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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved.
Project ManagementProject Management
OPIM 310-Lecture #9
Instructor: Jose Cruz
To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved.
Elements of Project Elements of Project ManagementManagement
Project teamProject team Individuals from different departments within Individuals from different departments within
companycompany
Matrix organizationMatrix organization Team structure with members from different Team structure with members from different
functional areas depending on skills neededfunctional areas depending on skills needed
Project managerProject manager Leader of project teamLeader of project team
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Project PlanningProject PlanningStatement of workStatement of work
Written description of goals, work & Written description of goals, work & time frame of projecttime frame of project
Activities require labor, resources & Activities require labor, resources & timetime
Precedence relationship shows Precedence relationship shows sequential relationship of project sequential relationship of project activitiesactivities
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Project PlanningProject PlanningStatement of workStatement of work
written description of goals, work & written description of goals, work & time frame of projecttime frame of project
Activities require labor, resources & Activities require labor, resources & timetime
Precedence relationship shows Precedence relationship shows sequential relationship of project sequential relationship of project activitiesactivities
Construct forms Pour concrete1 32
Simplified Project Network
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Elements of Elements of Project PlanningProject Planning
Define project objective(s)Define project objective(s) Identify activitiesIdentify activitiesEstablish precedence relationshipsEstablish precedence relationshipsMake time estimatesMake time estimatesDetermine project completion timeDetermine project completion timeCompare project schedule objectivesCompare project schedule objectivesDetermine resource requirements to Determine resource requirements to
meet objectivemeet objective
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Work Breakdown Work Breakdown StructureStructure
Hierarchical organization of work to Hierarchical organization of work to be done on a projectbe done on a project
Project broken down into modulesProject broken down into modules Modules subdivided into Modules subdivided into
subcomponents, activities, and taskssubcomponents, activities, and tasks Identifies individual tasks, workloads, Identifies individual tasks, workloads,
and resource requirementsand resource requirements
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Work Breakdown Work Breakdown StructureStructure
Hierarchical organization of work to Hierarchical organization of work to be done on a projectbe done on a project
Project broken down into modulesProject broken down into modules Modules subdivided into Modules subdivided into
subcomponents, activities, and taskssubcomponents, activities, and tasks Identifies individual tasks, workloads, Identifies individual tasks, workloads,
and resource requirementsand resource requirements
Dinner
Pasta Sauce Salad Bread Wine Setting
Table Atmosphere
Purchase Purchase Purchase Purchase Purchase Set table Light candles
Boil water Add tomato Wash Butter top Open Turn on musicsauce/paste lettuce
Cook Sauté Drain Slice Tasteonion & garlic lettuce
Drain Cool Tear Heat Servemeatballs lettuce
Add Serve Add spices croutons/ Serve
dressing
Cook sauce Mix
Serve Serve Figure 6.1
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Project ControlProject ControlAll activities identified and includedAll activities identified and includedCompleted in proper sequenceCompleted in proper sequenceResource needs identifiedResource needs identifiedSchedule adjustedSchedule adjustedMaintain schedule and Maintain schedule and
budgetbudgetComplete on timeComplete on time
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A Gantt ChartA Gantt Chart
Popular tool for project schedulingPopular tool for project schedulingGraph with bar for representing the Graph with bar for representing the
time for each tasktime for each taskProvides visual display of project Provides visual display of project
schedulescheduleAlso shows slack for activitiesAlso shows slack for activities
Amount of time activity can be Amount of time activity can be delayed without delaying projectdelayed without delaying project
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A Gantt ChartA Gantt Chart| | | | |
Activity
Design house and obtain financing
Lay foundation
Order and receive materials
Build house
Select paint
Select carpet
Finish work
00 22 44 66 88 1010MonthMonth
MonthMonth11 33 55 77 99
Figure 6.2Figure 6.2
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CPM/PERTCPM/PERT Critical Path Method (CPM)Critical Path Method (CPM)
