Problem formulation for to satisfy the demand for a list of products

Answered

Krzysztof Suwada

• August 20, 2024 14:04

I would like to introduce a penalty connected with the number of parcels sent from one location to another.

Something like: 
- if the number of parcels sent is < 15 then the penalty is 0
- [15, 20) penalty is 10
- [20, 30) penalty is 50
- [30, infinity) penalty is 1000000

I have a variable the counts number of packages sent from one location to another count_parcels[(loc_from, loc_to)] how to create the penalty?

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• Official comment

  

  Juan Orozco

  Gurobi Staff

  • August 20, 2024 19:24

  You can use the method model.setPWLObj(), so I suggest to read the associated documentation, as well as the section Objectives of our reference manual.
• 

  Krzysztof Suwada

  • August 22, 2024 10:11
  • Edited

  

  

  Ok, and what if I want it to be a part of a variable?
  something like this code

  for loc_a in locations:
          for loc_b in locations:
              if loc_a != loc_b:
                  m.addConstr(total_value[loc_a, loc_b] == quicksum(x[loc_a, loc_b, p]*price[p] for p in products))
                 if total_value[loc_a, loc_b] < 1500 and total_value[loc_a, loc_b] > 1000:
                       m.addConstr(value_penalty[loc_a, loc_b] = 1500 - total_value[loc_a, loc_b])
                 else:
                      m.addConstr(value_penalty[loc_a, loc_b] = 2*(1500 - total_value[loc_a, loc_b])) 

   

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• 

  Krzysztof Suwada

  • August 22, 2024 10:16

  

  

  And then I want to sum-up all the penalties and add it to a objective function.

   

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• 

  Jonasz Staszek

  Community Moderator

  • August 30, 2024 12:35
  • Edited

  

  

  

  Hi Krzysztof,

  I would suggest that you proceed in the way suggested by Juan.

  Perhaps the following code snippet will be an inspiration for you:

  for loc_a in locations:
          for loc_b in locations:
              if loc_a != loc_b:
                  m.setPWLObj(total_value[loc_a, loc_b], [0, 15, 20, 30], [0, 10, 50, 1000000])

  It should generally do everything you are after: define a piecewise-linear penalty for your variables and include them in your objective function.

  Hope this helps.

  Best regards
  Jonasz

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