Defining a set dependent on an other set

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Tiril Amundsen

2022年05月08日 11:32

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Hi, 

I'm trying to define a set that is dependent on another set, like this:

K: Set of commodities, denoted k

R^k: Set of feasible routes for transporting commodity k, denoted r

I have two commodities, [0,1], and I want R^1 to be [0,1,2,3] and R^2 to be [0,1,2,3,4,5,6]. I also have a binary variable x_r, how will this be defined when r is dependent on k?

How do I implement this in Gurobi?

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  Simranjit Kaur

  • Gurobi Staff

  2025年11月16日 23:37

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  Jonasz Staszek

  • Community Moderator

  2022年05月09日 09:04 編集済み

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  Hi Tiril,

  you would need two indices per variable for that - one for the commodity and the other one for the route. You implement it just like any other variable:

  import gurobipy as gp
  
  m = gp.Model()
  
  R = dict()
  R[1] = [0, 1, 2, 3]
  R[2] = [0,1,2,3,4,5,6]
  
  K = [1, 2]
  x = gp.tupledict()
  for k in K:
      for r in R[k]:
          x[k, r] = m.addVar(vtype="B", name=f"x_{k}_{r}")

  Best regards
  Jonasz

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  Tiril Amundsen

  2022年05月09日 08:50

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  Hi, thank you for the answer! But when running only the above I get the error message "KeyError: 0". It seems to be for the "for r in R[k].

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  Jonasz Staszek

  • Community Moderator

  2022年05月09日 09:04

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  You're right, I just corrected the error.

  Best regards
  Jonasz

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  Tiril Amundsen

  2022年05月09日 10:59 編集済み

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  Thank you so much. Another question arised when implementing the complete model. I have a table of variables that is dependent on both commodity, routes and nodes. When adding constraints I have to sum over these sets, but I'm not sure how to model the matrices. Until now I have defined them for each commodity, like this: M1[r,n], M2[r,n], but I'm not sure how I can also sum over k in commodities.  

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  Jonasz Staszek

  • Community Moderator

  2022年05月09日 13:44

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  I'm not sure I understood your challenge.

  If M1 and M2 were corresponding to various nodes, you could instead have them as on dict with a 3-tuples as keys, for example, the following way

  # for illustration only, not replicable
  M = dict()
  for n in nodes:
      for r in routes:
          for k in commodities:
              M[n, r, k] = ...

  If that's not what you have trouble with, I'd need a better clarification, perhaps with a code example.

  Best regards
  Jonasz

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