A decomposition-basedstochasticprogrammingapproachforthe project schedulingproblemundertime/costtrade-offsettingsand uncertain durations

Resourceallocationinprojectnetworksallowsforthecontroloftheprocessingtimeofanactivity under time–costtradeoffsettings.Inpractice,projectdecisionsaremadeinadvancewhenactivity durationsarestillhighlyuncertain.Givenanactivity-on-nodeprojectnetworkandasetofexecution modesforeachactivity,weconsidertheproblemofdecidinghowandwhentoexecuteeachactivityto minimizeprojectcompletiontimeortotalcostwithrespecttocapturedactivitydurations.Theinherent stochasticityisrepresentedusingasetofdiscretescenariosinwhicheachscenarioisassociatedwitha probabilityofoccurrenceandarealizationofactivitydurations.Inthispaper,weproposeapath-based two-stagestochasticintegerprogrammingapproachinwhichtheexecutionmodesaredeterminedin the firststagewhilethesecondstageperformsactivityschedulingaccordingtotherealizationsof activitydurations,hence,providingflexibilityintheschedulingprocessatsubsequentstages.The solution methodologyisbasedonadecompositionalgorithmwhichhasbeenimplementedandwidely tested usingalargenumberoftestinstancesofvaryingsizeanduncertainty.Thereported computationalresultsdemonstratethattheproposedalgorithmconvergesfasttotheoptimalsolution and presentthebenefitsofusingthestochasticmodelasopposedtothetraditionaldeterministicmodel that considersonlyexpectedvaluesofactivitydurations.