': 'B', 'cost': 933}, {'facility': 'F4', 'customer': 'C', 'cost': 294}, {'facility': 'F4', 'customer': 'D', 'cost': 328}, {'facility': 'F4', 'customer': 'E', 'cost': 863}, {'facility': 'F4', 'customer': 'F', 'cost': 224}, {'facility': 'F4', 'customer': 'G', 'cost': 693}, {'facility': 'F4', 'customer': 'H', 'cost': 312}], 'objective': 5285.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",18,csv,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.

# num_kitchens=2
# num_people_in_need=5
# KITCHENS
kitchen_id,kitchen_funding_cost
F1,2139
F2,9278
# PERSONS
person_id
A
B
C
D
E
# TRAVELS
kitchen_id,person_id,travel_cost
F1,A,429
F1,B,393
F1,C,476
F1,D,235
F1,E,750
F2,A,826
F2,B,514
F2,C,844
F2,D,812
F2,E,775

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': [2139, 9278], 'connection_costs': [[429, 393, 476, 235, 750], [826, 514, 844, 812, 775]], 'objective': 4422.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0]}",4422.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 2139}, {'id': 'F2', 'opening_cost': 9278}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 429}, {'facility': 'F1', 'customer': 'B', 'cost': 393}, {'facility': 'F1', 'customer': 'C', 'cost': 476}, {'facility': 'F1', 'customer': 'D', 'cost': 235}, {'facility': 'F1', 'customer': 'E', 'cost': 750}, {'facility': 'F2', 'customer': 'A', 'cost': 826}, {'facility': 'F2', 'customer': 'B', 'cost': 514}, {'facility': 'F2', 'customer': 'C', 'cost': 844}, {'facility': 'F2', 'customer': 'D', 'cost': 812}, {'facility': 'F2', 'customer': 'E', 'cost': 775}], 'objective': 4422.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1']}",19,csv,names
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 3 candidate servers to power for 6 devices, with server startup costs 2000, 2000, 2000.
Candidate server F1 can be powered at startup cost 2000.
Candidate server F2 can be powered at startup cost 2000.
Candidate server F3 can be powered at startup cost 2000.
If device 0 is attached to server F1, it incurs latency cost 560.
If device 1 is attached to server F1, it incurs latency cost 625.
If device 2 is attached to server F1, it incurs latency cost 469.
If device 3 is attached to server F1, it incurs latency cost 353.
If device 4 is attached to server F1, it incurs latency cost 749.
If device 5 is attached to server F1, it incurs latency cost 692.
If device 0 is attached to server F2, it incurs latency cost 256.
If device 1 is attached to server F2, it incurs latency cost 38.
If device 2 is attached to server F2, it incurs latency cost 864.
If device 3 is attached to server F2, it incurs latency cost 70.
If device 4 is attached to server F2, it incurs latency cost 654.
If device 5 is attached to server F2, it incurs latency cost 344.
If device 0 is attached to server F3, it incurs latency cost 599.
If device 1 is attached to server F3, it incurs latency cost 889.
If device 2 is attached to server F3, it incurs latency cost 674.
If device 3 is attached to server F3, it incurs latency cost 667.
If device 4 is attached to server F3, it incurs latency cost 98.
If device 5 is attached to server F3, it incurs latency cost 598.
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': [2000, 2000, 2000], 'connection_costs': [[560, 625, 469, 353, 749, 692], [256, 38, 864, 70, 654, 344], [599, 889, 674, 667, 98, 598]], 'objective': 4226.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1]}",4226.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 560}, {'facility': 'F1', 'customer': 1, 'cost': 625}, {'facility': 'F1', 'customer': 2, 'cost': 469}, {'facility': 'F1', 'customer': 3, 'cost': 353}, {'facility': 'F1', 'customer': 4, 'cost': 749}, {'facility': 'F1', 'customer': 5, 'cost': 692}, {'facility': 'F2', 'customer': 0, 'cost': 256}, {'facility': 'F2', 'customer': 1, 'cost': 38}, {'facility': 'F2', 'customer': 2, 'cost': 864}, {'facility': 'F2', 'customer': 3, 'cost': 70}, {'facility': 'F2', 'customer': 4, 'cost': 654}, {'facility': 'F2', 'customer': 5, 'cost': 344}, {'facility': 'F3', 'customer': 0, 'cost': 599}, {'facility': 'F3', 'customer': 1, 'cost': 889}, {'facility': 'F3', 'customer': 2, 'cost': 674}, {'facility': 'F3', 'customer': 3, 'cost': 667}, {'facility': 'F3', 'customer': 4, 'cost': 98}, {'facility': 'F3', 'customer': 5, 'cost': 598}], 'objective': 4226.0}","{'selected': ['F2'], 'assignments': ['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 3 stations and 7 users in this instance.

**Stations**
| station_id | activation_cost |
|---|---|
| F1 | 1000 |
| F2 | 1000 |
| F3 | 1000 |

**Users**
| user_id |
|---|
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| 7 |

**Detour Cost**
| station_id | user_id | detour_cost |
|---|---|---|
| F1 | 1 | 513 |
| F1 | 2 | 435 |
| F1 | 3 | 467 |
| F1 | 4 | 305 |
| F1 | 5 | 376 |
| F1 | 6 | 152 |
| F1 | 7 | 427 |
| F2 | 1 | 121 |
| F2 | 2 | 448 |
| F2 | 3 | 114 |
| F2 | 4 | 325 |
| F2 | 5 | 583 |
| F2 | 6 | 307 |
| F2 | 7 | 910 |
| F3 | 1 | 764 |
| F3 | 2 | 746 |
| F3 | 3 | 284 |
| F3 | 4 | 44 |
| F3 | 5 | 40 |
| F3 | 6 | 443 |
| F3 | 7 | 140 |

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': [1000, 1000, 1000], 'connection_costs': [[513, 435, 467, 305, 376, 152, 427], [121, 448, 114, 325, 583, 307, 910], [764, 746, 284, 44, 40, 443, 140]], 'objective': 3214.0}","{'open_facilities': [1, 2], 'assignments': [1, 1, 1, 2, 2, 1, 2]}",3214.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 513}, {'facility': 'F1', 'customer': 2, 'cost': 435}, {'facility': 'F1', 'customer': 3, 'cost': 467}, {'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': 'F2', 'customer': 1, 'cost': 121}, {'facility': 'F2', 'customer': 2, 'cost': 448}, {'facility': 'F2', 'customer': 3, 'cost': 114}, {'facility': 'F2', 'customer': 4, 'cost': 325}, {'facility': 'F2', 'customer': 5, 'cost': 583}, {'facility': 'F2', 'customer': 6, 'cost': 307}, {'facility': 'F2', 'customer': 7, 'cost': 910}, {'facility': 'F3', 'customer': 1, 'cost': 764}, {'facility': 'F3', 'customer': 2, 'cost': 746}, {'facility': 'F3', 'customer': 3, 'cost': 284}, {'facility': 'F3', 'customer': 4, 'cost': 44}, {'facility': 'F3', 'customer': 5, 'cost': 40}, {'facility': 'F3', 'customer': 6, 'cost': 443}, {'facility': 'F3', 'customer': 7, 'cost': 140}], 'objective': 3214.0}","{'selected': ['F2', 'F3'], 'assignments': ['F2', 'F2', 'F2', 'F3', 'F3', 'F2', 'F3']}",21,markdown_table,1
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.

There are 3 rooms and 6 students in this instance.

**Rooms**
| room_id | room_rental_cost |
|---|---|
| F1 | 6680 |
| F2 | 1941 |
| F3 | 7239 |

**Students**
| student_id |
|---|
| 0 |
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |

**Student Travel Cost**
| room_id | student_id | student_travel_cost |
|---|---|---|
| F1 | 0 | 348 |
| F1 | 1 | 559 |
| F1 | 2 | 952 |
| F1 | 3 | 970 |
| F1 | 4 | 615 |
| F1 | 5 | 859 |
| F2 | 0 | 942 |
| F2 | 1 | 162 |
| F2 | 2 | 937 |
| F2 | 3 | 462 |
| F2 | 4 | 68 |
| F2 | 5 | 70 |
| F3 | 0 | 392 |
| F3 | 1 | 965 |
| F3 | 2 | 694 |
| F3 | 3 | 699 |
| F3 | 4 | 288 |
| F3 | 5 | 257 |

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': [6680, 1941, 7239], 'connection_costs': [[348, 559, 952, 970, 615, 859], [942, 162, 937, 462, 68, 70], [392, 965, 694, 699, 288, 257]], 'objective': 4582.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1]}",4582.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 6680}, {'id': 'F2', 'opening_cost': 1941}, {'id': 'F3', 'opening_cost': 7239}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 348}, {'facility': 'F1', 'customer': 1, 'cost': 559}, {'facility': 'F1', 'customer': 2, 'cost': 952}, {'facility': 'F1', 'customer': 3, 'cost': 970}, {'facility': 'F1', 'customer': 4, 'cost': 615}, {'facility': 'F1', 'customer': 5, 'cost': 859}, {'facility': 'F2', 'customer': 0, 'cost': 942}, {'facility': 'F2', 'customer': 1, 'cost': 162}, {'facility': 'F2', 'customer': 2, 'cost': 937}, {'facility': 'F2', 'customer': 3, 'cost': 462}, {'facility': 'F2', 'customer': 4, 'cost': 68}, {'facility': 'F2', 'customer': 5, 'cost': 70}, {'facility': 'F3', 'customer': 0, 'cost': 392}, {'facility': 'F3', 'customer': 1, 'cost': 965}, {'facility': 'F3', 'customer': 2, 'cost': 694}, {'facility': 'F3', 'customer': 3, 'cost': 699}, {'facility': 'F3', 'customer': 4, 'cost': 288}, {'facility': 'F3', 'customer': 5, 'cost': 257}], 'objective': 4582.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",22,markdown_table,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=2
# num_patrons=5
# STOPS
stop_id,stop_operating_cost
F1,2000
F2,2000
# PATRONS
patron_id
0
1
2
3
4
# TRAVEL_DISTANCES
stop_id,patron_id,travel_distance_cost
F1,0,100
F1,1,954
F1,2,299
F1,3,587
F1,4,675
F2,0,859
F2,1,691
F2,2,25
F2,3,356
F2,4,19

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': [2000, 2000], 'connection_costs': [[100, 954, 299, 587, 675], [859, 691, 25, 356, 19]], 'objective': 3950.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1]}",3950.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 100}, {'facility': 'F1', 'customer': 1, 'cost': 954}, {'facility': 'F1', 'customer': 2, 'cost': 299}, {'facility': 'F1', 'customer': 3, 'cost': 587}, {'facility': 'F1', 'customer': 4, 'cost': 675}, {'facility': 'F2', 'customer': 0, 'cost': 859}, {'facility': 'F2', 'customer': 1, 'cost': 691}, {'facility': 'F2', 'customer': 2, 'cost': 25}, {'facility': 'F2', 'customer': 3, 'cost': 356}, {'facility': 'F2', 'customer': 4, 'cost': 19}], 'objective': 3950.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2']}",23,csv,0
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=8
# DISTRIBUTION_POINTS
distribution_point_id,setup_cost
F1,1000
F2,1000
F3,1000
F4,1000
# VENDORS
vendor_id
0
1
2
3
4
5
6
7
# HAULINGS
distribution_point_id,vendor_id,hauling_cost
F1,0,977
F1,1,562
F1,2,257
F1,3,810
F1,4,909
F1,5,5
F1,6,691
F1,7,852
F2,0,17
F2,1,635
F2,2,81
F2,3,864
F2,4,747
F2,5,971
F2,6,638
F2,7,723
F3,0,814
F3,1,543
F3,2,684
F3,3,456
F3,4,503
F3,5,773
F3,6,4
F3,7,122
F4,0,594
F4,1,368
F4,2,416
F4,3,219
F4,4,940
F4,5,251
F4,6,816
F4,7,762

