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CPM calculatlono Path

- A connectedequence,f activitieseading rornthe startingevent o theendingevent' CriticalPathThe ongest ath time);determinesheprojectduratione CriticalActivities

- A11 f theactivitieshatmake p thecriticalpath

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ForwardPasso EarliestStartTime(ES)earliestime an activitycanstartES- maximumEF of immediate redecessorso Earliest inish ime(EF)earliestime an activitvcan inishearliest art imeplus activity imeEF:ES+tBackwardPassr LatestStartTime LS)

Latest imeanactivity anstartwithout elaying ritical athtimeLS=LF t

rLatest inish ime(LF)latest imean activity anbe completed ithout elayingcritical ath ime darla/smbs/vit 23LS= minimum S of immediate redecessors

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CPM analysisDrawthe CPM networkAnalyze hepaths hrough henetworkDetermine he float for eachactivity

Computehe activity's loatfloat: LS - ES LF - EF

Float s themaximumamountof time that his activitycanbedelay n its completion efore t becomes criticalactivity,i.e.,delays ompletion f theproject. Find thecriticalpath s that he sequencef activitiesandeventswhere here s no "slack" i.e. ZetoslackLongestpath hrougha network

. Find heprojectdurations minimumproject ompletionimedarla/smbs/vit 24

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CPM Example:o CPM Network

a,6

j, 12

15

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CPMExampleo ES and EF Times f 15

c,5

26

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CPMExamplec E,Sand EF Times

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CPMExampleo ES and EF Times

ar6

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CPMExampleo LS and LF Times f,15

29

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CPMExampleo LS and LF Times f,15

17O

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CPMExamplec Float

e,9J I

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CPMExample. Critical Path

ar6

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PtrRT. PERT s based n theassumptionhat an activity'sdurationfollowsaprobability istributionnstead f beinga single alue

pessimisticime(to - the ime heactivitywould ake f{--thingsdidnotgowellmost ikely time(t* ) - theconsensusestestimate f theactivity'sdurationoptimistic ime(t")didgowell

- the imethe activitywould ake f things

Three ime estimatesan activity'sdurationare equiredo computehe pararnetersfdistribution:

n(**puC#dil.,.liit . '*T;.'*,u,a aJ J

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PtrR.T nalysisDrawthenetwork.Analyze hepaths hrough he networkandfind the c;rltical ath.The engthof the criticalpath s the meanof theprojectdurationprobabilitydistributionwhich s assumedo be normal

. Thestandard eviation f theprojectdurationprobabilitydistributions computed y adding hevariances f the criticalactivities all of the activitieshatmakeup the criticalpath)andtaking he squareootof thatsum' Probability omputationsannow be madeusing he normal

distributionable.

34arla/smbsiit

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ProbabilityomputationDetermine robability hatproject s completedwithin specifiedime

x-pZ- o'wherep - to projectmean ime

o - projectstandardmean imex

- (proposed) specifiedime

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NormalDistribution f ProjectTime

'u*' '-;it'j':i'7i:: r'::..;tt: ^i.,:.,f,1 ' : '::t".,.t:.;:.,'i':' , : : . . t . . ', : : . .ii;; :,,, . : ' , i - . ' ' ,

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PERTExampleOptimisticMostLikely

ActivitlrAB(1\-DEF'GHIJK

Immed.Predec.Time Hr.) Time Hr.) Time Hr.)

41aJ40.5aJ1522.53 darla/srnbs/r,it

Pessimistic

B5aJ61.5557B4.5737

;AAB,CB,CE,FE,rF'D,HG,I

61.535141.5652.755

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PERTExamplePERTNetwork

38arla/smbs/vit

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PERTExampleActivity

AExpected ime

6435I426535

darla/smbs/vit

Variance4194190U9U36U94t9U9IU94t9

39

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PERTExampleActivity ES EF LS LF Slack

AO 6 0 6 0*critical80459sc 6 9 6 9 0*D 6 11 15 20 9E 6 7 12 13 6F 9 13 9 13 0*G 9 11 16 18 7H 13 19 14 20 1I 13 18 13 18 0*J19K18 22w 2023118 23 0{