How to deal with a fraction of binary decision variables

Awaiting user input

Simon Kwon

November 24, 2022 21:14 Edited

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Dear whom it may concern,

I am writing this to request some help in modelling my formulation. My formulation contains a set of binary (x, z) , integer variables (y). My concern is that the formulation contains a set of constraints engaging a fraction of integer decision variables (y) as follows:

 

 

The variables y can be 0 but it would make the second constraint above undefined. I also tried to reformulate this as proposed in https://support.gurobi.com/hc/en-us/articles/360053259371-How-do-I-divide-by-a-variable-in-Gurobi-

However, the proposed way would require to have a lower bound > 0 on the variables which would not work in my case. 

I was wondering what could be a way to reformulate this without imposing the >0 lower bound?...

Thanks for your time.. 

Related to

• MIP
• Python

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  Jonasz Staszek

  • Community Moderator

  November 25, 2022 09:35

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  Dear Simon,

  the reason for the lower bound being set to \( x^L > 0 \) in the case you mention is to avoid  \( x \) assuming the value of \( 0 \).

  If you also need to include the case of negative values of \( x \), you may want to use indicator constraints (see here and here). They will allow you to model two cases: one for \( x > 0 \) and the other for \( x < 0 \). If you need more guidance, let me know.

  Best regards,
  Jonasz

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