Minimizing the makespans

With a constraint, or a surrogate constraint.

In the distributed school time-tabling example, the makespan of the solution can be minimized so that everybody can leave the school early at the end of the week.

To minimize the makespan:

  1. Add the following constraint: 
      makespan == max(r in InstanceSet) End[r];

    where the variable makespan is declared with: 

    dvar int makespan in Time;                            // ending date of last course

    and the Time range corresponds to the time table period (that is, a week):

    int HalfDayDuration = DayDuration div 2;
int MaxTime = DayDuration*NumberOfDaysPerPeriod;
range Time = 0..MaxTime-1;
  2. Optionally, to help proving optimality, add a surrogate constraint. 
      makespan >= max(c in Class) sum(r in InstanceSet : r.Class == c) r.Duration;