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1、DiscreteOptimizationMethodsandtheirRoleintheIntegrationofPlanningandScheduling*IgnacioE.Grossmann,SusaraA.vandenHeeverandIiroHarjunkoskiDepartmentofChemicalEngineeringCarnegieMellonUniversity,Pittsburgh,PA15213March1,2001AbstractTheneedforimprovementinprocessop
2、erations,logisticsandsupplychainmanagementhascreatedagreatdemandforthedevelopmentofoptimizationmodelsforplanningandscheduling.Inthispaperwefirstreviewthemajorclassesofplanningandschedulingmodelsthatariseinprocessoperations,andestablishtheunderlyingmathematicals
3、tructureoftheseproblems.Aswillbeshown,thenatureofthesemodelsisgreatlyaffectedbythetimerepresentation(discreteorcontinuous),andisoftendominatedbydiscretedecisions.Wethenbrieflyreviewthemajorrecentdevelopmentsinmixed-integerlinearandnonlinearprogramming,disjuncti
4、veprogrammingandconstraintprogramming,aswellasgeneraldecompositiontechniquesforsolvingtheseproblems.Wepresentageneralformulationforintegratingplanningandschedulingtoillustratethemodelsandmethodsdiscussedinthispaper.Keywords:planning,scheduling,optimization,mixe
5、d-integerprogramming.1.IntroductionThedevelopmentofoptimizationmodelsforplanningandschedulingofchemicalprocesseshasreceivedsignificantattentionoverthelast5-7years.Onemajorreasonhasbeentherealizationbyindustrythatlargepotentialsavingscanbeachievedbyimprovingthel
6、ogisticsofmanufacturinginchemicalprocesses.Examplesofsavingsincludelowerinventories,lowertransitioncosts,andreductioninproductionshortfalls.Theinterestinplanningandschedulinghasfurtherincreasedwithindustry’sgoalofimprovingthemanagementanddynamicsoftheirsupplych
7、ains.Finally,majoradvancesinlarge-scalecomputationandmathematicalprogramminghavepromotedtheinterestinapplyingthesetechniquestoplanningandschedulingproblems.Thegoalofthispaperistoprovideanoverviewoftheoptimizationbasedmodelsforplanningandscheduling,reviewthesolu
8、tionstrategiesandmathematicalprogrammingmethodsthatareavailableforsolvingtheseproblems,andproposeaconceptualmodelforintegratingplanningandscheduling.Finally,wepresentthreeex
