Simple If condition with a decision variable

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Jack Kaz

2022年11月02日 06:34 編集済み

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Hi, I am new with Gurobi and have a question about using if clause in my Python program. My variable can only be Q = 0 or Q > 0 and its upper bound is defined 1000. A separat function should give a 0 back If Q==0. I saw this post https://support.gurobi.com/hc/en-us/articles/4414392016529-How-do-I-model-conditional-statements-in-Gurobi- but don't get it for this simple way. Thank you for answers.

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  Simranjit Kaur

  • Gurobi Staff

  2025年11月16日 23:25

  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.
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  Jaromił Najman

  • Gurobi Staff

  2022年11月02日 09:57 編集済み

  Hi Jack,

  You can then add a binary variable \(b\) and define  constraints \(Q \leq Q^u\cdot b\), \( Q^l\cdot b \leq Q\), where

  \(b \in \{0,1\}, Q \in [0, Q^u]\) and \(0 < Q^l \leq Q^u\) is a positive lower bound on \(Q>0\). Then if \(Q = 0\), then \(b= 0\) and if \(Q \in [Q^l, Q^u]\) then \(b=1\).

  Best regards, 
  Jaromił

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  Jack Kaz

  2022年11月02日 13:00

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  Hi Jaromil, 

  thank you very much for your advice. In Python code it should look like this, right?

  UB = 1000
  LB = 0
  
  Q  = model.addVar(lb=LB , ub=UB , vtype=GRB.CONTINUOUS, name="Q")
  bQ = model.addVar(vtype=GRB.BINARY, name="bQ")
  iQ = model.addVar(vtype=GRB.CONTINUOUS, name="iQ")
  
  model.addConstr(Q >= LB * bQ)
  model.addConstr(Q <= UB * bQ)
  
  model.addConstr((bQ == 1) >> (iQ == 1))
  model.addConstr((bQ == 0) >> (iQ == 0))

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  Jaromił Najman

  • Gurobi Staff

  2022年11月02日 13:06 編集済み

  Hi Jack,

  This will not work with \(\texttt{LB=0}\). You have to define a small threshold because Gurobi does not accept strict inequality constraints. You could go with

  UB = 1000
  LB = 1e-4 # shouldn't be too small. Anything >= 1e-5 should be OK
  
  Q  = model.addVar(lb=0 , ub=UB , vtype=GRB.CONTINUOUS, name="Q")
  bQ = model.addVar(vtype=GRB.BINARY, name="bQ")
  
  model.addConstr(Q >= LB * bQ)
  model.addConstr(Q <= UB * bQ)

  Note that you don't need the \(\texttt{iQ}\) variable, because it holds that

  \[\begin{align*}
  b = 0 &\rightarrow LB \cdot 0 \leq Q \leq UB \cdot 0 \\
  b = 1 &\rightarrow LB \cdot 1 \leq Q \leq UB \cdot 1
  \end{align*}\]

  Best regards, 
  Jaromił

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