Indicator constraint for multiplying two binary variables

Answered

Charitha Heendeniya

• July 08, 2022 12:04
• Edited

Dear community,

I have a constraint of the form:

if x(i, j, k) == 1: sum (over t) {p(i, j, k, t) * u(i, j, t)} == 1

Could you please advise me on how to model it using Gurobi? Here x, u, and t are binary variables. Below is how I tried and then I get the error "TypeError: must be real number, not gurobipy.QuadExpr". 

for i in I:
    for j in J:
        for k in K:
            model.addConstr((x[i, j, k] == 1) >> (quicksum(p[i, j, k, t] * u[i, j, t] for t in T) == 1))

Regards

Buddi

1

• 

  Mario Ruthmair

  Gurobi Staff

  • July 08, 2022 12:31

  Hi Charitha,

  Indicator constraints only allow linear constraints. What you could do is to introduce additional variables that model the binary products and use those new variables in your indicator constraint, i.e.:

  f(i, j, k, t) = p(i, j, k, t) * u(i, j, t)
  if x(i, j, k) = 1: sum (over t) f(i, j, k, t) = 1

  Apart from that, would it work to immediately reformulate the indicator constraint to the following?

  sum (over t) f(i, j, k, t) = x(i, j, k)

  Best regards,
  Mario

  0
• 

  Charitha Heendeniya

  • July 12, 2022 13:22

  

  

  Thank you. I think this works for me.

  I also have another question, but since it is not directly a follow-up to this thread, I posted it here. 

  Appreciate if you could have a look at it as well. 

  Best,

  Charitha

  0

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