Solve the Problem

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To solve the problem, we use a combination of the Concert Technology IloGenerate goal and Scheduler's IloSetTimesForward.

    IloEnv env;
    IloNumVar totalCost;
    IloNumVarArray costs;
    IloSchedulerSolution solution(env);

    IloModel model = DefineModel(env, maxMakespan, totalCost, costs, solution);

    IloSolver solver(model);
    IloGoal goal = IloGenerate(env, costs) && 
                   IloSetTimesForward(env);

IloGenerate will first instantiate the costs to their minimal possible value. Then, IloSetTimesForward will schedule the activities at a convenient start time, given their duration.