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': [1000, 1000, 1000, 1000], 'connection_costs': [[977, 562, 257, 810, 909, 5, 691, 852], [17, 635, 81, 864, 747, 971, 638, 723], [814, 543, 684, 456, 503, 773, 4, 122], [594, 368, 416, 219, 940, 251, 816, 762]], 'objective': 4477.0}","{'open_facilities': [2, 3], 'assignments': [3, 3, 3, 3, 2, 3, 2, 2]}",4477.0,"{'problem_type': 'UFLP', 'num_facilities': 4, 'num_customers': 8, '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}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 977}, {'facility': 'F1', 'customer': 1, 'cost': 562}, {'facility': 'F1', 'customer': 2, 'cost': 257}, {'facility': 'F1', 'customer': 3, 'cost': 810}, {'facility': 'F1', 'customer': 4, 'cost': 909}, {'facility': 'F1', 'customer': 5, 'cost': 5}, {'facility': 'F1', 'customer': 6, 'cost': 691}, {'facility': 'F1', 'customer': 7, 'cost': 852}, {'facility': 'F2', 'customer': 0, 'cost': 17}, {'facility': 'F2', 'customer': 1, 'cost': 635}, {'facility': 'F2', 'customer': 2, 'cost': 81}, {'facility': 'F2', 'customer': 3, 'cost': 864}, {'facility': 'F2', 'customer': 4, 'cost': 747}, {'facility': 'F2', 'customer': 5, 'cost': 971}, {'facility': 'F2', 'customer': 6, 'cost': 638}, {'facility': 'F2', 'customer': 7, 'cost': 723}, {'facility': 'F3', 'customer': 0, 'cost': 814}, {'facility': 'F3', 'customer': 1, 'cost': 543}, {'facility': 'F3', 'customer': 2, 'cost': 684}, {'facility': 'F3', 'customer': 3, 'cost': 456}, {'facility': 'F3', 'customer': 4, 'cost': 503}, {'facility': 'F3', 'customer': 5, 'cost': 773}, {'facility': 'F3', 'customer': 6, 'cost': 4}, {'facility': 'F3', 'customer': 7, 'cost': 122}, {'facility': 'F4', 'customer': 0, 'cost': 594}, {'facility': 'F4', 'customer': 1, 'cost': 368}, {'facility': 'F4', 'customer': 2, 'cost': 416}, {'facility': 'F4', 'customer': 3, 'cost': 219}, {'facility': 'F4', 'customer': 4, 'cost': 940}, {'facility': 'F4', 'customer': 5, 'cost': 251}, {'facility': 'F4', 'customer': 6, 'cost': 816}, {'facility': 'F4', 'customer': 7, 'cost': 762}], 'objective': 4477.0}","{'selected': ['F3', 'F4'], 'assignments': ['F4', 'F4', 'F4', 'F4', 'F3', 'F4', 'F3', 'F3']}",24,csv,0
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.

# num_candidate_booths=3
# num_attendees=6
# BOOTHS
booth_id,staffing_fee
F1,1880
F2,1974
F3,1670
# ATTENDEES
attendee_id
0
1
2
3
4
5
# WALKINGS
booth_id,attendee_id,walking_cost
F1,0,126
F1,1,49
F1,2,835
F1,3,506
F1,4,880
F1,5,787
F2,0,691
F2,1,682
F2,2,214
F2,3,100
F2,4,292
F2,5,568
F3,0,447
F3,1,909
F3,2,652
F3,3,896
F3,4,625
F3,5,16

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': [1880, 1974, 1670], 'connection_costs': [[126, 49, 835, 506, 880, 787], [691, 682, 214, 100, 292, 568], [447, 909, 652, 896, 625, 16]], 'objective': 4521.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1]}",4521.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 1880}, {'id': 'F2', 'opening_cost': 1974}, {'id': 'F3', 'opening_cost': 1670}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 126}, {'facility': 'F1', 'customer': 1, 'cost': 49}, {'facility': 'F1', 'customer': 2, 'cost': 835}, {'facility': 'F1', 'customer': 3, 'cost': 506}, {'facility': 'F1', 'customer': 4, 'cost': 880}, {'facility': 'F1', 'customer': 5, 'cost': 787}, {'facility': 'F2', 'customer': 0, 'cost': 691}, {'facility': 'F2', 'customer': 1, 'cost': 682}, {'facility': 'F2', 'customer': 2, 'cost': 214}, {'facility': 'F2', 'customer': 3, 'cost': 100}, {'facility': 'F2', 'customer': 4, 'cost': 292}, {'facility': 'F2', 'customer': 5, 'cost': 568}, {'facility': 'F3', 'customer': 0, 'cost': 447}, {'facility': 'F3', 'customer': 1, 'cost': 909}, {'facility': 'F3', 'customer': 2, 'cost': 652}, {'facility': 'F3', 'customer': 3, 'cost': 896}, {'facility': 'F3', 'customer': 4, 'cost': 625}, {'facility': 'F3', 'customer': 5, 'cost': 16}], 'objective': 4521.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",25,csv,0
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"": 8,
  ""depots"": [
    {
      ""depot_id"": ""F1"",
      ""depot_startup_cost"": 2000
    },
    {
      ""depot_id"": ""F2"",
      ""depot_startup_cost"": 2000
    },
    {
      ""depot_id"": ""F3"",
      ""depot_startup_cost"": 2000
    }
  ],
  ""deliverys"": [
    {
      ""depot_id"": ""F1"",
      ""delivery_id"": ""A"",
      ""delivery_cost"": 103
    },
    {
      ""depot_id"": ""F1"",
      ""delivery_id"": ""B"",
      ""delivery_cost"": 174
    },
    {
      ""depot_id"": ""F1"",
      ""delivery_id"": ""C"",
      ""delivery_cost"": 349
    },
    {
      ""depot_id"": ""F1"",
      ""delivery_id"": ""D"",
      ""delivery_cost"": 896
    },
    {
      ""depot_id"": ""F1"",
      ""delivery_id"": ""E"",
      ""delivery_cost"": 735
    },
    {
      ""depot_id"": ""F1"",
      ""delivery_id"": ""F"",
      ""delivery_cost"": 225
    },
    {
      ""depot_id"": ""F1"",
      ""delivery_id"": ""G"",
      ""delivery_cost"": 197
    },
    {
      ""depot_id"": ""F1"",
      ""delivery_id"": ""H"",
      ""delivery_cost"": 641
    },
    {
      ""depot_id"": ""F2"",
      ""delivery_id"": ""A"",
      ""delivery_cost"": 897
    },
    {
      ""depot_id"": ""F2"",
      ""delivery_id"": ""B"",
      ""delivery_cost"": 244
    },
    {
      ""depot_id"": ""F2"",
      ""delivery_id"": ""C"",
      ""delivery_cost"": 402
    },
    {
      ""depot_id"": ""F2"",
      ""delivery_id"": ""D"",
      ""delivery_cost"": 953
    },
    {
      ""depot_id"": ""F2"",
      ""delivery_id"": ""E"",
      ""delivery_cost"": 477
    },
    {
      ""depot_id"": ""F2"",
      ""delivery_id"": ""F"",
      ""delivery_cost"": 208
    },
    {
      ""depot_id"": ""F2"",
      ""delivery_id"": ""G"",
      ""delivery_cost"": 659
    },
    {
      ""depot_id"": ""F2"",
      ""delivery_id"": ""H"",
      ""delivery_cost"": 687
    },
    {
      ""depot_id"": ""F3"",
      ""delivery_id"": ""A"",
      ""delivery_cost"": 491
    },
    {
      ""depot_id"": ""F3"",
      ""delivery_id"": ""B"",
      ""delivery_cost"": 754
    },
    {
      ""depot_id"": ""F3"",
      ""delivery_id"": ""C"",
      ""delivery_cost"": 260
    },
    {
      ""depot_id"": ""F3"",
      ""delivery_id"": ""D"",
      ""delivery_cost"": 391
    },
    {
      ""depot_id"": ""F3"",
      ""delivery_id"": ""E"",
      ""delivery_cost"": 337
    },
    {
      ""depot_id"": ""F3"",
      ""delivery_id"": ""F"",
      ""delivery_cost"": 619
    },
    {
      ""depot_id"": ""F3"",
      ""delivery_id"": ""G"",
      ""delivery_cost"": 363
    },
    {
      ""depot_id"": ""F3"",
      ""delivery_id"": ""H"",
      ""delivery_cost"": 72
    }
  ]
}

