Indicator constraint for multiplying two binary variables

Answered

Charitha Buddhika Heendeniya

July 08, 2022 12:04 Edited

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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

• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 16, 2025 23:33

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
• 

  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 Buddhika Heendeniya

  July 12, 2022 13:22

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  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

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