gurobi indicator constraints multiple variables

Answered

Leon Irsig

January 09, 2023 11:09

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Hello,

I would like to add an indicator condition to my model. This is to sum over a variable and if the sum is greater than 0 set a binary variable to 1

My idea: 
z and r are binary variables
routes[t][k] returns the corresponding indexes for the z variable 
t and k are two superior for loops
mod.addConstr((gp.quicksum(z[i,t,k] for i in routes[t][k]) >= 1) >> (r[t,k] == 1))

Related to

• Python
• Indicator Constraints

0

• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 13, 2026 01:50

  This post is more than two 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.
• 

  Jaromił Najman

  • Gurobi Staff

  January 09, 2023 12:53 Edited

  Hi Leon,

  This is discussed in the Knowledge Base article How do I model conditional statements in Gurobi?

  In particular, you will not need an \(\epsilon > 0\), since your condition is a \(\geq\) and not a strict inequality.

  Moreover, if your condition reads "if sum is greater or equal than 0 then set b = 1 else b = 0", then you don't need the additional indicator variables discussed in the linked Knowledge Base article, because \(b\) then already holds the value of your binary.

  In your special case, you can use the constraint

  \[\begin{align*}
  \sum z \leq M \cdot r
  \end{align*}\]

  where \(M\) is a big-M constant equal to the number of binary variables \(z\). This way, if \(\sum z \geq 1\) holds, then \(r\) has to be set to \(1\).. Note that in this case if \(\sum z = 0\), then \(r\) can be \(0\) or \(1\).

  Best regards, 
  Jaromił

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  Leon Irsig

  January 09, 2023 15:42

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  Hi Jaromił,

  Thanks for your help!

  Best regards,
  Leon

  0

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