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': [2000, 2000, 2000], 'connection_costs': [[103, 174, 349, 896, 735, 225, 197, 641], [897, 244, 402, 953, 477, 208, 659, 687], [491, 754, 260, 391, 337, 619, 363, 72]], 'objective': 5287.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2]}",5287.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 8, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}, {'id': 'H'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 103}, {'facility': 'F1', 'customer': 'B', 'cost': 174}, {'facility': 'F1', 'customer': 'C', 'cost': 349}, {'facility': 'F1', 'customer': 'D', 'cost': 896}, {'facility': 'F1', 'customer': 'E', 'cost': 735}, {'facility': 'F1', 'customer': 'F', 'cost': 225}, {'facility': 'F1', 'customer': 'G', 'cost': 197}, {'facility': 'F1', 'customer': 'H', 'cost': 641}, {'facility': 'F2', 'customer': 'A', 'cost': 897}, {'facility': 'F2', 'customer': 'B', 'cost': 244}, {'facility': 'F2', 'customer': 'C', 'cost': 402}, {'facility': 'F2', 'customer': 'D', 'cost': 953}, {'facility': 'F2', 'customer': 'E', 'cost': 477}, {'facility': 'F2', 'customer': 'F', 'cost': 208}, {'facility': 'F2', 'customer': 'G', 'cost': 659}, {'facility': 'F2', 'customer': 'H', 'cost': 687}, {'facility': 'F3', 'customer': 'A', 'cost': 491}, {'facility': 'F3', 'customer': 'B', 'cost': 754}, {'facility': 'F3', 'customer': 'C', 'cost': 260}, {'facility': 'F3', 'customer': 'D', 'cost': 391}, {'facility': 'F3', 'customer': 'E', 'cost': 337}, {'facility': 'F3', 'customer': 'F', 'cost': 619}, {'facility': 'F3', 'customer': 'G', 'cost': 363}, {'facility': 'F3', 'customer': 'H', 'cost': 72}], 'objective': 5287.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",26,json,names
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: 3 candidate locker locations, 6 borrowers, installation costs 2140, 4636, 2117.
Locker F1: installation cost 2140.
Locker F2: installation cost 4636.
Locker F3: installation cost 2117.
Borrower A to locker F1: retrieval effort 574.
Borrower B to locker F1: retrieval effort 242.
Borrower C to locker F1: retrieval effort 819.
Borrower D to locker F1: retrieval effort 278.
Borrower E to locker F1: retrieval effort 959.
Borrower F to locker F1: retrieval effort 750.
Borrower A to locker F2: retrieval effort 653.
Borrower B to locker F2: retrieval effort 38.
Borrower C to locker F2: retrieval effort 135.
Borrower D to locker F2: retrieval effort 997.
Borrower E to locker F2: retrieval effort 182.
Borrower F to locker F2: retrieval effort 591.
Borrower A to locker F3: retrieval effort 906.
Borrower B to locker F3: retrieval effort 246.
Borrower C to locker F3: retrieval effort 900.
Borrower D to locker F3: retrieval effort 642.
Borrower E to locker F3: retrieval effort 418.
Borrower F to locker F3: retrieval effort 513.
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': [2140, 4636, 2117], 'connection_costs': [[574, 242, 819, 278, 959, 750], [653, 38, 135, 997, 182, 591], [906, 246, 900, 642, 418, 513]], 'objective': 5742.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2]}",5742.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 2140}, {'id': 'F2', 'opening_cost': 4636}, {'id': 'F3', 'opening_cost': 2117}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 574}, {'facility': 'F1', 'customer': 'B', 'cost': 242}, {'facility': 'F1', 'customer': 'C', 'cost': 819}, {'facility': 'F1', 'customer': 'D', 'cost': 278}, {'facility': 'F1', 'customer': 'E', 'cost': 959}, {'facility': 'F1', 'customer': 'F', 'cost': 750}, {'facility': 'F2', 'customer': 'A', 'cost': 653}, {'facility': 'F2', 'customer': 'B', 'cost': 38}, {'facility': 'F2', 'customer': 'C', 'cost': 135}, {'facility': 'F2', 'customer': 'D', 'cost': 997}, {'facility': 'F2', 'customer': 'E', 'cost': 182}, {'facility': 'F2', 'customer': 'F', 'cost': 591}, {'facility': 'F3', 'customer': 'A', 'cost': 906}, {'facility': 'F3', 'customer': 'B', 'cost': 246}, {'facility': 'F3', 'customer': 'C', 'cost': 900}, {'facility': 'F3', 'customer': 'D', 'cost': 642}, {'facility': 'F3', 'customer': 'E', 'cost': 418}, {'facility': 'F3', 'customer': 'F', 'cost': 513}], 'objective': 5742.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",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 2 candidate sites, 6 residents, and the sequence of site operating costs 1000, 1000.
Site F1: if we open it its operating cost is 1000.
Site F2: if we open it its operating cost is 1000.
Resident 1 — if we assign them to site F1 — would incur travel cost 200.
Resident 2 — if we assign them to site F1 — would incur travel cost 608.
Resident 3 — if we assign them to site F1 — would incur travel cost 584.
Resident 4 — if we assign them to site F1 — would incur travel cost 226.
Resident 5 — if we assign them to site F1 — would incur travel cost 653.
Resident 6 — if we assign them to site F1 — would incur travel cost 781.
Resident 1 — if we assign them to site F2 — would incur travel cost 812.
Resident 2 — if we assign them to site F2 — would incur travel cost 258.
Resident 3 — if we assign them to site F2 — would incur travel cost 916.
Resident 4 — if we assign them to site F2 — would incur travel cost 40.
Resident 5 — if we assign them to site F2 — would incur travel cost 580.
Resident 6 — if we assign them to site F2 — would incur travel cost 233.
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': [1000, 1000], 'connection_costs': [[200, 608, 584, 226, 653, 781], [812, 258, 916, 40, 580, 233]], 'objective': 3839.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1]}",3839.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 200}, {'facility': 'F1', 'customer': 2, 'cost': 608}, {'facility': 'F1', 'customer': 3, 'cost': 584}, {'facility': 'F1', 'customer': 4, 'cost': 226}, {'facility': 'F1', 'customer': 5, 'cost': 653}, {'facility': 'F1', 'customer': 6, 'cost': 781}, {'facility': 'F2', 'customer': 1, 'cost': 812}, {'facility': 'F2', 'customer': 2, 'cost': 258}, {'facility': 'F2', 'customer': 3, 'cost': 916}, {'facility': 'F2', 'customer': 4, 'cost': 40}, {'facility': 'F2', 'customer': 5, 'cost': 580}, {'facility': 'F2', 'customer': 6, 'cost': 233}], 'objective': 3839.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",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"": 2,
  ""num_clients"": 5,
  ""tents"": [
    {
      ""tent_id"": ""F1"",
      ""tent_setup_cost"": 2000
    },
    {
      ""tent_id"": ""F2"",
      ""tent_setup_cost"": 2000
    }
  ],
  ""clients"": [
    {
      ""client_id"": ""A""
    },
    {
      ""client_id"": ""B""
    },
    {
      ""client_id"": ""C""
    },
    {
      ""client_id"": ""D""
    },
    {
      ""client_id"": ""E""
    }
  ],
  ""client_travels"": [
    {
      ""tent_id"": ""F1"",
      ""client_id"": ""A"",
      ""client_travel_cost"": 378
    },
    {
      ""tent_id"": ""F1"",
      ""client_id"": ""B"",
      ""client_travel_cost"": 235
    },
    {
      ""tent_id"": ""F1"",
      ""client_id"": ""C"",
      ""client_travel_cost"": 194
    },
    {
      ""tent_id"": ""F1"",
      ""client_id"": ""D"",
      ""client_travel_cost"": 403
    },
    {
      ""tent_id"": ""F1"",
      ""client_id"": ""E"",
      ""client_travel_cost"": 706
    },
    {
      ""tent_id"": ""F2"",
      ""client_id"": ""A"",
      ""client_travel_cost"": 715
    },
    {
      ""tent_id"": ""F2"",
      ""client_id"": ""B"",
      ""client_travel_cost"": 93
    },
    {
      ""tent_id"": ""F2"",
      ""client_id"": ""C"",
      ""client_travel_cost"": 863
    },
    {
      ""tent_id"": ""F2"",
      ""client_id"": ""D"",
      ""client_travel_cost"": 376
    },
    {
      ""tent_id"": ""F2"",
      ""client_id"": ""E"",
      ""client_travel_cost"": 516
    }
  ]
}

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': [2000, 2000], 'connection_costs': [[378, 235, 194, 403, 706], [715, 93, 863, 376, 516]], 'objective': 3916.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0]}",3916.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 378}, {'facility': 'F1', 'customer': 'B', 'cost': 235}, {'facility': 'F1', 'customer': 'C', 'cost': 194}, {'facility': 'F1', 'customer': 'D', 'cost': 403}, {'facility': 'F1', 'customer': 'E', 'cost': 706}, {'facility': 'F2', 'customer': 'A', 'cost': 715}, {'facility': 'F2', 'customer': 'B', 'cost': 93}, {'facility': 'F2', 'customer': 'C', 'cost': 863}, {'facility': 'F2', 'customer': 'D', 'cost': 376}, {'facility': 'F2', 'customer': 'E', 'cost': 516}], 'objective': 3916.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1']}",29,json,names
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.

# num_dropoff_sites=3
# num_households=7
# DROPOFF_SITES
dropoff_site_id,site_maintenance_cost
F1,1060
F2,1291
F3,1755
# HOUSEHOLDS
household_id
A
B
C
D
E
F
G
# HOUSEHOLD_TRAVELS
dropoff_site_id,household_id,household_travel_cost
F1,A,740
F1,B,776
F1,C,608
F1,D,119
F1,E,768
F1,F,296
F1,G,954
F2,A,179
F2,B,352
F2,C,816
F2,D,671
F2,E,491
F2,F,169
F2,G,758
F3,A,950
F3,B,866
F3,C,561
F3,D,477
F3,E,111
F3,F,435
F3,G,761

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': [1060, 1291, 1755], 'connection_costs': [[740, 776, 608, 119, 768, 296, 954], [179, 352, 816, 671, 491, 169, 758], [950, 866, 561, 477, 111, 435, 761]], 'objective': 4727.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1, 1]}",4727.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 1060}, {'id': 'F2', 'opening_cost': 1291}, {'id': 'F3', 'opening_cost': 1755}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 740}, {'facility': 'F1', 'customer': 'B', 'cost': 776}, {'facility': 'F1', 'customer': 'C', 'cost': 608}, {'facility': 'F1', 'customer': 'D', 'cost': 119}, {'facility': 'F1', 'customer': 'E', 'cost': 768}, {'facility': 'F1', 'customer': 'F', 'cost': 296}, {'facility': 'F1', 'customer': 'G', 'cost': 954}, {'facility': 'F2', 'customer': 'A', 'cost': 179}, {'facility': 'F2', 'customer': 'B', 'cost': 352}, {'facility': 'F2', 'customer': 'C', 'cost': 816}, {'facility': 'F2', 'customer': 'D', 'cost': 671}, {'facility': 'F2', 'customer': 'E', 'cost': 491}, {'facility': 'F2', 'customer': 'F', 'cost': 169}, {'facility': 'F2', 'customer': 'G', 'cost': 758}, {'facility': 'F3', 'customer': 'A', 'cost': 950}, {'facility': 'F3', 'customer': 'B', 'cost': 866}, {'facility': 'F3', 'customer': 'C', 'cost': 561}, {'facility': 'F3', 'customer': 'D', 'cost': 477}, {'facility': 'F3', 'customer': 'E', 'cost': 111}, {'facility': 'F3', 'customer': 'F', 'cost': 435}, {'facility': 'F3', 'customer': 'G', 'cost': 761}], 'objective': 4727.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",30,csv,names
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.

There are 2 nodes and 5 users in this instance.

**Nodes**
| node_id | node_activation_cost |
|---|---|
| F1 | 2000 |
| F2 | 2000 |

**Users**
| user_id |
|---|
| A |
| B |
| C |
| D |
| E |

**Latency Cost**
| node_id | user_id | latency_cost |
|---|---|---|
| F1 | A | 832 |
| F1 | B | 325 |
| F1 | C | 869 |
| F1 | D | 365 |
| F1 | E | 186 |
| F2 | A | 19 |
| F2 | B | 933 |
| F2 | C | 753 |
| F2 | D | 542 |
| F2 | E | 701 |

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], 'connection_costs': [[832, 325, 869, 365, 186], [19, 933, 753, 542, 701]], 'objective': 4577.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0]}",4577.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 832}, {'facility': 'F1', 'customer': 'B', 'cost': 325}, {'facility': 'F1', 'customer': 'C', 'cost': 869}, {'facility': 'F1', 'customer': 'D', 'cost': 365}, {'facility': 'F1', 'customer': 'E', 'cost': 186}, {'facility': 'F2', 'customer': 'A', 'cost': 19}, {'facility': 'F2', 'customer': 'B', 'cost': 933}, {'facility': 'F2', 'customer': 'C', 'cost': 753}, {'facility': 'F2', 'customer': 'D', 'cost': 542}, {'facility': 'F2', 'customer': 'E', 'cost': 701}], 'objective': 4577.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1']}",31,markdown_table,names
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.

There are 3 kitchens and 6 recipients in this instance.

