Flexible solutionsindisjunctivescheduling:Generalformulationandstudyofthe flow-shop case

We considerthecontextofdecisionsupportforschedulemodificationafterthecomputationoff-lineofa predictive optimal(ornearoptimal)schedule.Thepurposeofthisworkistoprovidethedecisionmaker a characterizationofpossiblemodificationsofthepredictiveschedulewhilepreservingoptimality.In the contextofmachinescheduling,theanticipatedmodificationsarechangesinthepredictiveorderof operations onthemachines.Toachievethisgoal,aflexiblesolutionfeasiblew.r.ttooperationsdeadlines, is providedinsteadofasinglepredictiveschedule.Aflexiblesolutionrepresentsasetofsemi-active schedules andischaracterizedbyapartialorderoneachmachine,sothatthetotalordercanbeset on-line, asrequiredbythedecisionmaker.Aflexiblesolutionisfeasibleifallthecompleteschedules that canbeobtainedbyextensionarealsofeasible. In thispaperwedeveloptwomainissues.Thefirstoneconcernstheevaluationofaflexiblesolution in theworstcaseallowingtocertifyifthesolutionisfeasible.Thesecondissueisthecomputationof feasible (w.r.tdeadlines)flexiblesolutionsofmaximalflexibilityimposedbythedecisionmaker.Under an epsilon-constraint framework,solvingthisproblemallowstofindcompromisesolutionsfortheflexi- bility criterionandanyminmaxregularschedulingcriterion.Thespecialcaseoftheflow-shopscheduling problem isstudiedandcomputationalexperimentsarecarriedout.