Event-based MILPmodelsforresource-constrainedprojectscheduling problems

In thispaperwemakeacomparativestudyofseveralmixedintegerlinearprogramming(MILP) formulationsforresource-constrainedprojectschedulingproblems(RCPSPs). First, wepresentthreediscreteandcontinuoustimeMILPformulationsissuedfromtheliterature. Second,insteadofrelyingonthetraditionaldiscretizationofthetimehorizon,weproposeMILP formulationsfortheRCPSPbasedontheconceptof event: the Start/End formulationandthe On/Off formulation.Theseformulationspresenttheadvantageofinvolvingfewervariablesthanthe formulationsindexedbytime.Becausethevariablesofthistypeofformulationsarenotfunctionof the timehorizon,wehaveabettercapacitytodealwithinstancesofverylargeschedulinghorizon. Finally, weillustrateourcontributionwithaseriesoftestsonvarioustypesofinstancewiththe MILP formulationsissuedfromtheliterature,togetherwithournewformulations.Wealsocompareour results witharecentRCPSP-specificexactmethod.Weshowthat,intermsofexactsolving,noMILP formulationclassdominatestheotheronesandthatastate-of-theartspecialized(non-MILP)method for theRCPSPisevenoutperformedbyMILPonasetofhardinstances.Furthermore,onanothersetof hard ‘‘highlycumulative’’RCPSPinstanceswithahighprocessingtimerange,ourOn/Offformulation outperformsalltheothersMILPformulationsandobtainsresultsclosetotheonesofthespecialized method.