**Kitchens**
| kitchen_id | kitchen_opening_cost |
|---|---|
| F1 | 2000 |
| F2 | 2000 |
| F3 | 2000 |

**Recipients**
| recipient_id |
|---|
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |

**Pickup Delivery Cost**
| kitchen_id | recipient_id | pickup_delivery_cost |
|---|---|---|
| F1 | 1 | 75 |
| F1 | 2 | 449 |
| F1 | 3 | 492 |
| F1 | 4 | 712 |
| F1 | 5 | 22 |
| F1 | 6 | 433 |
| F2 | 1 | 363 |
| F2 | 2 | 837 |
| F2 | 3 | 696 |
| F2 | 4 | 574 |
| F2 | 5 | 836 |
| F2 | 6 | 610 |
| F3 | 1 | 842 |
| F3 | 2 | 52 |
| F3 | 3 | 44 |
| F3 | 4 | 331 |
| F3 | 5 | 859 |
| F3 | 6 | 333 |

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], 'connection_costs': [[75, 449, 492, 712, 22, 433], [363, 837, 696, 574, 836, 610], [842, 52, 44, 331, 859, 333]], 'objective': 4183.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0]}",4183.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 75}, {'facility': 'F1', 'customer': 2, 'cost': 449}, {'facility': 'F1', 'customer': 3, 'cost': 492}, {'facility': 'F1', 'customer': 4, 'cost': 712}, {'facility': 'F1', 'customer': 5, 'cost': 22}, {'facility': 'F1', 'customer': 6, 'cost': 433}, {'facility': 'F2', 'customer': 1, 'cost': 363}, {'facility': 'F2', 'customer': 2, 'cost': 837}, {'facility': 'F2', 'customer': 3, 'cost': 696}, {'facility': 'F2', 'customer': 4, 'cost': 574}, {'facility': 'F2', 'customer': 5, 'cost': 836}, {'facility': 'F2', 'customer': 6, 'cost': 610}, {'facility': 'F3', 'customer': 1, 'cost': 842}, {'facility': 'F3', 'customer': 2, 'cost': 52}, {'facility': 'F3', 'customer': 3, 'cost': 44}, {'facility': 'F3', 'customer': 4, 'cost': 331}, {'facility': 'F3', 'customer': 5, 'cost': 859}, {'facility': 'F3', 'customer': 6, 'cost': 333}], 'objective': 4183.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",32,markdown_table,1
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=2
# num_customer_groups=5
# BOOTHS
booth_id,booth_rental_fee
F1,1812
F2,1161
# GROUPS
group_id
1
2
3
4
5
# GROUP_TRAVEL_SERVICES
booth_id,group_id,group_travel_service_cost
F1,1,650
F1,2,887
F1,3,786
F1,4,145
F1,5,915
F2,1,779
F2,2,922
F2,3,542
F2,4,979
F2,5,954

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': [1812, 1161], 'connection_costs': [[650, 887, 786, 145, 915], [779, 922, 542, 979, 954]], 'objective': 5195.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0]}",5195.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 1812}, {'id': 'F2', 'opening_cost': 1161}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 650}, {'facility': 'F1', 'customer': 2, 'cost': 887}, {'facility': 'F1', 'customer': 3, 'cost': 786}, {'facility': 'F1', 'customer': 4, 'cost': 145}, {'facility': 'F1', 'customer': 5, 'cost': 915}, {'facility': 'F2', 'customer': 1, 'cost': 779}, {'facility': 'F2', 'customer': 2, 'cost': 922}, {'facility': 'F2', 'customer': 3, 'cost': 542}, {'facility': 'F2', 'customer': 4, 'cost': 979}, {'facility': 'F2', 'customer': 5, 'cost': 954}], 'objective': 5195.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', '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.

There are 2 stations and 6 riders in this instance.

**Stations**
| station_id | station_opening_fee |
|---|---|
| F1 | 2000 |
| F2 | 2000 |

**Riders**
| rider_id |
|---|
| A |
| B |
| C |
| D |
| E |
| F |

**Access Inconvenience**
| station_id | rider_id | access_inconvenience |
|---|---|---|
| F1 | A | 325 |
| F1 | B | 981 |
| F1 | C | 332 |
| F1 | D | 457 |
| F1 | E | 452 |
| F1 | F | 856 |
| F2 | A | 534 |
| F2 | B | 599 |
| F2 | C | 238 |
| F2 | D | 432 |
| F2 | E | 610 |
| F2 | F | 9 |

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': [2000, 2000], 'connection_costs': [[325, 981, 332, 457, 452, 856], [534, 599, 238, 432, 610, 9]], 'objective': 4422.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1]}",4422.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 325}, {'facility': 'F1', 'customer': 'B', 'cost': 981}, {'facility': 'F1', 'customer': 'C', 'cost': 332}, {'facility': 'F1', 'customer': 'D', 'cost': 457}, {'facility': 'F1', 'customer': 'E', 'cost': 452}, {'facility': 'F1', 'customer': 'F', 'cost': 856}, {'facility': 'F2', 'customer': 'A', 'cost': 534}, {'facility': 'F2', 'customer': 'B', 'cost': 599}, {'facility': 'F2', 'customer': 'C', 'cost': 238}, {'facility': 'F2', 'customer': 'D', 'cost': 432}, {'facility': 'F2', 'customer': 'E', 'cost': 610}, {'facility': 'F2', 'customer': 'F', 'cost': 9}], 'objective': 4422.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",34,markdown_table,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.

There are 2 hubs and 5 learners in this instance.

**Hubs**
| hub_id | activation_cost |
|---|---|
| F1 | 2000 |
| F2 | 2000 |

**Learners**
| learner_id |
|---|
| 0 |
| 1 |
| 2 |
| 3 |
| 4 |

**Travel Cost**
| hub_id | learner_id | travel_cost |
|---|---|---|
| F1 | 0 | 901 |
| F1 | 1 | 390 |
| F1 | 2 | 81 |
| F1 | 3 | 769 |
| F1 | 4 | 315 |
| F2 | 0 | 780 |
| F2 | 1 | 348 |
| F2 | 2 | 695 |
| F2 | 3 | 82 |
| F2 | 4 | 630 |

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': [2000, 2000], 'connection_costs': [[901, 390, 81, 769, 315], [780, 348, 695, 82, 630]], 'objective': 4456.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0]}",4456.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 901}, {'facility': 'F1', 'customer': 1, 'cost': 390}, {'facility': 'F1', 'customer': 2, 'cost': 81}, {'facility': 'F1', 'customer': 3, 'cost': 769}, {'facility': 'F1', 'customer': 4, 'cost': 315}, {'facility': 'F2', 'customer': 0, 'cost': 780}, {'facility': 'F2', 'customer': 1, 'cost': 348}, {'facility': 'F2', 'customer': 2, 'cost': 695}, {'facility': 'F2', 'customer': 3, 'cost': 82}, {'facility': 'F2', 'customer': 4, 'cost': 630}], 'objective': 4456.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1']}",35,markdown_table,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.

There are 2 depots and 5 households in this instance.

**Depots**
| depot_id | depot_opening_cost |
|---|---|
| F1 | 1550 |
| F2 | 1374 |

**Households**
| household_id |
|---|
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |

**Pickup Effort**
| depot_id | household_id | pickup_effort |
|---|---|---|
| F1 | 1 | 984 |
| F1 | 2 | 377 |
| F1 | 3 | 321 |
| F1 | 4 | 950 |
| F1 | 5 | 625 |
| F2 | 1 | 95 |
| F2 | 2 | 781 |
| F2 | 3 | 600 |
| F2 | 4 | 567 |
| F2 | 5 | 411 |

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': [1550, 1374], 'connection_costs': [[984, 377, 321, 950, 625], [95, 781, 600, 567, 411]], 'objective': 3828.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1]}",3828.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 5, 'facilities': [{'id': 'F1', 'opening_cost': 1550}, {'id': 'F2', 'opening_cost': 1374}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 984}, {'facility': 'F1', 'customer': 2, 'cost': 377}, {'facility': 'F1', 'customer': 3, 'cost': 321}, {'facility': 'F1', 'customer': 4, 'cost': 950}, {'facility': 'F1', 'customer': 5, 'cost': 625}, {'facility': 'F2', 'customer': 1, 'cost': 95}, {'facility': 'F2', 'customer': 2, 'cost': 781}, {'facility': 'F2', 'customer': 3, 'cost': 600}, {'facility': 'F2', 'customer': 4, 'cost': 567}, {'facility': 'F2', 'customer': 5, 'cost': 411}], 'objective': 3828.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2']}",36,markdown_table,1
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 3 candidate pickup points and 8 clients; pickup point operation fees are 6399, 8454, 2329.
Pickup point F1 has an operation fee of 6399.
Pickup point F2 has an operation fee of 8454.
Pickup point F3 has an operation fee of 2329.
For client 0, the cost to use pickup point F1 is 854.
For client 1, the cost to use pickup point F1 is 556.
For client 2, the cost to use pickup point F1 is 45.
For client 3, the cost to use pickup point F1 is 759.
For client 4, the cost to use pickup point F1 is 613.
For client 5, the cost to use pickup point F1 is 981.
For client 6, the cost to use pickup point F1 is 37.
For client 7, the cost to use pickup point F1 is 186.
For client 0, the cost to use pickup point F2 is 136.
For client 1, the cost to use pickup point F2 is 553.
For client 2, the cost to use pickup point F2 is 462.
For client 3, the cost to use pickup point F2 is 513.
For client 4, the cost to use pickup point F2 is 578.
For client 5, the cost to use pickup point F2 is 862.
For client 6, the cost to use pickup point F2 is 352.
For client 7, the cost to use pickup point F2 is 496.
For client 0, the cost to use pickup point F3 is 905.
For client 1, the cost to use pickup point F3 is 541.
For client 2, the cost to use pickup point F3 is 908.
For client 3, the cost to use pickup point F3 is 257.
For client 4, the cost to use pickup point F3 is 605.
For client 5, the cost to use pickup point F3 is 326.
For client 6, the cost to use pickup point F3 is 729.
For client 7, the cost to use pickup point F3 is 830.
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': [6399, 8454, 2329], 'connection_costs': [[854, 556, 45, 759, 613, 981, 37, 186], [136, 553, 462, 513, 578, 862, 352, 496], [905, 541, 908, 257, 605, 326, 729, 830]], 'objective': 7430.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2]}",7430.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 8, 'facilities': [{'id': 'F1', 'opening_cost': 6399}, {'id': 'F2', 'opening_cost': 8454}, {'id': 'F3', 'opening_cost': 2329}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 854}, {'facility': 'F1', 'customer': 1, 'cost': 556}, {'facility': 'F1', 'customer': 2, 'cost': 45}, {'facility': 'F1', 'customer': 3, 'cost': 759}, {'facility': 'F1', 'customer': 4, 'cost': 613}, {'facility': 'F1', 'customer': 5, 'cost': 981}, {'facility': 'F1', 'customer': 6, 'cost': 37}, {'facility': 'F1', 'customer': 7, 'cost': 186}, {'facility': 'F2', 'customer': 0, 'cost': 136}, {'facility': 'F2', 'customer': 1, 'cost': 553}, {'facility': 'F2', 'customer': 2, 'cost': 462}, {'facility': 'F2', 'customer': 3, 'cost': 513}, {'facility': 'F2', 'customer': 4, 'cost': 578}, {'facility': 'F2', 'customer': 5, 'cost': 862}, {'facility': 'F2', 'customer': 6, 'cost': 352}, {'facility': 'F2', 'customer': 7, 'cost': 496}, {'facility': 'F3', 'customer': 0, 'cost': 905}, {'facility': 'F3', 'customer': 1, 'cost': 541}, {'facility': 'F3', 'customer': 2, 'cost': 908}, {'facility': 'F3', 'customer': 3, 'cost': 257}, {'facility': 'F3', 'customer': 4, 'cost': 605}, {'facility': 'F3', 'customer': 5, 'cost': 326}, {'facility': 'F3', 'customer': 6, 'cost': 729}, {'facility': 'F3', 'customer': 7, 'cost': 830}], 'objective': 7430.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",37,nl,0
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.

