11 Project Scheduling and PERT CPM

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<p>OperationsResearch</p> <p>Unit11</p> <p>Unit11Structure</p> <p>ProjectSchedulingandPERTCPM</p> <p>11.1.Introduction 11.2.BasicdifferencebetweenPERTandCPM 11.2.1 PERT 11.2.2 CPM 11.2.3 ProjectschedulingbyPERTCPM</p> <p>11.3.PERT/CPMnetworkcomponentsandprecedencerelationship 11.3.1 CriticalPathCalculations 11.3.2 DeterminationoftheCriticalPath 11.3.3 11.4. DeterminationofFloats</p> <p>ProjectManagementPERT</p> <p>11.5.Summary TerminalQuestions AnswerstoSAQsandTQs</p> <p>11.1. Introduction Aprojectsuchasconstructionofabridge,highway,powerplant,repairandmaintenanceofanoil refinery or an air plane design, development and marketing a new product, research and developmentetc.,maybedefinedasacollectionofinterrelatedactivities(ortasks)whichmust becompletedinaspecifiedtimeaccordingtoaspecifiedsequenceandrequireresourcessuch aspersonnel,money,materials,facilitiesetc. Thegrowingcomplexitiesoftodaysprojectshaddemandedmoresystematicandmoreeffective planning techniques with the objective of optimizing the efficiency of executing the project. Efficiencyhereimplieseffectingtheutmostreductioninthetimerequiredtocompletetheproject whileaccountingfortheeconomicfeasibilityofusingavailableresources. Projectmanagementhasevolvedasanewfieldwiththedevelopmentoftwoanalytictechniques forplanning,schedulingandcontrollingprojects.ThesearetheCriticalPathMethod(CPM)and the Project Evaluation and Review Technique (PERT). PERT and CPM are basically time orientedmethodsinthesensethattheybothleadtothedeterminationofatimeschedule.</p> <p>SikkimManipalUniversity</p> <p>182</p> <p>OperationsResearch LearningObjectives: Afterstudyingthisunit,youshouldbeabletounderstandthefollowing</p> <p>Unit11</p> <p>1. Whatisaproject? 2. Whatisprojectmanagement? 3. ApplicationofPERT/CPMmethodtonetworkanalysis</p> <p>11.2. BasicdifferencebetweenPERTandCPM Though there are no essential differences between PERT and CPM as both of them share in common the determination of a critical path and are based on the network representation of activitiesandtheirschedulingthatdeterminesthemostcriticalactivitiestobecontrolledsoasto meetthecompletiondateoftheproject. 11.2.1</p> <p>PERT</p> <p>1. SincePERTwasdevelopedinconnectionwithanRandDwork,thereforeithadtocopewith theuncertaintieswhichareassociatedwithRandDactivities.InPERT,totalprojectduration isregardedasarandomvariableandthereforeassociatedprobabilitiesarecalculatedsoas tocharacteriseit. 2. Itisaneventorientednetworkbecauseintheanalysisofnetworkemphasisisgivenanimportant stages of completion of task rather than the activities required to be performed to reach to a particulareventortask. 3. PERTisnormallyusedforprojectsinvolvingactivitiesofnonrepetitivenatureinwhichtime estimatesareuncertain. 4. Ithelpsinpinpointingcriticalareasinaprojectsothatnecessaryadjustmentcanbemadeto meetthescheduledcompletiondateoftheproject.</p> <p>11.2.2 CPM 1. Since CPM was developed in connection with a construction project which consisted of routinetaskswhoseresourcesrequirementanddurationwasknownwithcertainty,therefore itisbasicallydeterministic. 2. CPMissuitableforestablishingatradeoffforoptimumbalancingbetweenscheduletimeand costoftheproject. 3. CPMisusedforprojectsinvolvingactivitiesofrepetitivenature.SikkimManipalUniversity 183</p> <p>OperationsResearch</p> <p>Unit11</p> <p>11.2.3ProjectschedulingbyPERTCPM Itconsistsofthreebasicphases:planning,schedulingandcontrolling. 