Author/Authors :
F. Guerriero ، نويسنده , , L.Talarico، نويسنده ,
Abstract :
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.
Keywords :
Activity network , Critical path , Time-constrained network , Time-window constraint , Time-schedule constraint , Time-switch constraint
