Conditional logic in linear expression

Answered

Ritesh Agrawal

• May 22, 2019 23:45
• Edited

Hi,

 

I have an linear expression with conditional logic. Gurobi doesn't complain but is giving wrong results. The linear expression essentially converts into a constant value. 

 

Cost = quicksum(data[t].cost for t in range(T) if quicksum(X[q] for q in data[t]) >= 1)

 

where X is a binary decision variable. 

Is there any other way to express this. 

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• Official comment

  

  Michael Winkler

  Gurobi Staff

  • May 23, 2019 15:14

  Hi Ritesh,

   

  you cannot directly model constraints conditionally on the result of another constraint.

  Lets assume that you want to minimize your Cost. Then what you could do is add constraints for each t in T quicksum(X[q] for q in data[t]) - |data[t]|*y[t] <= 0 (|data[t]| being the cardinality of elements in data[t], y[t] an additional binary).

  Then you objective function would be to minimize quicksum(data[t].cost * y[t] for t in range(T)). (Then the objective would always push y[t] down to zero if non of the X[q] with q in data[t] are one in a solution.)

   

  Best,

  Michael
• 

  Ritesh Agrawal

  • May 28, 2019 12:35

  

  

  

  Hi Michael,

   

  Thanks for the idea. That worked nicely. 

   

  Ritesh

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