bab4b project schedulling
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Project SchedullingProject Schedulling
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Characteristics of a ProjectCharacteristics of a ProjectCharacteristics of a ProjectCharacteristics of a Project
* Memerlukan penyelesaian dari sejumlah aktivitas yg* Memerlukan penyelesaian dari sejumlah aktivitas yg
saling terkait (presaling terkait (pre--requested).requested).
Resources terbatas, spt waktu dan/atau biaya.Resources terbatas, spt waktu dan/atau biaya.
Biasanya memiliki struktur manajemen tersendiri.Biasanya memiliki struktur manajemen tersendiri.
Anggota tim berasal dari berbagai departemen danAnggota tim berasal dari berbagai departemen dan
bekerja secara temporer serta bertanggung jawab atasbekerja secara temporer serta bertanggung jawab atas
perencanaan (planning), penjadwalan (schedulling)perencanaan (planning), penjadwalan (schedulling)
dan pengendalian (controlling) project hingga selesai.dan pengendalian (controlling) project hingga selesai.
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Project TeamProject TeamProject TeamProject Team
ProjectProject
PlanPlan
ManagementManagement
InformationInformation
SystemSystem
ProjectProject
ScheduleSchedule
ProjectProjectManagerManager
ProjectProject
TeamTeam
Resources:Resources:
InternalInternal
Exec.Mgt.Exec.Mgt.
MarketingMarketing
EngineeringEngineeringProductionProduction
Qual.ControlQual.Control
Hum.Res.Hum.Res.
PurchasingPurchasing
ExternalExternal
SuppliersSuppliers
Subcontract.Subcontract.
UpdateUpdate
and Reviseand Revise
ScheduleSchedule
Update andUpdate and
Revise PlanRevise Plan
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Scheduling and Control ChartsScheduling and Control ChartsScheduling and Control ChartsScheduling and Control Charts
Horizontal Bar ChartsHorizontal Bar Charts
A version of the Gantt chartA version of the Gantt chart
Used to plan and schedule activitiesUsed to plan and schedule activities
As the project progresses, the status of activities isAs the project progresses, the status of activities isplotted on the chart, compared to the plan, and, ifplotted on the chart, compared to the plan, and, if
necessary, corrective action is takennecessary, corrective action is taken
more more
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Scheduling and Control ChartsScheduling and Control ChartsScheduling and Control ChartsScheduling and Control Charts
Horizontal Bar Charts (continued)Horizontal Bar Charts (continued)
AdvantagesAdvantages
Easy to understandEasy to understand
Easy to modify and updateEasy to modify and update Low costLow cost
DisadvantagesDisadvantages
Cumbersome for large projectCumbersome for large project
Must be keep up to dateMust be keep up to date Does not indicate the relationships among theDoes not indicate the relationships among the
activitiesactivities
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Horizontal Bar ChartHorizontal Bar ChartHorizontal Bar ChartHorizontal Bar Chart
a. Prelim. Propulsion Designa. Prelim. Propulsion Design
b. Prelim. Flight Sys. Designb. Prelim. Flight Sys. Design
c. Static Tests Ac. Static Tests Ad. Propulsion Design Modif.d. Propulsion Design Modif.
e. Static Tests Be. Static Tests B
f. Flight Tests Af. Flight Tests A
g. Flight Sys. Design Modif.g. Flight Sys. Design Modif.
h. Flight Tests Bh. Flight Tests Bi. Matl & Component Costsi. Matl & Component Costs
j. Labor & Overheads Costsj. Labor & Overheads Costs
Apr.Apr. MayMay JuneJune JulyJuly Aug.Aug.
