How to formulate a constraint that models the maximum of a maximum value?

Answered

Benjamin Brandt

• September 11, 2023 21:04

Hi,

I proposed a model and implemented it in CPLEX using Python. Now I'm trying to switch to Gurobi, but I can't find a way to model a constraint that finds the maximum value of some maximum values.

This is the constraint:

for j in N:
        mdl.add_constraint(a[0] + mdl.max( [ (mdl.max( [t_d[0,k] + s_d[k] + t_d[k,j] - t_t[0,j], 0] ) )*z[0,k,j] for k in N if j != k] )
        <= a[j] + M)

• "a" and "z" are continuous variables
• "t_d", "s_d", "t_t" and "M" are constants 

Related to

• MIP

0

• 

  Riley Clement

  Gurobi Staff

  • September 12, 2023 03:39

  Hi Benjamin,

  The addGenConstrMax function is our equivalent.  As noted in the description of the function you can also use gp.max_

  In this particular case though I think using the max function will introduce unnecessary variables and constraints and I suggest trying the following alternative:

  for j in N:
       m.addConstr(a[0] <= a[j] + M)
       for k in N if j != k:
           m.addConstr(a[0] + (t_d[0,k] + s_d[k] + t_d[k,j] - t_t[0,j])*z[0,k,j]] <= a[j] + M)

  - Riley

  1
• 

  Benjamin Brandt

  • September 14, 2023 19:23

  

  

  

  Thank you!

  0

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