a Variable which is the upper bound of a sum

Answered

ibtissam labriji

April 26, 2020 22:38

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Hello, 

I would like to know if it is possible to model the following expression in gurobi and if gurobi is able to solve it: 

M is an integer variable that takes value 1, 2, 3 or  4.

This variable is actually presents in the upperbound of a summation: 

1-sum_{i from 1 to M } P_i

P_i are given in the problem 

Regards, 

Ibtissam

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 03:14 Edited

  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 why not try our AI Gurobot?.
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  Richard Oberdieck

  • Gurobi Staff

  April 28, 2020 12:20

  Hi,

  I would model this using auxiliary variables /(y_i/):

  M = m.addVar(vtype=GRB.INTEGER,lb=1,ub=4)
  y_i = m.addVars(4, vtype=GRB.BINARY, name='y')
  
  1-sum(P_i*y_i) # The constraint you want
  m.addConstrs(i*y_i <= M for i in range(4)) # This forces y_i to be 1 only if M reaches it

  Is this what you are looking for?

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  ibtissam labriji

  April 29, 2020 11:10

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  Hello Richard, 

  Thank you for your response. Yes it does the trick. Although, I think that : the range should go to 5. So that y_4 can be taken into consideration : 

  m.addConstrs(i*y_i <= M for i in range(5))

  Please, correct me if I am wrong.

  Regards, 

  Ibtissam

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  Richard Oberdieck

  • Gurobi Staff

  April 29, 2020 18:42

  Yes, you are right, it actually should be

  m.addConstrs(i*y_i <= M for i in range(1,5))

  since y_0 does not exist.

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