aa
cc
dd
bb
ee ff
ggdd
dd
Project ActivitiesProject Activities
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Critical Path Method (CPM)Critical Path Method (CPM)Critical Path Method (CPM)Critical Path Method (CPM)
Designed to provide intense microDesigned to provide intense micro--controlcontrol
The system is dynamic; it continues to provideThe system is dynamic; it continues to provide
periodic reports as the project progressesperiodic reports as the project progresses
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Managers View ofCPMManagers View ofCPMManagers View ofCPMManagers View ofCPM
INPUTSINPUTS List of project activitiesList of project activities Precedence relationship among activitiesPrecedence relationship among activities Estimate of each activitys durationEstimate of each activitys duration
OUTPUTSOUTPUTS Estimated duration of projectEstimated duration of project Identification of critical activitiesIdentification of critical activities Amount of slack for each activityAmount of slack for each activity
CPM processing proceduresCPM processing procedures
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CPMCPM TerminologyTerminologyCPMCPM TerminologyTerminology
ActivityActivity
A task or a certain amount of work required in theA task or a certain amount of work required in theprojectproject
Requires time to completeRequires time to complete
Represented by an arrowRepresented by an arrow
Dummy ActivityDummy Activity
Indicates only precedence relationshipsIndicates only precedence relationships
Does not require any time of effortDoes not require any time of effort
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CPM TerminologyCPM TerminologyCPM TerminologyCPM Terminology
EventEvent
Signals the beginning or ending of an activitySignals the beginning or ending of an activity
Designates a point in timeDesignates a point in time
Represented by a circle (node)
Represented by a circle (node)
NetworkNetwork
Shows the sequential relationships amongShows the sequential relationships among
activities using nodes and arrowsactivities using nodes and arrows
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CPM TerminologyCPM TerminologyCPM TerminologyCPM Terminology
PathPath
A connected sequence of activities leading fromA connected sequence of activities leading fromthe starting event to the ending eventthe starting event to the ending event
CriticalP
athCriticalP
ath The longest path (time); determines the projectThe longest path (time); determines the project
durationduration
Critical ActivitiesCritical Activities
All of the activities that make up the critical pathAll of the activities that make up the critical path
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CPM TerminologyCPM TerminologyCPM TerminologyCPM Terminology
Earliest Start (ES)Earliest Start (ES)
The earliest that an activity can begin; assumes allThe earliest that an activity can begin; assumes all
preceding activities have been completedpreceding activities have been completed
Earliest Finish (EF)Earliest Finish (EF) ES + activity timeES + activity time
Latest Finish (LF)Latest Finish (LF)
The latest that an activity can finish and not changeThe latest that an activity can finish and not change
the project completion timethe project completion time
Latest Start (LS)Latest Start (LS)
LFLF -- activity timeactivity time
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CPM NetworkConventionsCPM NetworkConventionsCPM NetworkConventionsCPM NetworkConventions
11aa bbII
11aa
bb
cc
IIII
11
aa
bb
cc
IIIIII
ccaa11
ddbb
IVIV
cc
dd
aa
bb33
22
11
VV
22aa cc
11bb dd
VIVI
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Steps in CPM AnalysisSteps in CPM AnalysisSteps in CPM AnalysisSteps in CPM Analysis
Draw the CPM networkDraw the CPM network
A graphic view of the relationships among theA graphic view of the relationships among the
required activitiesrequired activities
Analyze the paths through the networkAnalyze the paths through the network Determine the length of each path (the timeDetermine the length of each path (the time
required to complete each path)required to complete each path)
Starting at the beginning of the network andStarting at the beginning of the network and
working toward the end (from left to right),working toward the end (from left to right),determine the ES and the EF for each activitydetermine the ES and the EF for each activity
. . . more. . . more
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Steps in CPM AnalysisSteps in CPM AnalysisSteps in CPM AnalysisSteps in CPM Analysis
Path analysis (continued)Path analysis (continued)
Identify the critical path(s) (the longest path[s]Identify the critical path(s) (the longest path[s]
through the network)through the network)
The critical path(s) determines how long theThe critical path(s) determines how long theproject will takeproject will take
. . . more. . . more
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Steps in CPM AnalysisSteps in CPM AnalysisSteps in CPM AnalysisSteps in CPM Analysis
Determine the slack for each activityDetermine the slack for each activity
