Variable with different indices

Answered

Tim

October 23, 2023 09:36

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Hi everyone,

I try to model an optimization problem where I have a variable with changing indices.

I am ignoring the randomness in the objective function in the first place. 

In the objective function, p is summed over c while in the first constraint the index is just f and I have to make this constraint valid for all f. So is there a way to model the variable with two indices but just using the one needed in the respective equation?

Many thanks

Tim

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  Eli Towle

  • Gurobi Staff

  October 23, 2023 18:24 Edited

  It looks to me like the indexing of \( p \) in the objective function is consistent with the indexing of \( p \) in the constraints. Namely, in the objective function, \( p \) is indexed by a single element of \( F \). However, that single index is \(\bar{f}_{r,c}\), meaning different combinations of \( c \in C \) and \( r \in R\) could correspond to different elements of \( F \).

  To translate this into code, you would need to define the dictionary \( \bar{f} \) that maps \( r \in R \) and \( c \in C \) to an element of \( F \). As long as your \( p \) variables are indexed by \( F \), you can then index \( p \) by \( \bar{f}_{r,c} \in F\). Below is a short Python script that shows one way to approach this.

  import gurobipy as gp
  
  R = [0, 1, 2, 3, 4]
  C = [0, 1, 2]
  
  # F = [0, ..., 14]
  F = list(range(len(R) * len(C)))
  print(f"F = {F}")
  
  # fbar maps each (r, c) pair an index of F
  fbar = {(r, c): len(C) * r + c for r in R for c in C}
  print(f"fbar = {fbar}")
  
  m = gp.Model()
  
  # Create p variables, indexed by F
  p = m.addVars(F, name="p")
  m.update()
  print(f"p = {p}")
  
  for r in R:
      for c in C:
          print(
              f"r={r}, c={c}: fbar[r,c]={fbar[r,c]}, p[fbar[r,c]] = {p[fbar[r,c]]}"
          )

   

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