{
  ""num_packing_centers"": 2,
  ""num_orders"": 6,
  ""packing_centers"": [
    {
      ""packing_center_id"": ""F1"",
      ""opening_fee"": 3074
    },
    {
      ""packing_center_id"": ""F2"",
      ""opening_fee"": 4989
    }
  ],
  ""orders"": [
    {
      ""order_id"": 1
    },
    {
      ""order_id"": 2
    },
    {
      ""order_id"": 3
    },
    {
      ""order_id"": 4
    },
    {
      ""order_id"": 5
    },
    {
      ""order_id"": 6
    }
  ],
  ""shippings"": [
    {
      ""packing_center_id"": ""F1"",
      ""order_id"": 1,
      ""shipping_cost"": 629
    },
    {
      ""packing_center_id"": ""F1"",
      ""order_id"": 2,
      ""shipping_cost"": 217
    },
    {
      ""packing_center_id"": ""F1"",
      ""order_id"": 3,
      ""shipping_cost"": 881
    },
    {
      ""packing_center_id"": ""F1"",
      ""order_id"": 4,
      ""shipping_cost"": 421
    },
    {
      ""packing_center_id"": ""F1"",
      ""order_id"": 5,
      ""shipping_cost"": 950
    },
    {
      ""packing_center_id"": ""F1"",
      ""order_id"": 6,
      ""shipping_cost"": 780
    },
    {
      ""packing_center_id"": ""F2"",
      ""order_id"": 1,
      ""shipping_cost"": 252
    },
    {
      ""packing_center_id"": ""F2"",
      ""order_id"": 2,
      ""shipping_cost"": 593
    },
    {
      ""packing_center_id"": ""F2"",
      ""order_id"": 3,
      ""shipping_cost"": 282
    },
    {
      ""packing_center_id"": ""F2"",
      ""order_id"": 4,
      ""shipping_cost"": 160
    },
    {
      ""packing_center_id"": ""F2"",
      ""order_id"": 5,
      ""shipping_cost"": 960
    },
    {
      ""packing_center_id"": ""F2"",
      ""order_id"": 6,
      ""shipping_cost"": 235
    }
  ]
}

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': [3074, 4989], 'connection_costs': [[629, 217, 881, 421, 950, 780], [252, 593, 282, 160, 960, 235]], 'objective': 6952.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0]}",6952.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 3074}, {'id': 'F2', 'opening_cost': 4989}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 629}, {'facility': 'F1', 'customer': 2, 'cost': 217}, {'facility': 'F1', 'customer': 3, 'cost': 881}, {'facility': 'F1', 'customer': 4, 'cost': 421}, {'facility': 'F1', 'customer': 5, 'cost': 950}, {'facility': 'F1', 'customer': 6, 'cost': 780}, {'facility': 'F2', 'customer': 1, 'cost': 252}, {'facility': 'F2', 'customer': 2, 'cost': 593}, {'facility': 'F2', 'customer': 3, 'cost': 282}, {'facility': 'F2', 'customer': 4, 'cost': 160}, {'facility': 'F2', 'customer': 5, 'cost': 960}, {'facility': 'F2', 'customer': 6, 'cost': 235}], 'objective': 6952.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",38,json,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 3 stops and 6 commuters in this instance.

**Stops**
| stop_id | activation_cost |
|---|---|
| F1 | 1001 |
| F2 | 1781 |
| F3 | 1777 |

**Commuters**
| commuter_id |
|---|
| 0 |
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |

**Travel Cost**
| stop_id | commuter_id | travel_cost |
|---|---|---|
| F1 | 0 | 182 |
| F1 | 1 | 386 |
| F1 | 2 | 395 |
| F1 | 3 | 900 |
| F1 | 4 | 215 |
| F1 | 5 | 275 |
| F2 | 0 | 565 |
| F2 | 1 | 775 |
| F2 | 2 | 756 |
| F2 | 3 | 636 |
| F2 | 4 | 922 |
| F2 | 5 | 454 |
| F3 | 0 | 933 |
| F3 | 1 | 824 |
| F3 | 2 | 691 |
| F3 | 3 | 619 |
| F3 | 4 | 222 |
| F3 | 5 | 770 |

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': [1001, 1781, 1777], 'connection_costs': [[182, 386, 395, 900, 215, 275], [565, 775, 756, 636, 922, 454], [933, 824, 691, 619, 222, 770]], 'objective': 3354.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0]}",3354.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 1001}, {'id': 'F2', 'opening_cost': 1781}, {'id': 'F3', 'opening_cost': 1777}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 182}, {'facility': 'F1', 'customer': 1, 'cost': 386}, {'facility': 'F1', 'customer': 2, 'cost': 395}, {'facility': 'F1', 'customer': 3, 'cost': 900}, {'facility': 'F1', 'customer': 4, 'cost': 215}, {'facility': 'F1', 'customer': 5, 'cost': 275}, {'facility': 'F2', 'customer': 0, 'cost': 565}, {'facility': 'F2', 'customer': 1, 'cost': 775}, {'facility': 'F2', 'customer': 2, 'cost': 756}, {'facility': 'F2', 'customer': 3, 'cost': 636}, {'facility': 'F2', 'customer': 4, 'cost': 922}, {'facility': 'F2', 'customer': 5, 'cost': 454}, {'facility': 'F3', 'customer': 0, 'cost': 933}, {'facility': 'F3', 'customer': 1, 'cost': 824}, {'facility': 'F3', 'customer': 2, 'cost': 691}, {'facility': 'F3', 'customer': 3, 'cost': 619}, {'facility': 'F3', 'customer': 4, 'cost': 222}, {'facility': 'F3', 'customer': 5, 'cost': 770}], 'objective': 3354.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",39,markdown_table,0
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.

# num_outlets=3
# num_blocks=8
# OUTLETS
outlet_id,setup_fee
F1,2000
F2,2000
F3,2000
# BLOCKS
block_id
1
2
3
4
5
6
7
8
# DELIVERY_TRAVELS
outlet_id,block_id,delivery_travel_cost
F1,1,946
F1,2,845
F1,3,248
F1,4,505
F1,5,515
F1,6,678
F1,7,991
F1,8,569
F2,1,988
F2,2,34
F2,3,225
F2,4,956
F2,5,887
F2,6,708
F2,7,714
F2,8,593
F3,1,302
F3,2,622
F3,3,267
F3,4,578
F3,5,52
F3,6,719
F3,7,884
F3,8,765

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': [2000, 2000, 2000], 'connection_costs': [[946, 845, 248, 505, 515, 678, 991, 569], [988, 34, 225, 956, 887, 708, 714, 593], [302, 622, 267, 578, 52, 719, 884, 765]], 'objective': 6189.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2, 2]}",6189.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 8, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 946}, {'facility': 'F1', 'customer': 2, 'cost': 845}, {'facility': 'F1', 'customer': 3, 'cost': 248}, {'facility': 'F1', 'customer': 4, 'cost': 505}, {'facility': 'F1', 'customer': 5, 'cost': 515}, {'facility': 'F1', 'customer': 6, 'cost': 678}, {'facility': 'F1', 'customer': 7, 'cost': 991}, {'facility': 'F1', 'customer': 8, 'cost': 569}, {'facility': 'F2', 'customer': 1, 'cost': 988}, {'facility': 'F2', 'customer': 2, 'cost': 34}, {'facility': 'F2', 'customer': 3, 'cost': 225}, {'facility': 'F2', 'customer': 4, 'cost': 956}, {'facility': 'F2', 'customer': 5, 'cost': 887}, {'facility': 'F2', 'customer': 6, 'cost': 708}, {'facility': 'F2', 'customer': 7, 'cost': 714}, {'facility': 'F2', 'customer': 8, 'cost': 593}, {'facility': 'F3', 'customer': 1, 'cost': 302}, {'facility': 'F3', 'customer': 2, 'cost': 622}, {'facility': 'F3', 'customer': 3, 'cost': 267}, {'facility': 'F3', 'customer': 4, 'cost': 578}, {'facility': 'F3', 'customer': 5, 'cost': 52}, {'facility': 'F3', 'customer': 6, 'cost': 719}, {'facility': 'F3', 'customer': 7, 'cost': 884}, {'facility': 'F3', 'customer': 8, 'cost': 765}], 'objective': 6189.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",40,csv,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.

There are 3 candidate food truck spots, 7 attendee areas, and the spot rental fees are 2000, 2000, 2000.
Spot F1 has a rental fee of 2000.
Spot F2 has a rental fee of 2000.
Spot F3 has a rental fee of 2000.
If attendee area A is assigned to spot F1, the walking distance is 415.
If attendee area B is assigned to spot F1, the walking distance is 259.
If attendee area C is assigned to spot F1, the walking distance is 818.
If attendee area D is assigned to spot F1, the walking distance is 61.
If attendee area E is assigned to spot F1, the walking distance is 372.
If attendee area F is assigned to spot F1, the walking distance is 657.
If attendee area G is assigned to spot F1, the walking distance is 875.
If attendee area A is assigned to spot F2, the walking distance is 896.
If attendee area B is assigned to spot F2, the walking distance is 250.
If attendee area C is assigned to spot F2, the walking distance is 867.
If attendee area D is assigned to spot F2, the walking distance is 369.
If attendee area E is assigned to spot F2, the walking distance is 79.
If attendee area F is assigned to spot F2, the walking distance is 549.
If attendee area G is assigned to spot F2, the walking distance is 963.
If attendee area A is assigned to spot F3, the walking distance is 698.
If attendee area B is assigned to spot F3, the walking distance is 858.
If attendee area C is assigned to spot F3, the walking distance is 889.
If attendee area D is assigned to spot F3, the walking distance is 557.
If attendee area E is assigned to spot F3, the walking distance is 825.
If attendee area F is assigned to spot F3, the walking distance is 873.
If attendee area G is assigned to spot F3, the walking distance is 514.
The organizers must use these details to decide which spots to staff and how to assign each area so the sum of rental fees plus walking distances is minimized.