Working from the end of the project networkWorking from the end of the project network
(from right to left), find the LF and the LS for each(from right to left), find the LF and the LS for each
activityactivity Compute the activitys slackCompute the activitys slack
slack = LSslack = LS -- ES = LFES = LF -- EFEF
Slack is the maximum amount of time that thisSlack is the maximum amount of time that this
activity can be delay in its completion before itactivity can be delay in its completion before itbecomes a critical activity, i.e., delays completionbecomes a critical activity, i.e., delays completion
of the projectof the project
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CPM ExampleCPM ExampleCPM ExampleCPM Example
TaskTask PredecessorPredecessor Time, hTime, h
aa -- 66
bb -- 88
cc -- 55
dd bb 1313
ee cc 99
ff aa 1515
gg aa 1717
hh ff 99
ii gg 66
jj d, ed, e 1212
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CPM ExampleCPM ExampleCPM ExampleCPM Example
CPM NetworkCPM Network
a, 6a, 6
f, 15f, 15
b, 8b, 8
c, 5c, 5e, 9e, 9
d, 13d, 13
g, 17g, 17 h, 9h, 9
i, 6i, 6
j, 12j, 12
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CPM ExampleCPM ExampleCPM ExampleCPM Example
Paths EnumeratedPaths Enumerated
PathPath Length of PathLength ofPath
aa--ff--hh 6 + 15 + 9 = 306 + 15 + 9 = 30
aa--gg--II 6 + 17 + 6 = 296 + 17 + 6 = 29
bb--dd--jj 8 + 13 + 12 = 33*8 + 13 + 12 = 33*
cc--ee--jj 5 + 9 + 12 = 265 + 9 + 12 = 26
* Critical path* Critical path
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CPM ExampleCPM ExampleCPM ExampleCPM Example
ES and EF TimesES and EF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
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CPM ExampleCPM ExampleCPM ExampleCPM Example
ES and EF TimesES and EF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
5 14
8 21
6 23
6 21
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CPM ExampleCPM ExampleCPM ExampleCPM Example
ES and EF TimesES and EF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
5 14
8 21 21 33
6 2321 30
23 29
6 21
Projects EF = 33Projects EF = 33
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CPM ExampleCPM ExampleCPM ExampleCPM Example
LS and LF TimesLS and LF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17
h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
5 14
8 2121 33
6 23
21 30
23 29
6 21
21 33
27 33
24 33
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CPM ExampleCPM ExampleCPM ExampleCPM Example
LS and LF TimesLS and LF Times
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17
h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
0 6
0 8
0 5
5 14
8 2121 33
6 23
21 30
23 29
6 21
4 10
0 8
7 12
12 21
21 33
27 33
8 21
10 27
24 33
18 24
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CPM ExampleCPM ExampleCPM ExampleCPM Example
Critical PathCritical Path
a, 6a, 6a, 6a, 6
f, 15f, 15f, 15f, 15
b, 8b, 8b, 8b, 8
c, 5c, 5c, 5c, 5
e, 9e, 9e, 9e, 9
d, 13d, 13d, 13d, 13
g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9
i, 6i, 6i, 6i, 6
j, 12j, 12j, 12j, 12
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Program EvaluationProgram Evaluation
and Review Technique (PERT)and Review Technique (PERT)
Program EvaluationProgram Evaluation
and Review Technique (PERT)and Review Technique (PERT)
The technique is based on the assumption that anThe technique is based on the assumption that anactivitys duration follows a probability distributionactivitys duration follows a probability distribution
instead of being a single value.instead of being a single value.
The probabilistic information about the activities isThe probabilistic information about the activities is
translated into probabilistic information about thetranslated into probabilistic information about the
project.project.
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PERTPERTPERTPERT
Three time estimates are required to compute theThree time estimates are required to compute theparameters of an activitys duration distribution:parameters of an activitys duration distribution:
pessimistic timepessimistic time (t(tpp )) -- the time the activity wouldthe time the activity would
take if things did not go welltake if things did not go well
most likely timemost likely time (t(tmm )) -- the consensus best estimatethe consensus best estimate
of the activitys durationof the activitys duration
optimistic timeoptimistic time (t(too )) -- the time the activity wouldthe time the activity would
take if things did go welltake if things did go well . . . more. . . more
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From these three time estimates about an activity, twoFrom these three time estimates about an activity, twoprobability distribution parameters are calculated: theprobability distribution parameters are calculated: the
mean (tmean (tee ) and the variance (V) and the variance (Vtt ).).
ttee = ( t= ( too + 4t+ 4tmm + t+ tpp ) / 6) / 6
VVtt = [ ( t= [ ( tpp -- ttoo ) / 6 ]) / 6 ]22
PERTPERTPERTPERT
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Steps in PERT AnalysisSteps in PERT AnalysisSteps in PERT AnalysisSteps in PERT Analysis
Draw the network.Draw the network.