1. ProjectPlanning:Thevariousstepsinvolvedduringthisphasearegivenbelow: i) Identifyvariousactivities(taskorworkelements)tobeperformedintheproject. ii) Determiningrequirementofresourcessuchasmen,materials,machinesetc.,forcarrying outactivitieslistedabove. iii) Estimatingcostsandtimesforvariousactivities. iv) Specifyingtheinterrelationshipamongvariousactivities. v) Developing a network diagram showing the sequential interrelationships between the variousactivities. 2. Scheduling:Oncetheplanningphaseisover,schedulingoftheproject,iswheneachofthe activitiesrequiredtobeperformed,istakenup.Thevariousstepsinvolvedduringthisphase arelistedbelow: 1. Estimatingthedurationsofactivities,takingintoconsiderationstheresourcesrequiredfor theseexecutioninmosteconomicmanner. 2. Basedonthesetimeestimates,preparingatimechartshowingthestartandfinishtimes for each activity, and hence calculation of total project duration by applying network analysis techniques such asforward (backward) pass and floats calculationidentifying the critical path carrying out resource smoothing (or levelling) exercise for critical or scarce resources including recosting of the schedule taking into account resource constraints. 3. ProjectControl:Projectcontrol referstorevaluatingactualprogressagainsttheplan.If significantdifferencesareobservedthenreschedulingmustbedonetoupdate andrevisetheuncompletedpartoftheproject. SelfAssessmentQuestions1 VerifywhetherthefollowingstatementsareTrueorFalse</p> <p>1. Projectconsistsofinterrelatedactivities. 2. Projectactivitiesaretobecompletedinaspecifiedtimeaccordingtospecifiedsequence. 3. PERTandCPMidentifiesnoncriticalactivities. 4. PERTisactivityorientednetwork.SikkimManipalUniversity 184</p> <p>OperationsResearch</p> <p>Unit11</p> <p>5. CPMisusedforprojectsthatarerepetitiveinnature.</p> <p>11.3 PERT/CPMNetworkComponents And PrecedenceRelationshipPERT/CPMnetworksconsistsoftwomajorcomponentsasdiscussedbelow: a) Events: An event represents apointin time that signifies the completion of some activities and the beginning of new ones. The beginning and end points of an activity are thus described by 2 events usually known as the Tail and head events. Events are commonly represented by circles (nodes) in the network diagram. They do not consume time and Resource b) Activities:Activitiesofthenetworkrepresentprojectoperationsortasktobeconducted.An arrow is commonly used to represent an activity, with its head indicating the direction of progress in the project. Activities originating from a certain event cannot start until the activities terminating at the same event have been completed. They consume time and Resource. Eventsinthenetworkdiagramareidentifiedbynumbers.Numbersaregiventoeventssuchthat arrowheadnumbermustbegreaterthanarrowtailnumber. Activitiesareidentifiedbythenumbers oftheirstarting(tail)eventand ending(head)event.An arrow(i.J)extendedbetweentwoevents,thetaileventirepresentsthestartoftheactivityand theheadeventJrepresentsthecompletionoftheactivityasshowninFig.9.1:</p> <p>Activity i J</p> <p>Startingevent</p> <p>CompletionEvent Fig.9.1</p> <p>SikkimManipalUniversity</p> <p>185</p> <p>OperationsResearch</p> <p>Unit11</p> <p>Figure9.2showsanotherexample,whereactivities(1,3)and(2,3)mustbecompletedbefore activity(3,4)canstart. 1 3 2 Fig.9.2 Therulesforconstructingthearrowdiagramareasfollows: 1. Eachactivityisrepresentedbyoneandonlyonearrowinthenetwork. 2. Notwoactivitiescanbeidentifiedbythesameheadandtailevents. 