fash punya
TRANSCRIPT
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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
darla/smbs/vit
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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
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CPMExamplec E,Sand EF Times
darla/smbs/vit 27
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CPMExampleo ES and EF Times
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darla/smbs/vit
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CPMExampleo LS and LF Times f,15
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CPMExampleo LS and LF Times f,15
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CPMExamplec Float
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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.
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ProbabilityomputationDetermine robability hatproject s completedwithin specifiedime
x-pZ- o'wherep - to projectmean ime
o - projectstandardmean imex
- (proposed) specifiedime
darlaismbs/vit 35
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NormalDistribution f ProjectTime
'u*' '-;it'j':i'7i:: r'::..;tt: ^i.,:.,f,1 ' : '::t".,.t:.;:.,'i':' , : : . . t . . ', : : . .ii;; :,,, . : ' , i - . ' ' ,
darla/srnbs/vit
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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
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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{