Not equal binary variables in a constraint

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Ana Guasque Ortega

2023年10月20日 10:18

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Good morning,

I want to model an allocation problem in which items are allocated to bins. Items have a characteristic (for example, color) so I need a constraint that ensure that If two items have different colors, they have to be allocated to different bins. 

 m.addConstrs( (a[i,b] != a[ii,b]  for b in bins for i in items for ii in items if( i!=ii and Color[i]!=Color[ii])), "c1" ) 

a is the binary variable whose value is 1 if task i is allocated to bin b and 0 otherwise.

The problem is that not equal is not permitted in a constraint. I found this post but I don't get the point.

 

Thanks in advance.

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  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:36

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  Matthias Miltenberger

  • Gurobi Staff

  2023年10月20日 10:56

  Hi Ana,

  If you have binary variables that need to be different, you can model that quite easily:

  a = m.addVar(vtype=GRB.BINARY, name="a")
  b = m.addVar(vtype=GRB.BINARY, name="b")
  m.addConstr(a + b == 1)

  I hope that helps!

  Cheers,
  Matthias

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  Riley Clement

  • Gurobi Staff

  2023年10月20日 13:54 編集済み

  Hi Ana,

  I will also add to Matthias' answer by noting that I think your logical conditions that you want to model will not succeed for your problem.

  Say that Color[0] = blue, Color[1] = red, Color[2] = green, and for a particular bin b, we have a[0,b] =1, so that item 0 is put in bin b.

  From the logic you are trying to model, we must have a[1,b] = 0 and a[2,b] = 0 since they are not blue.  But then this violates a constraint which says that "item 1 and 2 have different colors so then a[1,b] != a[2,b]".

  Using Matthias' example a slight adjustment to use

  m.addConstr(a + b <= 1)

  will model the logic I think you need.  And if you have n variables a, b, c, ... which correspond to the one bin, but all different colors then you can use a stronger constraint of

  m.addConstr(a + b + c + .... <= 1)

  since only once of them can be chosen.

  - Riley

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  Ana Guasque Ortega

  2023年10月23日 06:36

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  Thank you both very much!! I'm trying to implement it. 

  Best, Ana.

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