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], 'connection_costs': [[415, 259, 818, 61, 372, 657, 875], [896, 250, 867, 369, 79, 549, 963], [698, 858, 889, 557, 825, 873, 514]], 'objective': 5457.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0]}",5457.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 415}, {'facility': 'F1', 'customer': 'B', 'cost': 259}, {'facility': 'F1', 'customer': 'C', 'cost': 818}, {'facility': 'F1', 'customer': 'D', 'cost': 61}, {'facility': 'F1', 'customer': 'E', 'cost': 372}, {'facility': 'F1', 'customer': 'F', 'cost': 657}, {'facility': 'F1', 'customer': 'G', 'cost': 875}, {'facility': 'F2', 'customer': 'A', 'cost': 896}, {'facility': 'F2', 'customer': 'B', 'cost': 250}, {'facility': 'F2', 'customer': 'C', 'cost': 867}, {'facility': 'F2', 'customer': 'D', 'cost': 369}, {'facility': 'F2', 'customer': 'E', 'cost': 79}, {'facility': 'F2', 'customer': 'F', 'cost': 549}, {'facility': 'F2', 'customer': 'G', 'cost': 963}, {'facility': 'F3', 'customer': 'A', 'cost': 698}, {'facility': 'F3', 'customer': 'B', 'cost': 858}, {'facility': 'F3', 'customer': 'C', 'cost': 889}, {'facility': 'F3', 'customer': 'D', 'cost': 557}, {'facility': 'F3', 'customer': 'E', 'cost': 825}, {'facility': 'F3', 'customer': 'F', 'cost': 873}, {'facility': 'F3', 'customer': 'G', 'cost': 514}], 'objective': 5457.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",41,nl,names
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 3 candidate depots, 6 clinics, and the depot operating fees are 7095, 4049, 1987.
Someone on the logistics team can open depot F1 at a fixed operating fee of 7095.
Someone on the logistics team can open depot F2 at a fixed operating fee of 4049.
Someone on the logistics team can open depot F3 at a fixed operating fee of 1987.
Someone on the logistics team would assign clinic 0 to depot F1 with a transport cost of 329.
Someone on the logistics team would assign clinic 1 to depot F1 with a transport cost of 601.
Someone on the logistics team would assign clinic 2 to depot F1 with a transport cost of 48.
Someone on the logistics team would assign clinic 3 to depot F1 with a transport cost of 309.
Someone on the logistics team would assign clinic 4 to depot F1 with a transport cost of 439.
Someone on the logistics team would assign clinic 5 to depot F1 with a transport cost of 837.
Someone on the logistics team would assign clinic 0 to depot F2 with a transport cost of 514.
Someone on the logistics team would assign clinic 1 to depot F2 with a transport cost of 791.
Someone on the logistics team would assign clinic 2 to depot F2 with a transport cost of 23.
Someone on the logistics team would assign clinic 3 to depot F2 with a transport cost of 60.
Someone on the logistics team would assign clinic 4 to depot F2 with a transport cost of 139.
Someone on the logistics team would assign clinic 5 to depot F2 with a transport cost of 14.
Someone on the logistics team would assign clinic 0 to depot F3 with a transport cost of 558.
Someone on the logistics team would assign clinic 1 to depot F3 with a transport cost of 205.
Someone on the logistics team would assign clinic 2 to depot F3 with a transport cost of 336.
Someone on the logistics team would assign clinic 3 to depot F3 with a transport cost of 56.
Someone on the logistics team would assign clinic 4 to depot F3 with a transport cost of 301.
Someone on the logistics team would assign clinic 5 to depot F3 with a transport cost of 772.
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': [7095, 4049, 1987], 'connection_costs': [[329, 601, 48, 309, 439, 837], [514, 791, 23, 60, 139, 14], [558, 205, 336, 56, 301, 772]], 'objective': 4215.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2]}",4215.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 7095}, {'id': 'F2', 'opening_cost': 4049}, {'id': 'F3', 'opening_cost': 1987}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 329}, {'facility': 'F1', 'customer': 1, 'cost': 601}, {'facility': 'F1', 'customer': 2, 'cost': 48}, {'facility': 'F1', 'customer': 3, 'cost': 309}, {'facility': 'F1', 'customer': 4, 'cost': 439}, {'facility': 'F1', 'customer': 5, 'cost': 837}, {'facility': 'F2', 'customer': 0, 'cost': 514}, {'facility': 'F2', 'customer': 1, 'cost': 791}, {'facility': 'F2', 'customer': 2, 'cost': 23}, {'facility': 'F2', 'customer': 3, 'cost': 60}, {'facility': 'F2', 'customer': 4, 'cost': 139}, {'facility': 'F2', 'customer': 5, 'cost': 14}, {'facility': 'F3', 'customer': 0, 'cost': 558}, {'facility': 'F3', 'customer': 1, 'cost': 205}, {'facility': 'F3', 'customer': 2, 'cost': 336}, {'facility': 'F3', 'customer': 3, 'cost': 56}, {'facility': 'F3', 'customer': 4, 'cost': 301}, {'facility': 'F3', 'customer': 5, 'cost': 772}], 'objective': 4215.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",42,nl,0
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"": 3,
  ""total_shops"": 7,
  ""hubs"": [
    {
      ""hub_id"": ""F1"",
      ""activation_fee"": 1000
    },
    {
      ""hub_id"": ""F2"",
      ""activation_fee"": 1000
    },
    {
      ""hub_id"": ""F3"",
      ""activation_fee"": 1000
    }
  ],
  ""shops"": [
    {
      ""shop_id"": 0
    },
    {
      ""shop_id"": 1
    },
    {
      ""shop_id"": 2
    },
    {
      ""shop_id"": 3
    },
    {
      ""shop_id"": 4
    },
    {
      ""shop_id"": 5
    },
    {
      ""shop_id"": 6
    }
  ],
  ""shipments"": [
    {
      ""hub_id"": ""F1"",
      ""shop_id"": 0,
      ""shipment_cost"": 293
    },
    {
      ""hub_id"": ""F1"",
      ""shop_id"": 1,
      ""shipment_cost"": 415
    },
    {
      ""hub_id"": ""F1"",
      ""shop_id"": 2,
      ""shipment_cost"": 518
    },
    {
      ""hub_id"": ""F1"",
      ""shop_id"": 3,
      ""shipment_cost"": 514
    },
    {
      ""hub_id"": ""F1"",
      ""shop_id"": 4,
      ""shipment_cost"": 794
    },
    {
      ""hub_id"": ""F1"",
      ""shop_id"": 5,
      ""shipment_cost"": 484
    },
    {
      ""hub_id"": ""F1"",
      ""shop_id"": 6,
      ""shipment_cost"": 282
    },
    {
      ""hub_id"": ""F2"",
      ""shop_id"": 0,
      ""shipment_cost"": 512
    },
    {
      ""hub_id"": ""F2"",
      ""shop_id"": 1,
      ""shipment_cost"": 361
    },
    {
      ""hub_id"": ""F2"",
      ""shop_id"": 2,
      ""shipment_cost"": 433
    },
    {
      ""hub_id"": ""F2"",
      ""shop_id"": 3,
      ""shipment_cost"": 447
    },
    {
      ""hub_id"": ""F2"",
      ""shop_id"": 4,
      ""shipment_cost"": 127
    },
    {
      ""hub_id"": ""F2"",
      ""shop_id"": 5,
      ""shipment_cost"": 890
    },
    {
      ""hub_id"": ""F2"",
      ""shop_id"": 6,
      ""shipment_cost"": 689
    },
    {
      ""hub_id"": ""F3"",
      ""shop_id"": 0,
      ""shipment_cost"": 553
    },
    {
      ""hub_id"": ""F3"",
      ""shop_id"": 1,
      ""shipment_cost"": 982
    },
    {
      ""hub_id"": ""F3"",
      ""shop_id"": 2,
      ""shipment_cost"": 641
    },
    {
      ""hub_id"": ""F3"",
      ""shop_id"": 3,
      ""shipment_cost"": 842
    },
    {
      ""hub_id"": ""F3"",
      ""shop_id"": 4,
      ""shipment_cost"": 897
    },
    {
      ""hub_id"": ""F3"",
      ""shop_id"": 5,
      ""shipment_cost"": 260
    },
    {
      ""hub_id"": ""F3"",
      ""shop_id"": 6,
      ""shipment_cost"": 715
    }
  ]
}

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': [1000, 1000, 1000], 'connection_costs': [[293, 415, 518, 514, 794, 484, 282], [512, 361, 433, 447, 127, 890, 689], [553, 982, 641, 842, 897, 260, 715]], 'objective': 4300.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0]}",4300.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 293}, {'facility': 'F1', 'customer': 1, 'cost': 415}, {'facility': 'F1', 'customer': 2, 'cost': 518}, {'facility': 'F1', 'customer': 3, 'cost': 514}, {'facility': 'F1', 'customer': 4, 'cost': 794}, {'facility': 'F1', 'customer': 5, 'cost': 484}, {'facility': 'F1', 'customer': 6, 'cost': 282}, {'facility': 'F2', 'customer': 0, 'cost': 512}, {'facility': 'F2', 'customer': 1, 'cost': 361}, {'facility': 'F2', 'customer': 2, 'cost': 433}, {'facility': 'F2', 'customer': 3, 'cost': 447}, {'facility': 'F2', 'customer': 4, 'cost': 127}, {'facility': 'F2', 'customer': 5, 'cost': 890}, {'facility': 'F2', 'customer': 6, 'cost': 689}, {'facility': 'F3', 'customer': 0, 'cost': 553}, {'facility': 'F3', 'customer': 1, 'cost': 982}, {'facility': 'F3', 'customer': 2, 'cost': 641}, {'facility': 'F3', 'customer': 3, 'cost': 842}, {'facility': 'F3', 'customer': 4, 'cost': 897}, {'facility': 'F3', 'customer': 5, 'cost': 260}, {'facility': 'F3', 'customer': 6, 'cost': 715}], 'objective': 4300.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",43,json,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.

{
  ""num_branches"": 3,
  ""num_schools"": 7,
  ""branchs"": [
    {
      ""branch_id"": ""F1"",
      ""branch_opening_fee"": 2090
    },
    {
      ""branch_id"": ""F2"",
      ""branch_opening_fee"": 3751
    },
    {
      ""branch_id"": ""F3"",
      ""branch_opening_fee"": 6554
    }
  ],
  ""schools"": [
    {
      ""school_id"": ""A""
    },
    {
      ""school_id"": ""B""
    },
    {
      ""school_id"": ""C""
    },
    {
      ""school_id"": ""D""
    },
    {
      ""school_id"": ""E""
    },
    {
      ""school_id"": ""F""
    },
    {
      ""school_id"": ""G""
    }
  ],
  ""deliverys"": [
    {
      ""branch_id"": ""F1"",
      ""school_id"": ""A"",
      ""delivery_cost"": 290
    },
    {
      ""branch_id"": ""F1"",
      ""school_id"": ""B"",
      ""delivery_cost"": 434
    },
    {
      ""branch_id"": ""F1"",
      ""school_id"": ""C"",
      ""delivery_cost"": 680
    },
    {
      ""branch_id"": ""F1"",
      ""school_id"": ""D"",
      ""delivery_cost"": 231
    },
    {
      ""branch_id"": ""F1"",
      ""school_id"": ""E"",
      ""delivery_cost"": 448
    },
    {
      ""branch_id"": ""F1"",
      ""school_id"": ""F"",
      ""delivery_cost"": 783
    },
    {
      ""branch_id"": ""F1"",
      ""school_id"": ""G"",
      ""delivery_cost"": 133
    },
    {
      ""branch_id"": ""F2"",
      ""school_id"": ""A"",
      ""delivery_cost"": 337
    },
    {
      ""branch_id"": ""F2"",
      ""school_id"": ""B"",
      ""delivery_cost"": 961
    },
    {
      ""branch_id"": ""F2"",
      ""school_id"": ""C"",
      ""delivery_cost"": 369
    },
    {
      ""branch_id"": ""F2"",
      ""school_id"": ""D"",
      ""delivery_cost"": 691
    },
    {
      ""branch_id"": ""F2"",
      ""school_id"": ""E"",
      ""delivery_cost"": 560
    },
    {
      ""branch_id"": ""F2"",
      ""school_id"": ""F"",
      ""delivery_cost"": 470
    },
    {
      ""branch_id"": ""F2"",
      ""school_id"": ""G"",
      ""delivery_cost"": 772
    },
    {
      ""branch_id"": ""F3"",
      ""school_id"": ""A"",
      ""delivery_cost"": 903
    },
    {
      ""branch_id"": ""F3"",
      ""school_id"": ""B"",
      ""delivery_cost"": 463
    },
    {
      ""branch_id"": ""F3"",
      ""school_id"": ""C"",
      ""delivery_cost"": 756
    },
    {
      ""branch_id"": ""F3"",
      ""school_id"": ""D"",
      ""delivery_cost"": 901
    },
    {
      ""branch_id"": ""F3"",
      ""school_id"": ""E"",
      ""delivery_cost"": 187
    },
    {
      ""branch_id"": ""F3"",
      ""school_id"": ""F"",
      ""delivery_cost"": 43
    },
    {
      ""branch_id"": ""F3"",
      ""school_id"": ""G"",
      ""delivery_cost"": 284
    }
  ]
}

