How to write max function in models

Answered

Ankit khare

January 25, 2021 04:00 Edited

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I have tried Model.addGenConstrMin() and max_ . But couldn't able to run the model.

what i want is to write following line of Python-Cplex into Python-Gurobi

Python-Cplex - mdl.minimize(mdl.sum(mdl.max((ct[nStage,j]-D[j-1]),0) for j in job))

 

Cplex-OPL- minimize sum(j in job) maxl((ct[nStage][j]-D[j]),0);

 

Lingo:  @SMAX((CT[nStage][j]-D[j]),0);

 

How to write this line in Python-gurobi

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 03:01 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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  Jaromił Najman

  • Gurobi Staff

  January 26, 2021 11:20 Edited

  Hi Ankit,

  The max function works a bit different in Gurobi. It is used to define a max constraint

  \[ z = \max\{x_1,x_2,1,2\},\]

  where \(z,x_1,x_2\) are optimization variables and \(1,2\) constant values. The term \(\texttt{ct[nStage,j]-D[j]}\) describes a linear expression and not an optimization variable. Thus, in order to model the objective function, you have to introduce 2 additional auxiliary variables for each \(j\). Then, your code might look something like

  import gurobipy as gp
  from gurobipy import GRB
  
  m = gp.Model('test')
  # some arbitrarily picked values
  job = [1,2,3,4,5]
  nStage = 3 
  
  ct   = m.addVars(4, job, vtype=GRB.CONTINUOUS, name="ct")
  D    = m.addVars(job, vtype=GRB.CONTINUOUS, name="D")
  # define auxiliary variables
  aux1 = m.addVars(job, vtype=GRB.CONTINUOUS, name="aux1")
  aux2 = m.addVars(job, vtype=GRB.CONTINUOUS, name="aux2")
  
  # add constraints defining ct_j - D_j = aux1_j
  m.addConstrs( (ct[nStage,j]-D[j] - aux1[j] == 0 for j in job), name="aux_constr1")
  # add constraints defining aux2_j = max(aux1_j, 0)
  m.addConstrs( (aux2[j] == gp.max_([aux1[j],0.0]) for j in job), name="aux_constr2")
  
  # set objective to be the sum of all aux2 variables
  m.setObjective( gp.quicksum(aux2[j] for j in job))

  Best regards,
  Jaromił

   

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  Ankit khare

  January 30, 2021 01:54 Edited

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  Thanks for the reply. It worked.

  I am facing the same problem with one constraint.

   mdl.add_constraints(ct[g,j1])>= mdl.max(ct[g-1,j1], ct[g,j]) + PT[g-1][j1-1] for f in factory for j in job for j1 in job if j1!=j for g in stage if g>1 for i in machine[g-1] ) 

   

  where ct is the decision variable. I tried as follows but couldn't able to run it

   

  First approach:

   

  mdl.addConstrs(ct[g,j1] >= gp.max_(ct[g-1,j1],ct[g,j]) + PT[g-1][j1-1] for f in factory for j in job for j1 in job if j1!=j for g in stage if g>1 for i in machine[g-1] )

   

  Second approach:

   

  mdl.addConstrs((aux3[g,j] == gp.max_(ct[g-1,j1],ct[g,j]) for j in job for j1 in job if j1!=j for g in stage if g>1), name="aux_constr3")

   

  mdl.addConstrs(ct[g,j1] >= aux3[g,j] + PT[g-1][j1-1] for f in factory for j in job for j1 in job if j1!=j for g in stage if g>1 for i in machine[g-1] )

   

   

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  Jaromił Najman

  • Gurobi Staff

  February 01, 2021 08:32 Edited

  Hi Ankit,

  The max_() function has to be used in an equality constraint. Thus, your second approach is the way to go. Could you provide the error message and (if possible) a minimal working example? How do you define your variables \(\texttt{ct}\)?

  Best regards,
  Jaromił

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• 

  Shiyang Huang

  October 31, 2022 16:25

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  Does Gurobi linearize max_ constraints automatically? could this lead to slower computation?

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  Jaromił Najman

  • Gurobi Staff

  November 02, 2022 08:33

  Does Gurobi linearize max_ constraints automatically?

  Yes.

  could this lead to slower computation?

  Do you mean in comparison to treating the \(\max\) function as a nondifferentiable function? It is possible that there are cases where treating the \(\max\) function without linearization via additional binary variables and auxiliary constraints might be beneficial. I would say that linearization should work very well in most of cases.

   

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