Do Variable Bounds create constraints in the solver?

Answered

Iason Liagkas

April 10, 2024 08:59

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Hello guys, I am working on the Benders algorithm. I am wondering if I have a problem with a variable x with an upper bound of 1. Does that create a constraint of x<=1 on the solver? Because if that is the case I would have to create a cut for this to debug my algorithm.

Kind  regards
Iason

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• Sensitivity

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 13, 2026 01:26

  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.
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  Mario Ruthmair

  • Gurobi Staff

  April 15, 2024 08:01

  Hi Iason,

  Variable bounds are handled specially in the solver and not via an additional constraint. If you need to consider the dual values corresponding to those bounds in your Benders subproblem, you can access the reduced costs via variable attribute RC for basic solutions.

  • If a variable is fixed, then RC is unbounded.
  • If a variable has no bounds, then RC must be 0.
  • If a variable is at its lower bound, RC >= 0.
  • If a variable is at its upper bound, RC <= 0.

  Best regards,
  Mario

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  Iason Liagkas

  April 17, 2024 07:41

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  Thanks Mario.

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