If-Else condition for GUROBI C++ is not working

Answered

Mohammad Humyun Fuad Rahman

• May 30, 2023 02:31
• Edited

Hi,

I want to apply the If-Else condition to calculate the tardiness of each job and then, calculate the total tardiness for all jobs in a scheduling problem. The expression for calculating tardiness for each job can be represented as follows.

Tardiness of job i  =    maximum (0, completion time of job i - due date of job i)

From the above expression it is clear that the tardiness value can not be less than zero, i.e., if the completion time of a job is less than its due date then the its tardiness value is zero. 

Now, I use the Indicator constraint to express this relationship and used an additional binary variable b and Big M constraint to express this relationship. However, the indicator constraint isn't working as the value of tardiness for a job is 'zero' even though its completing time is greater than its due date. Hence, could you please help me to identify this issue?

Note that, I have followed the similar concept from this post: https://support.gurobi.com/hc/en-us/articles/4414392016529-How-do-I-model-conditional-statements-in-Gurobi-

 

        // Set objective: minimize total tardiness
        double bigM = 10000, eps_value = 0.0001;

        GRBQuadExpr totalTardiness = 0;
        for (int local_i = 0; local_i < job; local_i++)        
        {
            GRBVar job_tardy = model.addVar(0.0, GRB_INFINITY, 0.0, GRB_INTEGER);
            GRBVar b = model.addVar(0, 1, 1, GRB_BINARY);

            job_comtime = 0.0;
            
            for (int local_k = 0; local_k < mac; local_k++)
            {
                for (int local_l = 0; local_l < sequence; local_l++)
                {
                    job_comtime += jmalloc[local_i][local_k][local_l] * process_time[local_k][local_i]; 
                }
            }
            
            model.addConstr (job_comtime >= duedate[local_i]+ eps_value - bigM * (1-b));
            model.addConstr(job_comtime <= bigM * (1 - b));
           
            GRBQuadExpr test = model.addVar(0, INFINITY, 0, GRB_INTEGER);

            model.addGenConstrIndicator(b, true, (test == job_comtime));
            model.addGenConstrIndicator(b, false, (test == 0));
           

            totalTardiness += test ;
          
             
        }

        model.setObjective(totalTardiness, GRB_MINIMIZE);

        model.optimize();

0

• 

  Mario Ruthmair

  Gurobi Staff

  • May 30, 2023 08:58

  Hi Mohammad,

  Your code snippet is a bit confusing for me, e.g., variable job_tardy is never used after creating it.
  Additionally, you are using GRBQuadExpr, does your model contain quadratic terms?
  I guess jmalloc[][][] are variables, right?

  But I would model it in a different way, without BigM and indicator constraints:
  The variable job_tardy has lower bound 0 so it cannot get negative.
  Then, you push up job_tardy by the difference of completion time and due date:

  job_comtime - duedate <= job_tardy

  In the minimization objective you sum up all job_tardy variables, so in any optimal solution the job_tardy values will correspond exactly to the tardiness of a job since it does not make sense to set it to a higher value due to minimization.

  Best regards,
  Mario

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