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': [2090, 3751, 6554], 'connection_costs': [[290, 434, 680, 231, 448, 783, 133], [337, 961, 369, 691, 560, 470, 772], [903, 463, 756, 901, 187, 43, 284]], 'objective': 5089.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0]}",5089.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 2090}, {'id': 'F2', 'opening_cost': 3751}, {'id': 'F3', 'opening_cost': 6554}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 290}, {'facility': 'F1', 'customer': 'B', 'cost': 434}, {'facility': 'F1', 'customer': 'C', 'cost': 680}, {'facility': 'F1', 'customer': 'D', 'cost': 231}, {'facility': 'F1', 'customer': 'E', 'cost': 448}, {'facility': 'F1', 'customer': 'F', 'cost': 783}, {'facility': 'F1', 'customer': 'G', 'cost': 133}, {'facility': 'F2', 'customer': 'A', 'cost': 337}, {'facility': 'F2', 'customer': 'B', 'cost': 961}, {'facility': 'F2', 'customer': 'C', 'cost': 369}, {'facility': 'F2', 'customer': 'D', 'cost': 691}, {'facility': 'F2', 'customer': 'E', 'cost': 560}, {'facility': 'F2', 'customer': 'F', 'cost': 470}, {'facility': 'F2', 'customer': 'G', 'cost': 772}, {'facility': 'F3', 'customer': 'A', 'cost': 903}, {'facility': 'F3', 'customer': 'B', 'cost': 463}, {'facility': 'F3', 'customer': 'C', 'cost': 756}, {'facility': 'F3', 'customer': 'D', 'cost': 901}, {'facility': 'F3', 'customer': 'E', 'cost': 187}, {'facility': 'F3', 'customer': 'F', 'cost': 43}, {'facility': 'F3', 'customer': 'G', 'cost': 284}], 'objective': 5089.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",44,json,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.

# num_distribution_points=3
# num_community_groups=8
# DISTRIBUTION_POINTS
distribution_point_id,running_fee
F1,2000
F2,2000
F3,2000
# COMMUNITY_GROUPS
community_group_id
1
2
3
4
5
6
7
8
# DELIVERYS
distribution_point_id,community_group_id,delivery_cost
F1,1,728
F1,2,457
F1,3,245
F1,4,594
F1,5,923
F1,6,617
F1,7,679
F1,8,983
F2,1,317
F2,2,883
F2,3,858
F2,4,733
F2,5,162
F2,6,136
F2,7,711
F2,8,12
F3,1,792
F3,2,385
F3,3,647
F3,4,469
F3,5,909
F3,6,205
F3,7,862
F3,8,684

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': [2000, 2000, 2000], 'connection_costs': [[728, 457, 245, 594, 923, 617, 679, 983], [317, 883, 858, 733, 162, 136, 711, 12], [792, 385, 647, 469, 909, 205, 862, 684]], 'objective': 5812.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1, 1, 1]}",5812.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 8, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}, {'id': 8}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 728}, {'facility': 'F1', 'customer': 2, 'cost': 457}, {'facility': 'F1', 'customer': 3, 'cost': 245}, {'facility': 'F1', 'customer': 4, 'cost': 594}, {'facility': 'F1', 'customer': 5, 'cost': 923}, {'facility': 'F1', 'customer': 6, 'cost': 617}, {'facility': 'F1', 'customer': 7, 'cost': 679}, {'facility': 'F1', 'customer': 8, 'cost': 983}, {'facility': 'F2', 'customer': 1, 'cost': 317}, {'facility': 'F2', 'customer': 2, 'cost': 883}, {'facility': 'F2', 'customer': 3, 'cost': 858}, {'facility': 'F2', 'customer': 4, 'cost': 733}, {'facility': 'F2', 'customer': 5, 'cost': 162}, {'facility': 'F2', 'customer': 6, 'cost': 136}, {'facility': 'F2', 'customer': 7, 'cost': 711}, {'facility': 'F2', 'customer': 8, 'cost': 12}, {'facility': 'F3', 'customer': 1, 'cost': 792}, {'facility': 'F3', 'customer': 2, 'cost': 385}, {'facility': 'F3', 'customer': 3, 'cost': 647}, {'facility': 'F3', 'customer': 4, 'cost': 469}, {'facility': 'F3', 'customer': 5, 'cost': 909}, {'facility': 'F3', 'customer': 6, 'cost': 205}, {'facility': 'F3', 'customer': 7, 'cost': 862}, {'facility': 'F3', 'customer': 8, 'cost': 684}], 'objective': 5812.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",45,csv,1
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.

{
  ""num_posts"": 2,
  ""num_residential_clusters"": 6,
  ""posts"": [
    {
      ""post_id"": ""F1"",
      ""staffing_cost"": 3757
    },
    {
      ""post_id"": ""F2"",
      ""staffing_cost"": 3209
    }
  ],
  ""clusters"": [
    {
      ""cluster_id"": 1
    },
    {
      ""cluster_id"": 2
    },
    {
      ""cluster_id"": 3
    },
    {
      ""cluster_id"": 4
    },
    {
      ""cluster_id"": 5
    },
    {
      ""cluster_id"": 6
    }
  ],
  ""travels"": [
    {
      ""post_id"": ""F1"",
      ""cluster_id"": 1,
      ""travel_cost"": 569
    },
    {
      ""post_id"": ""F1"",
      ""cluster_id"": 2,
      ""travel_cost"": 311
    },
    {
      ""post_id"": ""F1"",
      ""cluster_id"": 3,
      ""travel_cost"": 937
    },
    {
      ""post_id"": ""F1"",
      ""cluster_id"": 4,
      ""travel_cost"": 235
    },
    {
      ""post_id"": ""F1"",
      ""cluster_id"": 5,
      ""travel_cost"": 798
    },
    {
      ""post_id"": ""F1"",
      ""cluster_id"": 6,
      ""travel_cost"": 391
    },
    {
      ""post_id"": ""F2"",
      ""cluster_id"": 1,
      ""travel_cost"": 412
    },
    {
      ""post_id"": ""F2"",
      ""cluster_id"": 2,
      ""travel_cost"": 180
    },
    {
      ""post_id"": ""F2"",
      ""cluster_id"": 3,
      ""travel_cost"": 152
    },
    {
      ""post_id"": ""F2"",
      ""cluster_id"": 4,
      ""travel_cost"": 479
    },
    {
      ""post_id"": ""F2"",
      ""cluster_id"": 5,
      ""travel_cost"": 343
    },
    {
      ""post_id"": ""F2"",
      ""cluster_id"": 6,
      ""travel_cost"": 15
    }
  ]
}

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': [3757, 3209], 'connection_costs': [[569, 311, 937, 235, 798, 391], [412, 180, 152, 479, 343, 15]], 'objective': 4790.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1]}",4790.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 3757}, {'id': 'F2', 'opening_cost': 3209}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 569}, {'facility': 'F1', 'customer': 2, 'cost': 311}, {'facility': 'F1', 'customer': 3, 'cost': 937}, {'facility': 'F1', 'customer': 4, 'cost': 235}, {'facility': 'F1', 'customer': 5, 'cost': 798}, {'facility': 'F1', 'customer': 6, 'cost': 391}, {'facility': 'F2', 'customer': 1, 'cost': 412}, {'facility': 'F2', 'customer': 2, 'cost': 180}, {'facility': 'F2', 'customer': 3, 'cost': 152}, {'facility': 'F2', 'customer': 4, 'cost': 479}, {'facility': 'F2', 'customer': 5, 'cost': 343}, {'facility': 'F2', 'customer': 6, 'cost': 15}], 'objective': 4790.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",46,json,1
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=3
# num_farms=8
# SITES
site_id,site_upkeep_cost
F1,2000
F2,2000
F3,2000
# FARMS
farm_id
0
1
2
3
4
5
6
7
# DELIVERYS
site_id,farm_id,delivery_cost
F1,0,289
F1,1,161
F1,2,926
F1,3,561
F1,4,616
F1,5,480
F1,6,727
F1,7,28
F2,0,498
F2,1,112
F2,2,793
F2,3,128
F2,4,559
F2,5,812
F2,6,167
F2,7,193
F3,0,783
F3,1,807
F3,2,169
F3,3,176
F3,4,662
F3,5,906
F3,6,764
F3,7,427

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], 'connection_costs': [[289, 161, 926, 561, 616, 480, 727, 28], [498, 112, 793, 128, 559, 812, 167, 193], [783, 807, 169, 176, 662, 906, 764, 427]], 'objective': 5262.0}","{'open_facilities': [1], 'assignments': [1, 1, 1, 1, 1, 1, 1, 1]}",5262.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 8, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}, {'id': 'F3', 'opening_cost': 2000}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}, {'id': 7}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 289}, {'facility': 'F1', 'customer': 1, 'cost': 161}, {'facility': 'F1', 'customer': 2, 'cost': 926}, {'facility': 'F1', 'customer': 3, 'cost': 561}, {'facility': 'F1', 'customer': 4, 'cost': 616}, {'facility': 'F1', 'customer': 5, 'cost': 480}, {'facility': 'F1', 'customer': 6, 'cost': 727}, {'facility': 'F1', 'customer': 7, 'cost': 28}, {'facility': 'F2', 'customer': 0, 'cost': 498}, {'facility': 'F2', 'customer': 1, 'cost': 112}, {'facility': 'F2', 'customer': 2, 'cost': 793}, {'facility': 'F2', 'customer': 3, 'cost': 128}, {'facility': 'F2', 'customer': 4, 'cost': 559}, {'facility': 'F2', 'customer': 5, 'cost': 812}, {'facility': 'F2', 'customer': 6, 'cost': 167}, {'facility': 'F2', 'customer': 7, 'cost': 193}, {'facility': 'F3', 'customer': 0, 'cost': 783}, {'facility': 'F3', 'customer': 1, 'cost': 807}, {'facility': 'F3', 'customer': 2, 'cost': 169}, {'facility': 'F3', 'customer': 3, 'cost': 176}, {'facility': 'F3', 'customer': 4, 'cost': 662}, {'facility': 'F3', 'customer': 5, 'cost': 906}, {'facility': 'F3', 'customer': 6, 'cost': 764}, {'facility': 'F3', 'customer': 7, 'cost': 427}], 'objective': 5262.0}","{'selected': ['F2'], 'assignments': ['F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2', 'F2']}",47,csv,0
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.

