Once all the constraints are added, we can use the non-deterministic programming primitives of Solver to generate a solution with minimal makespan. The first thing to do is to define a constrained makespan variable and specify that its value is greater than the end time of each activity. For each activity activities[i], the statement model.add(activities[i].endsBefore(makespan)); constrains the makespan variable to be greater than or equal to the end time of activities[i].

The second thing to do is to write a function that (a) generates a solution to the problem and (b) sets the constrained makespan variable to the makespan of the solution we get. We'll adopt the following algorithm for that purpose.

The correctness of this algorithm is easy to demonstrate: The activity A chosen at step 3 must either start at its earliest start time or must be postponed to start later, but starting A later makes sense only if other activities prevent A from starting at its earliest start time. In that case, the scheduling of these other activities must eventually result in the update of the earliest start and end times of A. Hence, a backtrack from step 4 signifies that all the activities which do not have fixed start and end times have been postponed. Such a situation would be absurd, as in any solution the activity which will start the earliest among those which have been postponed could be set to start at its earliest start time. Consequently, it is correct to backtrack from step 4 up to the most recent choice point.

IloMinimize sets the objective of minimizing makespan in the model.

    IloModel model(env);
    IloNumVar makespan;
    DefineProblem(model,
                  NumberOfActivities,
                  Durations,
                  Demands,
                  Capacity,
                  Precedences,
                  level,
                  makespan);
    
    model.add(IloMinimize(env, makespan));
    
    // Algorithm
    IloSolver solver(model);
    IloGoal goal = IloSetTimesForward(env, makespan, IloSelFirstActMinEndMin);
    
    if (solver.solve(goal)) {
      PrintSolution(IlcScheduler(solver));
      solver.printInformation();

#if defined(ILO_SDXLOUTPUT)
      IloSDXLOutput output(env);
      ofstream outFile("ship.xml");
      output.write(IlcScheduler(solver), outFile, solver.getIntVar(makespan));
      outFile.close();
#endif
    }
    else
      solver.out() << "No solution!" << endl;

    env.end();