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

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Krzysztof Suwada

2024年08月20日 14:04

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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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  Juan Orozco

  • Gurobi Staff

  2024年08月20日 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.
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  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:21

  This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
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  Krzysztof Suwada

  2024年08月22日 10:11 編集済み

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  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

  2024年08月22日 10:16

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  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

  2024年08月30日 12:35 編集済み

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  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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