A solutionapproachtofindthecriticalpathinatime-constrained activity network

Findingthelongestpathinanactivitynetwork,wheretimeconstraintsareattachedtoactivities,is generalizedfromthetraditionalcriticalpathproblem.Timeconstraintshaveattractedmuchresearch interest inrecentyears,becausetheycanbeusedtorepresentalargesetofrealsituations,arisingnot only inthefieldoftheprojectmanagement. In thispaper,weproposeageneralapproachforfindingthecriticalpathinadeterministicactivity- on-the-arcnetwork,consideringthreedifferenttypesoftimeconstraints.Thefirstoneisthe timewindow constraint,whichimposesthatanactivitycanstartonlyinapredefinedtimeinterval,whereas no constraintsareimposedontheactivitycompletiontime.Thesecondoneisthe time-schedule constraint,whichassumesthatanactivitycanstartitsexecutionatoneofthepre-specifiedinstantsof time. Thethirdoneisthe time-switch constraint,whichimposesaspecifiedstartingtimeontheproject activitiesandforcesthemtobeinactiveduringspecifiedtimeperiods. The algorithmintroducedinthispaperhasbeendevelopedbyredefiningandcombiningtogether two procedureswell-knowninthescientificliterature.Theformer,proposedbyChen,RinksandTangin 1997, canbeusedforfindingthecriticalpathinanactivitynetworkwheretime-scheduleandtime- windowconstraintsareconsidered.Thelatter,proposedbyYangandChenin2000,canbeappliedin activitynetworkswithonlytime-switchconstraints. The method,developedinthispaper,canbeusedtofindthecriticalpathinallthepractical situations,inwhichtheaforementionedtimeconstraintsaretakenintoaccountsimultaneously.The proposedapproachhasbeencodedinJavaandhasbeenvalidatedbyconsideringtwosetsofinstances: the formerhasbeentakenfromthepublicdomainprojectschedulingproblemlibrary, developedby Kolisch andSprecherin1997,whereasthelatterconsistsofrandomlygeneratedactivitynetworks. The computationalresultscollectedareverypromising,showingthatthesolutionprocessforthe consideredinstancesrequiredatmostfewseconds,usingacommercialPentiumclassPC.