SAMSUDINAHMADFacultyofGeoinformation andRealEstate
Universiti Teknologi Malaysia@Mail:samsudin@utm.my
Topic5PERTANDCPMNETWORKS
History
• Late1950s– ProgramEvaluationandReviewTechnique(PERT)
• U.S.Navy,Booz‐AllenHamilton,andLockeheedAircraft
• Probabilisticactivitydurations– CriticalPathMethod(CPM)
• DupontDeNemoursInc.• Deterministicactivitydurations
TheLanguageofPERT/CPM
• Activity– taskorsetoftasks– useresources
• Event– stateresultingfromcompletionofoneormoreactivities
– consumenoresourcesortime– predecessoractivitiesmustbecompleted
TheLanguageofPERT/CPMcontinued
• Milestones– eventsthatmarksignificantprogress
• Network– diagramofnodesandarcs– usedtoillustratetechnologicalrelationships
• Path– seriesofconnectedactivitiesbetweentwoevents
TheLanguageofPERT/CPMconcluded
• CriticalPath– setofactivitiesonapaththatifdelayedwilldelaycompletionofproject
• CriticalTime– timerequiredtocompleteallactivitiesonthecriticalpath
BuildingtheNetwork
SampleSetofProjectActivitiesandPrecedences
Task Predecessora --
b --
c a
d b
e b
f c, d
g e
Stage1ofaSampleAONNetwork
Stage2ofaSampleAONNetwork
ACompletedSampleAONNetwork
Stage1ofaSampleAOANetwork
Stage2ofaSampleAOANetwork
ACompletedSampleAOANetwork
ACompletedSampleAOANetworkShowingtheUseofaDummyTask
SampleProblemforFindingtheCriticalPathandCriticalTime
Activity Predecessor Duration
a -- 5 daysb -- 4c a 3d a 4e a 6f b, c 4g d 5h d, e 6i f 6j g, h 4
Stage1ofaSampleNetwork
InformationContentsinanAONNode
TheCriticalPathandTimeforSampleProject
CalculatingActivitySlack
• SlackorFloatLST‐ EST=LFT‐ EFT=Slack
AnMSPVersionofPERT/CPMNetwork
AModifiedVersionofMSPNetwork
PROJECTUNCERTAINTYANDRISKMANAGEMENT
CalculatingProbabilisticActivityTimes• ThreeTimeEstimates
– pessimistic(a)– mostlikely(m)– optimistic(b)
TheStatisticalDistributionofallPossibleTimesforanActivity
ActivityExpectedTimeandVariance
22
E
6)(Var
6)(
6)4(T
ab
ab
bma
95PercentLevel
• Taskwillbea orlower5percentofthetime
• Taskwillbeb orgreater5percentofthetime
3.3)( ab
90PercentLevel
• Taskwillbea orlower10percentofthetime
• Taskwillbeb orgreater10percentofthetime
6.2)( ab
95PercentLevel(AlternativeInterpretation)• Taskwillbebetweenaandb95percentofthetime
92.3)( ab
90PercentLevel(AlternativeInterpretation)• Taskwillbebetweenaandb90percentofthetime
29.3)( ab
AnMSPVersionofaSampleProblemNetwork
APert/CPMNetworkfortheDayCareProject
AnMSPCalendarfortheDayCareProject,4/16/00to5/27/00
TheProbabilityofCompletingtheProjectonTime
2
)(
DZ
=NORMDIST(D,,,TRUE)
TheStatisticalDistributionofCompletionTimesofthePatha‐b‐d‐g‐h
SelectingRiskandFindingD
2 ZD
NORMINV (probability, , , TRUE)
SIMULATION
MEM 612 Project Management
TraditionalStatisticsVersusSimulation• Similarities
– mustenumeratealternatepaths
• Differences– simulationdoesnotrequireassumptionofpathindependence
AGanttChartofaSampleProject
AGanttChartofSampleProjectShowingCriticalPath,PathConnections,Slack,EST,LST,EFT,andLFT
AGanttChartofaDayCareProjectShowingExpectedDurations,CriticalPath,Milestone,andResourceRequirements
AProgressReportonaDayCareProjectShowingActualProgressVersusBaseline
EXTENSIONSTOPERT/CPM
PrecedenceDiagramming
Finish‐to‐startlinkage
Start‐to‐startlinkage
Finish‐to‐finishlinkage
Start‐to‐finishlinkage
PrecedenceDiagrammingConventions
OtherMethods
• GraphicalEvaluationandReviewTechnique(GERT)– combinesflowgraphs,probabilisticnetworks,anddecisiontrees
– allowsloopsbacktoearliereventsandprobabilisticbranching
Reference
• Meredith,R.J.&Mantel,J.S.(1995).ProjectManagement– AManagerialApproach.JohnWiley&Sons,5thEdition.