3. Toensurethecorrectprecedencerelationshipinthearrowdiagram,thefollowingquestions mustbeansweredaseveryactivityisaddedtothenetwork: a) Whatactivitiesmustbecompletedimmediatelybeforetheseactivitycanstart? b) Whatactivitiesmustfollowthisactivity? c) Whatactivitymustoccurconcurrentlywiththisactivity? This rule is selfexplanatory. It actually allows for checking (and rechecking) the precedence relationshipsasoneprogressesinthedevelopmentofthenetwork. Example1:ConstructthearrowdiagramcomprisingactivitiesA,B,C..andLsuchthatthe followingrelationshipsaresatisfied: 1) A,BandCthefirstactivitiesoftheproject,canstartsimultaneously. 2) AandBprecedeD. 3) BprecedesE,FandH. 4) FandCprecedeG. 5) EandHprecedeIandJ. 6) C,D,FandJprecedeK. 7) KprecedesL. 8) I,GandLaretheterminalactivitiesoftheproject. 4</p> <p>SikkimManipalUniversity</p> <p>186</p> <p>OperationsResearch</p> <p>Unit11</p> <p>J</p> <p>Fig.9.3 The dummy activities D1 and D2 are used (dotted lines) to establish correct precedence relationships.D3 isusedtoidentifyactivitiesEandHwithuniqueendevents.Theeventsofthe projectarenumberedsuchthattheirascendingorderindicatesthedirectionoftheprogressinthe project. Note:Adummyactivityinaprojectnetworkanalysishaszeroduration.</p> <p>11.3.1. CriticalPathCalculationsThe application of PERT/CPM should ultimately yield a schedule specifying the start and completiontimeofeachactivity.Thearrowdiagramisthefirststeptowardsachievingthatgoal. The start and completion times are calculated directly on the arrow diagrams using simple arithmetic.Theendresultistoclassifytheactivitiesascriticalornoncritical.Anactivityissaid tobecriticalifadelayinthestartofthecoursemakesadelayinthecompletiontimeoftheentire project. A noncritical activity is such that the time between its earliest start and its latest completiontimeislongerthanitsactualduration.Anoncriticalactivityissaidtohaveaslackor floattime.</p> <p>11.3.2. DeterminationoftheCriticalPathAcriticalpathdefinesachainofcriticalactivitiesthatconnectsthestartandend eventsofthe arrowdiagram.Inotherwords,thecriticalpathidentifiesallthecriticalactivitiesoftheproject. The critical path calculations include two phases. The first phase is called the Forward Pass where all calculations begin from the start node and move to the end node. At each node a numberiscomputedrepresentingtheearliestoccurrencetimeofthecorrespondingevent.TheseSikkimManipalUniversity 187</p> <p>OperationsResearch</p> <p>Unit11</p> <p>numbersareshowninsquares.Inforwardpasswenotethenumberofheadsjoiningtheevent. We take the maximum earliest timing through these heads.The second phase called the Backwards Pass, begins calculationsfrom the end node and moves to the start node. The numbercomputedateachnodeisshowninatriangle D nearendpointwhichrepresentthelatest occurrencetimeofthecorrespondingevent.ConsidertheforwardpassInbackwardpasswesee thenumberoftailsandtakeminimumvaluethroughthesetails. LetESi betheearlieststarttimeofalltheactivitiesemanatingfromeventi,i.e.ESi represents the earliest occurrence time of event i, if i = 1 is the start event then conventionally, for the critical path calculations,ESi = 0 , Let Dij be the duration of the activity(i, j). Then theforward passcalculationsaregivenbytheformula: ES i =maxi {ESi+Dij},foralldefined(i,j)activitieswithESi=0.Thusinorder tocomputeEsJ for eventj,Esi forthetaileventsofalltheincomingactivities(i,j)mustbecomputedfirst. WiththecomputationofallESj,theforwardpasscalculationsarecompleted.Thebackwardpass startsfrom the endevent. The objectiveof this phase tocalculateLCi, thelatestcompletion timeforalltheactivitiescomingintotheeventi.Thusifi=nistheendeventLCn =ESn initiates thebackwardpass. Ingeneralforanynodei,LCi =min{LCjDij}foralldefinedactivitiesarecalculated,whichends thecalculationofbackwardpass. Thecriticalpathactivitiescannowbeidentifiedbyusingtheresultsoftheforwardandbackward