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I would like to express if then else statement in a set of constraints using Gurobi via Python API where B and A are binary decision variables.

Here is the statement I am stuck on :

If (B[r,u,v,x,y]) then A[r,u,x] or A[r,v,y]

Else set the value of B[r,u,v,x,y] == 0 when A[r,u,x] =1 and A[r,v,x]

I know how to express the first part of if then as :

B[r,u,v,x,y] >= A[r,u,x]

B[r,u,v,x,y] >= A[r,v,u]

But not sure how to formulate into constraints : when B[r,u,v,x,y] to be 0 if A[r,u,x] and A[r,v,y] are set to 1 in the else part.

Thanks

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  • Written like that it's ambiguous if not nonsense. Try to write it more formally, e.g by using pure propositional calculus (and state if those are binary-variables or integers; the else-line is unclear about that) Commented Oct 18, 2017 at 22:20
  • @sascha I edited my post, hopefully now it is more clear. thanks :) Commented Oct 19, 2017 at 2:28
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    Still unclear, but maybe it does not matter (if you know what to formulate): just follow propositional logic in your else too; and ignore the fact it's an else in your case! Just treat it as new expression: something like (prototype): (a_0 & a_1) -> B < DeMorgan-> (not a_0 or not a_1) or B. If needed you can create some auxiliary-variable for the first subexpression (not a_0 or not a_1 == new_var) (where not is for binaries a (1-var) and an equality are two implications. Commented Oct 19, 2017 at 2:32
  • thanks @sascha. I mean when A[r,u,x] =1 and A[r,v,x]=1 as I put the same index x I need to force B[r,u,v,x,y] to be 0, so do you suggest to follow the propositional logic ? Commented Oct 19, 2017 at 2:57
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    Yes. Given it's an implication it's just (1-A0) + (1-A1) + (1-B) >= 1 Commented Oct 19, 2017 at 10:47
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