Analyze the paths through the network and find the criticalAnalyze the paths through the network and find the critical
path.path.
The length of the critical path is the mean of the projectThe length of the critical path is the mean of the project
duration probability distribution which is assumed to beduration probability distribution which is assumed to benormal.normal.
The standard deviation of the project duration probabilityThe standard deviation of the project duration probability
distribution is computed by adding the variances of the criticaldistribution is computed by adding the variances of the critical
activities (all of the activities that make up the critical path)activities (all of the activities that make up the critical path)and taking the square root of that sumand taking the square root of that sum
Probability computations can now be made using the normalProbability computations can now be made using the normal
distribution table.distribution table.
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PERT ExamplePERT Example
Immed. Optimistic Most Likely PessimisticImmed. Optimistic Most Likely PessimisticActivityActivity Predec.Predec. Time (Hr.Time (Hr.)) Time (Hr.)Time (Hr.) Time (Hr.)Time (Hr.)
AA ---- 4 6 84 6 8
BB ---- 1 4.5 51 4.5 5
C A 3 3 3C A 3 3 3D A 4 5 6D A 4 5 6
E AE A 0.5 1 1.50.5 1 1.5
F B,C 3 4 5F B,C 3 4 5
G B,C 1 1.5 5G B,C 1 1.5 5
H E,F 5 6 7H E,F 5 6 7I E,F 2 5 8I E,F 2 5 8
J D,H 2.5 2.75 4.5J D,H 2.5 2.75 4.5
K G,I 3 5 7K G,I 3 5 7
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PERT ExamplePERT Example
PERT NetworkPERT Network
AA
DD
CC
BB
FF
EE
GG
II
HH
KK
JJ
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PERT ExamplePERT Example
Activity Expected Time and VarianceActivity Expected Time and VarianceActivityActivity Expected TimeExpected Time VarianceVariance
AA 66 4/94/9
BB 44 4/94/9
CC 33 00DD 55 1/91/9
EE 11 1/361/36
FF 44 1/91/9
GG 22 4/94/9
HH 66 1/91/9
II 55 11
JJ 33 1/91/9
KK 55 4/94/9
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PERT ExamplePERT Example
Earliest/Latest TimesEarliest/Latest Times
ActivityActivity ESES EFEF LSLS LFLF Slack Slack
A 0A 0 66 00 66 0 *critical0 *critical
B 0B 0 44 55 99 55
C 6C 6 99 66 99 0 *0 *D 6D 6 1111 1515 2020 99
E 6E 6 77 1212 1313 66
F 9F 9 1313 99 1313 0 *0 *
G 9G 9 1111 1616 1818 77HH 1313 1919 1414 2020 11
II 1313 1818 1313 1818 0 *0 *
JJ 1919 2222 2020 2323 11
KK 1818 2323 1818 2323 0 *0 *
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PERT ExamplePERT Example
Probability the project will be completed within 24
Probability the project will be completed within 24
hourshours
VVpathpath = V= VAA + V+ VCC + V+ VFF + V+ VII + V+ VKK
= 4/9 + 0 + 1/9 + 1 + 4/9= 4/9 + 0 + 1/9 + 1 + 4/9
= 2= 2
WWpathpath = 1.414= 1.414
zz = (24= (24 -- 23)/23)/W!W!(24(24--23)/1.414 = .7123)/1.414 = .71
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Standard Normal DistributionStandard Normal DistributionStandard Normal DistributionStandard Normal Distribution
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PERT ExamplePERT ExamplePERT ExamplePERT Example
Probability the project will be completed within 24Probability the project will be completed within 24hourshours
From the Standard Normal Distribution table:From the Standard Normal Distribution table:
P(zP(z
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End of Project SchedullingEnd of Project Schedulling
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