passes.Anactivity(i,j)liesonthecriticalpathifitsatisfiesthefollowingconditions. A) ESI =LCi B) ESJ =LCJ C) ESJESI =LCJLCI =DiJ Theseconditionsactuallyindicatethatthereisnofloatorslacktime betweentheearlieststand andthelateststartoftheactivity.Thustheactivitymustcritical.Inthearrowdiagramtheseare characterisedbynumbersinand D arethesameateachoftheheadandtaileventsandthe differencebetweenthenumberin(or D)attheheadeventandthenumberin(or D)atthetail eventinequaltothedurationoftheActivity. Thuswewillgetacriticalpath,whichischainofconnectedactivities,whichspansthenetwork formstarttoend.</p> <p>SikkimManipalUniversity</p> <p>188</p> <p>OperationsResearch</p> <p>Unit11</p> <p>Example 2: Consider a network which stands from node 1 and terminate at node 6, the time requiredtoperformeachactivityisindicatedonthearrows.</p> <p>Fig.9.4 LetusstartwithforwardpasswithESi =0. Sincethereisonlyoneincomingactivity(1,2)toevent2withD12 =3. ES2 =ES1+DS2 =0+3=3. Letusconsidertheend3,sincethereonlyoneincomingactivity(2,3)toevent3,withD23 =3. ES3 =ES2+D23 =3+3=6. ToobtainES4,sincetherearetwoactivitiesA(3,4)and(2,4)totheevent4withD24 =2andD34 =0. ES4=maxi=2,3 {ESi +De4} =max{ES2 +D24,ES3 +D34} =max{3+2,6+0}=6 SimilaryES5 =13andES6 =19 Whichcompletedfirstphase. Inthesecondphasewehave LC6=19=ES6 LC5 =196=13 LC4=minJ=5,6 {LCJ D4J}=6 LC3 =6,LC2 =3andLC1 =0 \ activities(1,2),(2,3)(3,4)(4,5)(5,6)arecriticaland(2,4)(4,6),(3,6),arenoncritical.</p> <p>SikkimManipalUniversity</p> <p>189</p> <p>OperationsResearch</p> <p>Unit11</p> <p>Thustheactivities(1,2)(2,3)(3,4)(4,5)and(5,6)definethecriticalpathwhichistheshortest possibletimetocompletetheproject.</p> <p>11.3.3. DeterminationofFloats Following the determination of the critical path, the floats for the noncritical activities must be computed. Note that for the critical activities this float is zero. Before showing how floats are determined,itisnecessarytodefinetwonewtimesthatareassociatedwitheachactivity.There areLatestStart(LS)andtheEarliestCompletion(EC)times,whicharedefinedactivity(i,J)by LSeJ=LCJ DiJ andECeJ =ESi +DiJ Therearetwoimportanttypesoffloatsnamely,TotalFloat(TF)andFreeFloat(FF).Thetotal floatTFiJ foractivity(i,J)isthedifferencebetweenthemaximumtimeavailabletoperformthe activity(=LCJ ESi)anditsduration(=DiJ ) Thatis, TFiJ =LCJESI DiJ =LCJ ECiJ =LS iJ ESi Thefreefloatisdefinedbyassumingthatalltheactivitiesstartasearlyaspossible.Inthiscase FFiJ foractivity(i,J)istheexcessofavailabletime(=ESi ESi)overitsdeviation(=DiJ ) thatis,FFiJ =ESi ESi =DiJ . Note that onlyfor a criticalactivity must have zero totalfloat.Thefreefloat mustalso be zero when the total float is zero. The converse is not true, that is in the sense that a noncritical activitymayhavezerofreefloats. Letusconsidertheexampletakenbeforethecriticalpathcalculationstogetherwiththefloatsfor thenoncriticalactivitiescanbesummarizedintheconvenientformshowninthefollowingtable:</p> <p>SikkimManipalUniversity</p> <p>190</p> <p>OperationsResearch</p> <p>Unit11</p> <p>Earliest Latest Activit Table Free Duration Start Completio Start Completio y Float Float n n DiJ ESi LSij (iJ) TFiJ FFiJ ECiJ DLCJ (1,2) (2,3) (2,4) (3,4) (3,5) (3,6) (4,5) (4,6) (5,6) 3 3 2 0 3 2 7 5 6 0 3 3 6 6 6 6 6 13 3 6 5 6 9 8 13 11 19 0 3 4 6 10 17 6 14 13 3 6 6 6 13 19 13 19 19 0* 0* 1 0* 4 11 0* 8 0* 0 0 1 0 4 11 0 8 0</p> <p>Note:Totalfloat=ESij =LFij ESij Freefloat=TotalfloatHeadslack *Criticalactivity* Example3:AprojectconsistsofaseriesoftasksA,B,C,D,E,F,G,H,Iwiththefollowing relationships. (W </p>

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