For this instance there are 2 candidate charging hubs, 6 parking zones, and the hub enabling fees are 2000, 2000.
Candidate hub F1 has an enabling fee of 2000.
Candidate hub F2 has an enabling fee of 2000.
Assigning parking zone 1 to hub F1 incurs a repositioning cost of 349.
Assigning parking zone 2 to hub F1 incurs a repositioning cost of 63.
Assigning parking zone 3 to hub F1 incurs a repositioning cost of 624.
Assigning parking zone 4 to hub F1 incurs a repositioning cost of 138.
Assigning parking zone 5 to hub F1 incurs a repositioning cost of 405.
Assigning parking zone 6 to hub F1 incurs a repositioning cost of 434.
Assigning parking zone 1 to hub F2 incurs a repositioning cost of 951.
Assigning parking zone 2 to hub F2 incurs a repositioning cost of 263.
Assigning parking zone 3 to hub F2 incurs a repositioning cost of 853.
Assigning parking zone 4 to hub F2 incurs a repositioning cost of 5.
Assigning parking zone 5 to hub F2 incurs a repositioning cost of 462.
Assigning parking zone 6 to hub F2 incurs a repositioning cost of 44.
The aim is to keep the combined enabling fees and repositioning costs as low as possible when choosing which hubs to enable and how to assign each zone.

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': [2000, 2000], 'connection_costs': [[349, 63, 624, 138, 405, 434], [951, 263, 853, 5, 462, 44]], 'objective': 4013.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0]}",4013.0,"{'problem_type': 'UFLP', 'num_facilities': 2, 'num_customers': 6, 'facilities': [{'id': 'F1', 'opening_cost': 2000}, {'id': 'F2', 'opening_cost': 2000}], 'customers': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}], 'connection_costs': [{'facility': 'F1', 'customer': 1, 'cost': 349}, {'facility': 'F1', 'customer': 2, 'cost': 63}, {'facility': 'F1', 'customer': 3, 'cost': 624}, {'facility': 'F1', 'customer': 4, 'cost': 138}, {'facility': 'F1', 'customer': 5, 'cost': 405}, {'facility': 'F1', 'customer': 6, 'cost': 434}, {'facility': 'F2', 'customer': 1, 'cost': 951}, {'facility': 'F2', 'customer': 2, 'cost': 263}, {'facility': 'F2', 'customer': 3, 'cost': 853}, {'facility': 'F2', 'customer': 4, 'cost': 5}, {'facility': 'F2', 'customer': 5, 'cost': 462}, {'facility': 'F2', 'customer': 6, 'cost': 44}], 'objective': 4013.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",48,nl,1
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.

There are 3 candidate centers and 7 shelters; the opening costs for the centers are 1000, 1000, 1000.
Candidate center F1 has an opening cost of 1000.
Candidate center F2 has an opening cost of 1000.
Candidate center F3 has an opening cost of 1000.
If shelter A is served from center F1, the transportation cost is 146.
If shelter B is served from center F1, the transportation cost is 295.
If shelter C is served from center F1, the transportation cost is 693.
If shelter D is served from center F1, the transportation cost is 766.
If shelter E is served from center F1, the transportation cost is 99.
If shelter F is served from center F1, the transportation cost is 47.
If shelter G is served from center F1, the transportation cost is 303.
If shelter A is served from center F2, the transportation cost is 690.
If shelter B is served from center F2, the transportation cost is 707.
If shelter C is served from center F2, the transportation cost is 915.
If shelter D is served from center F2, the transportation cost is 275.
If shelter E is served from center F2, the transportation cost is 668.
If shelter F is served from center F2, the transportation cost is 130.
If shelter G is served from center F2, the transportation cost is 106.
If shelter A is served from center F3, the transportation cost is 357.
If shelter B is served from center F3, the transportation cost is 276.
If shelter C is served from center F3, the transportation cost is 63.
If shelter D is served from center F3, the transportation cost is 953.
If shelter E is served from center F3, the transportation cost is 566.
If shelter F is served from center F3, the transportation cost is 467.
If shelter G is served from center F3, the transportation cost is 307.
The team will use these entries to evaluate and then minimize the combined opening and transportation costs.

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': [1000, 1000, 1000], 'connection_costs': [[146, 295, 693, 766, 99, 47, 303], [690, 707, 915, 275, 668, 130, 106], [357, 276, 63, 953, 566, 467, 307]], 'objective': 3349.0}","{'open_facilities': [0], 'assignments': [0, 0, 0, 0, 0, 0, 0]}",3349.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 1000}, {'id': 'F2', 'opening_cost': 1000}, {'id': 'F3', 'opening_cost': 1000}], 'customers': [{'id': 'A'}, {'id': 'B'}, {'id': 'C'}, {'id': 'D'}, {'id': 'E'}, {'id': 'F'}, {'id': 'G'}], 'connection_costs': [{'facility': 'F1', 'customer': 'A', 'cost': 146}, {'facility': 'F1', 'customer': 'B', 'cost': 295}, {'facility': 'F1', 'customer': 'C', 'cost': 693}, {'facility': 'F1', 'customer': 'D', 'cost': 766}, {'facility': 'F1', 'customer': 'E', 'cost': 99}, {'facility': 'F1', 'customer': 'F', 'cost': 47}, {'facility': 'F1', 'customer': 'G', 'cost': 303}, {'facility': 'F2', 'customer': 'A', 'cost': 690}, {'facility': 'F2', 'customer': 'B', 'cost': 707}, {'facility': 'F2', 'customer': 'C', 'cost': 915}, {'facility': 'F2', 'customer': 'D', 'cost': 275}, {'facility': 'F2', 'customer': 'E', 'cost': 668}, {'facility': 'F2', 'customer': 'F', 'cost': 130}, {'facility': 'F2', 'customer': 'G', 'cost': 106}, {'facility': 'F3', 'customer': 'A', 'cost': 357}, {'facility': 'F3', 'customer': 'B', 'cost': 276}, {'facility': 'F3', 'customer': 'C', 'cost': 63}, {'facility': 'F3', 'customer': 'D', 'cost': 953}, {'facility': 'F3', 'customer': 'E', 'cost': 566}, {'facility': 'F3', 'customer': 'F', 'cost': 467}, {'facility': 'F3', 'customer': 'G', 'cost': 307}], 'objective': 3349.0}","{'selected': ['F1'], 'assignments': ['F1', 'F1', 'F1', 'F1', 'F1', 'F1', 'F1']}",49,nl,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.

There are 3 candidate locker locations and 7 commuter catchments, with installation fees listed as 1925, 1348, 1194.
Candidate locker F1 would cost 1925 to install.
Candidate locker F2 would cost 1348 to install.
Candidate locker F3 would cost 1194 to install.
If catchment 0 is assigned to locker F1, commuters incur a detour cost of 826.
If catchment 1 is assigned to locker F1, commuters incur a detour cost of 363.
If catchment 2 is assigned to locker F1, commuters incur a detour cost of 974.
If catchment 3 is assigned to locker F1, commuters incur a detour cost of 636.
If catchment 4 is assigned to locker F1, commuters incur a detour cost of 719.
If catchment 5 is assigned to locker F1, commuters incur a detour cost of 499.
If catchment 6 is assigned to locker F1, commuters incur a detour cost of 769.
If catchment 0 is assigned to locker F2, commuters incur a detour cost of 688.
If catchment 1 is assigned to locker F2, commuters incur a detour cost of 697.
If catchment 2 is assigned to locker F2, commuters incur a detour cost of 736.
If catchment 3 is assigned to locker F2, commuters incur a detour cost of 269.
If catchment 4 is assigned to locker F2, commuters incur a detour cost of 113.
If catchment 5 is assigned to locker F2, commuters incur a detour cost of 321.
If catchment 6 is assigned to locker F2, commuters incur a detour cost of 362.
If catchment 0 is assigned to locker F3, commuters incur a detour cost of 196.
If catchment 1 is assigned to locker F3, commuters incur a detour cost of 210.
If catchment 2 is assigned to locker F3, commuters incur a detour cost of 297.
If catchment 3 is assigned to locker F3, commuters incur a detour cost of 922.
If catchment 4 is assigned to locker F3, commuters incur a detour cost of 390.
If catchment 5 is assigned to locker F3, commuters incur a detour cost of 530.
If catchment 6 is assigned to locker F3, commuters incur a detour cost of 462.
The planner will choose which lockers to install and assign each catchment to exactly one chosen locker so the total of installation fees and detour costs is minimized.

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': [1925, 1348, 1194], 'connection_costs': [[826, 363, 974, 636, 719, 499, 769], [688, 697, 736, 269, 113, 321, 362], [196, 210, 297, 922, 390, 530, 462]], 'objective': 4201.0}","{'open_facilities': [2], 'assignments': [2, 2, 2, 2, 2, 2, 2]}",4201.0,"{'problem_type': 'UFLP', 'num_facilities': 3, 'num_customers': 7, 'facilities': [{'id': 'F1', 'opening_cost': 1925}, {'id': 'F2', 'opening_cost': 1348}, {'id': 'F3', 'opening_cost': 1194}], 'customers': [{'id': 0}, {'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 5}, {'id': 6}], 'connection_costs': [{'facility': 'F1', 'customer': 0, 'cost': 826}, {'facility': 'F1', 'customer': 1, 'cost': 363}, {'facility': 'F1', 'customer': 2, 'cost': 974}, {'facility': 'F1', 'customer': 3, 'cost': 636}, {'facility': 'F1', 'customer': 4, 'cost': 719}, {'facility': 'F1', 'customer': 5, 'cost': 499}, {'facility': 'F1', 'customer': 6, 'cost': 769}, {'facility': 'F2', 'customer': 0, 'cost': 688}, {'facility': 'F2', 'customer': 1, 'cost': 697}, {'facility': 'F2', 'customer': 2, 'cost': 736}, {'facility': 'F2', 'customer': 3, 'cost': 269}, {'facility': 'F2', 'customer': 4, 'cost': 113}, {'facility': 'F2', 'customer': 5, 'cost': 321}, {'facility': 'F2', 'customer': 6, 'cost': 362}, {'facility': 'F3', 'customer': 0, 'cost': 196}, {'facility': 'F3', 'customer': 1, 'cost': 210}, {'facility': 'F3', 'customer': 2, 'cost': 297}, {'facility': 'F3', 'customer': 3, 'cost': 922}, {'facility': 'F3', 'customer': 4, 'cost': 390}, {'facility': 'F3', 'customer': 5, 'cost': 530}, {'facility': 'F3', 'customer': 6, 'cost': 462}], 'objective': 4201.0}","{'selected': ['F3'], 'assignments': ['F3', 'F3', 'F3', 'F3', 'F3', 'F3', 'F3']}",50,nl,0