项目管理 CPM

1Network-PlanningModels•Aprojectismadeupofasequenceofactivitiesthatformanetworkrepresentingaproject•Thepathtakinglongesttimethroughthisnetworkofactivitiesiscalledthe“criticalpath”•Thecriticalpathprovidesawiderangeofschedulinginformationusefulinmanagingaproject•CriticalPathMethod(CPM)helpstoidentifythecriticalpath(s)intheprojectnetworks2PrerequisitesforCriticalPathMethodologyAprojectmusthave:well-definedjobsortaskswhosecompletionmarkstheendoftheproject;independentjobsortasks;andtasksthatfollowagivensequence.3TypesofCriticalPathMethods•CPMwithaSingleTimeEstimate–Usedwhenactivitytimesareknownwithcertainty–Usedtodeterminetimingestimatesfortheproject,eachactivityintheproject,andslacktimeforactivities•CPMwithThreeActivityTimeEstimates–Usedwhenactivitytimesareuncertain–UsedtoobtainthesameinformationastheSingleTimeEstimatemodelandprobabilityinformation•Time-CostModels–Usedwhencosttrade-offinformationisamajorconsiderationinplanning–Usedtodeterminetheleastcostinreducingtotalprojecttime4StepsintheCPMwithSingleTimeEstimate•1.ActivityIdentification•2.ActivitySequencingandNetworkConstruction•3.Determinethecriticalpath–Fromthecriticalpathalloftheprojectandactivitytiminginformationcanbeobtained5Example1.CPMwithSingleTimeEstimateConsiderthefollowingconsultingproject:Developacriticalpathdiagramanddeterminethedurationofthecriticalpathandslacktimesforallactivities.ActivityDesignationImmed.Pred.Time(Weeks)Assesscustomer'sneedsANone2WriteandsubmitproposalBA1ObtainapprovalCB1DevelopservicevisionandgoalsDC2TrainemployeesEC5QualityimprovementpilotgroupsFD,E5WriteassessmentreportGF16Example1.CPMwithSingleTimeEstimateConsiderthefollowingconsultingproject:ActivityDesignationImmed.Pred.Time(Weeks)Assesscustomer'sneedsANone2WriteandsubmitproposalBA1ObtainapprovalCB1DevelopservicevisionandgoalsDC2TrainemployeesEC5QualityimprovementpilotgroupsFD,E5WriteassessmentreportGF1Developacriticalpathdiagramanddeterminethedurationofthecriticalpathandslacktimesforallactivities.7Example1:FirstdrawthenetworkA(2)B(1)C(1)D(2)E(5)F(5)G(1)ANone2BA1CB1DC2EC5FD,E5GF1Act.Imed.Pred.Time8Example1:DetermineearlystartsandearlyfinishtimesES=9EF=14ES=14EF=15ES=0EF=2ES=2EF=3ES=3EF=4ES=4EF=9ES=4EF=6A(2)B(1)C(1)D(2)E(5)F(5)G(1)Hint:StartwithES=0andgoforwardinthenetworkfromAtoG.9Example1:DeterminelatestartsandlatefinishtimesES=9EF=14ES=14EF=15ES=0EF=2ES=2EF=3ES=3EF=4ES=4EF=9ES=4EF=6A(2)B(1)C(1)D(2)E(5)F(5)G(1)LS=14LF=15LS=9LF=14LS=4LF=9LS=7LF=9LS=3LF=4LS=2LF=3LS=0LF=2Hint:StartwithLF=15orthetotaltimeoftheprojectandgobackwardinthenetworkfromGtoA.10Example1:CriticalPath&SlackES=9EF=14ES=14EF=15ES=0EF=2ES=2EF=3ES=3EF=4ES=4EF=9ES=4EF=6A(2)B(1)C(1)D(2)E(5)F(5)G(1)LS=14LF=15LS=9LF=14LS=4LF=9LS=7LF=9LS=3LF=4LS=2LF=3LS=0LF=2Duration=15weeksSlack=(7-4)=(9-6)=3Wks11Example2.CPMwithThreeActivityTimeEstimatesTaskImmediatePredecesorsOptimisticMostLikelyPessimisticANone3615BNone2414CA61230DA258EC51117FD3615GB3927HE,F147IG,H4192812Example2.ExpectedTimeCalculationsET(A)=3+4(6)+156ET(A)=42/6=7TaskImmediatePredecesorsExpectedTimeANone7BNone5.333CA14DA5EC11FD7GB11HE,F4IG,H18TaskImmediatePredecesorsOptimisticMostLikelyPessimisticANone3615BNone2414CA61230DA258EC51117FD3615GB3927HE,F147IG,H41928ExpectedTime=Opt.Time+4(MostLikelyTime)+Pess.Time613Example2.ExpectedTimeCalculationsTaskImmediatePredecesorsExpectedTimeANone7BNone5.333CA14DA5EC11FD7GB11HE,F4IG,H18ET(B)=32/6=5.333ET(B)=2+4(4)+146TaskImmediatePredecesorsOptimisticMostLikelyPessimisticANone3615BNone2414CA61230DA258EC51117FD3615GB3927HE,F147IG,H41928ExpectedTime=Opt.Time+4(MostLikelyTime)+Pess.Time614Example2.ExpectedTimeCalculationsTaskImmediatePredecesorsExpectedTimeANone7BNone5.333CA14DA5EC11FD7GB11HE,F4IG,H18ET(C)=6+4(12)+306ET(C)=84/6=14TaskImmediatePredecesorsOptimisticMostLikelyPessimisticANone3615BNone2414CA61230DA258EC51117FD3615GB3927HE,F147IG,H41928ExpectedTime=Opt.Time+4(MostLikelyTime)+Pess.Time615Example2.NetworkA(7)B(5.333)C(14)D(5)E(11)F(7)H(4)G(11)I(18)Duration=54Days16Example2.ProbabilityExerciseWhatistheprobabilityoffinishingthisprojectinlessthan53days?p(tD)TE=54Z=D-TEcp2tD=5317Activityvariance,=(Pessim.-Optim.6)22TaskOptimisticMostLikelyPessimisticVarianceA36154B2414C6123016D258E511174F3615G3927H1471I4192816(Sumthevariancealongthecriticalpath.)2=4118Thereisa43.8%probabilitythatthisprojectwillbecompletedinlessthan53weeks.p(Z-.156)=.438,or43.8%(NORMSDIST(-.156)Z=D-T=53-5441=-.156Ecp2TE=54p(tD)tD=5319Example2.AdditionalProbabilityExercise•Whatistheprobabilitythattheprojectdurationwillexceed56weeks?20Example2.AdditionalExerciseSolutiontTE=54p(tD)D=56Z=D-T=56-5441=.312Ecp2p(Z.312)=.378,or37.8%(1-NORMSDIST(.312))21Time-CostModels•BasicAssumption:Relationshipbetweenactivitycompletiontimeandprojectcost•TimeCostModels:Determinetheoptimumpointintime-costtradeoffs–Activitydirectcosts–Projectindirectcosts–Activitycompletiontimes22CPMAssumptions/Limitations•Projectactivitiescanbeidentifiedasentities(Thereisaclearbeginningandendingpointforeachactivity.)•Projectactivitysequencerelationshipscanbespecifiedandnetwork