If Constraint

回答済み

Rayan SAAD

2023年06月07日 19:45 編集済み

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Helloo,

I have 2 binary variables h[i,j,t] and u[i,j,t] and  I need to express this constraint in my model:

if for a given i : u[i,j,t]=1 then for all other i, h[i,j,t]=0,

the solution i found is :

But i dont know how to express it in Gurobipy,

thank you,

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• 正式なコメント

  

  Gwyneth Butera

  • Gurobi Staff

  2023年06月08日 11:19

  In addition, please see our Knowledge Base article How do I model conditional statements in Gurobi?
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  Simranjit Kaur

  • Gurobi Staff

  2023年06月08日 00:12 編集済み

  Hi Rayan,

  Your solution is correct. You can model this as follows:

  m.addConstrs( sum( h[k,j,t] for k in I if k != i) <= M *( 1- u[i,j,t] ) for i in I  for j in J for t in T )

  Please choose the smallest possible value of M carefully. One value can be the sum of the upper bounds on the h variables. 

  Alternatively, you can add an indicator constraint, which does not require you to choose the value of M :

  m.addConstrs( (u[i,j,t] ==1) >> (sum( h[k,j,t] for k in I if k != i) == 0 ) for i in I  for j in J for t in T )

  Best regards,

  Simran

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  Rayan SAAD

  2023年06月08日 13:15

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  It perfectly worked !

  Thanks a lot !!

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  Rayan SAAD

  2023年06月27日 12:42

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  Hello Simrane,

  I want to express the same constraint, but this time i have 4 index for my 2 variables :

  h[i,c,j,t] and u[i,c,j,t]

  if for a given i and c : u[i,c,j,t]=1 then for all other i, and c :  h[i,c,j,t]=0,

  I tried this formulation, but it doesn't work :

  model.addConstrs( (u[i,c,j,t] ==1) >> (gp.quicksum( h[k,d,j,t] for k in range(I) if k != i for d in range(C) if d != c) == 0 ) for i in range(I)  for j in range(J) for t in range(T) for c in range(C))

   

   

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  Simranjit Kaur

  • Gurobi Staff

  2023年06月28日 02:59

  Hi Rayan,

  Your implementation should work fine if you want to add the constraint:

                        u[i,c,j,t]=1 implies h[k,d,j,t] = 0 for all h variables where k != i and d !=c.

  However, if you want to add the constraint:

                       u[i,c,j,t]=1 implies h[k,d,j,t] = 0 for all h variables where k != i or d !=c,

  you will need to modify your indicator constraint as follows:

  m.addConstrs( (u[i,c,j,t] ==1) >> (gp.quicksum( h[k,d,j,t] for k in range(I) for d in range(C) if ( k != i or d != c) ) == 0 ) for i in range(I)  for j in range(J) for t in range(T) for c in range(C))

  Best regards,

  Simran

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