DuPont & Remington-Rand (1956)DuPont & Remington-Rand (1956) Deterministic task timesDeterministic task times Activity-on-node network constructionActivity-on-node network construction
Project Eval. & Review Technique (PERT)Project Eval. & Review Technique (PERT) US Navy, Booz, Allen & HamiltonUS Navy, Booz, Allen & Hamilton Multiple task time estimatesMultiple task time estimates Activity-on-arrow network Activity-on-arrow network
constructionconstruction
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The Project NetworkThe Project Network
Network consists of branches & nodes Network consists of branches & nodes
1 32
BranchBranch
NodeNode
Figure 6.3Figure 6.3
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Network ConstructionNetwork Construction In AON, nodes represent activities & In AON, nodes represent activities &
arrows show precedence relationshipsarrows show precedence relationships In AOA, arrows represent activities & In AOA, arrows represent activities &
nodes are events for points in timenodes are events for points in time An event is the completion or beginning of An event is the completion or beginning of
an activityan activity A dummy shows precedence for two A dummy shows precedence for two
activities with same start & end nodesactivities with same start & end nodes
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Project Network for a HouseProject Network for a House
3322 00
11
33
11 1111
1 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
Figure 6.4Figure 6.4
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Concurrent ActivitiesConcurrent Activities
2 3
Lay foundationLay foundation
Order materialOrder material
(a)(a) Incorrect precedence Incorrect precedence relationshiprelationship
(b)(b) Correct precedence Correct precedence relationshiprelationship
3
42
DummyDummyLay Lay foundationfoundation
Order materialOrder material
11
22 00
Figure 6.5Figure 6.5
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Critical PathCritical Path A path is a sequence of connected A path is a sequence of connected
activities running from start to end activities running from start to end node in networknode in network
The critical path is the The critical path is the path with the longest path with the longest duration in the networkduration in the network
Project cannot be Project cannot be completed in less than completed in less than the time of the critical the time of the critical pathpath
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The Critical The Critical PathPath
A:A: 1-2-3-4-6-71-2-3-4-6-73 + 2 + 0 + 3 + 1 = 93 + 2 + 0 + 3 + 1 = 9 months months
B:B: 1-2-3-4-5-6-71-2-3-4-5-6-73 + 2 + 0 + 1 + 1 + 1 = 83 + 2 + 0 + 1 + 1 + 1 = 8 months months
C:C: 1-2-4-6-71-2-4-6-73 + 1 + 3 + 1 = 83 + 1 + 3 + 1 = 8 months months
D:D: 1-2-4-5-6-71-2-4-5-6-73 + 1 + 1 + 1 + 1 = 73 + 1 + 1 + 1 + 1 = 7 months months
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
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The Critical The Critical PathPath
A:A: 1-2-3-4-6-71-2-3-4-6-73 + 2 + 0 + 3 + 1 = 93 + 2 + 0 + 3 + 1 = 9 months months
B:B: 1-2-3-4-5-6-71-2-3-4-5-6-73 + 2 + 0 + 1 + 1 + 1 = 83 + 2 + 0 + 1 + 1 + 1 = 8 months months
C:C: 1-2-4-6-71-2-4-6-73 + 1 + 3 + 1 = 83 + 1 + 3 + 1 = 8 months months
D:D: 1-2-4-5-6-71-2-4-5-6-73 + 1 + 1 + 1 + 1 = 73 + 1 + 1 + 1 + 1 = 7 months months
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
The Critical Path
The Critical Path
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The Critical The Critical PathPath
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
1 2 4 6 7
3
5
3
2 0
1
3
1 1
Start at 3 months
Start at 5 months
1
Finish at 9 months
Start at 8 months
Figure 6.6
Activity Start Times
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Early Early TimesTimes
ESES - earliest time activity can start - earliest time activity can start Forward pass starts at beginning of Forward pass starts at beginning of
CPM/PERT network to determine CPM/PERT network to determine ESES times times EF = ESEF = ES + activity time + activity time
ESESijij == maximum (EFmaximum (EFii))
EFEFijij == ESESijij - - ttijij
ESES1212 == 00
EFEF1212 == ESES1212 -- t t1212
== 0 + 3 = 30 + 3 = 3 monthsmonths
2003
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
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Computing Computing Early Early Times Times
ESES2323 = max EF = max EF22 = 3 months = 3 monthsESES4646 = max EF = max EF44 = max 5,4 = 5 months = max 5,4 = 5 monthsEFEF4646 = ES = ES4646 - t - t46 46 = 5 + 3 = 8 months= 5 + 3 = 8 monthsEFEF6767 = 9 months, = 9 months,
the project durationthe project duration
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
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Computing Computing Early Early Times Times
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
1 2 4 6 7
3
5
3
2 0
1
3
1 1
1
(ES = 0, EF = 3)
(ES = 5, EF = 8)
(ES = 3, EF = 5)
(ES = 3, EF = 4)
(ES = 5, EF = 6) (ES = 6, EF = 7)
(ES = 8, EF = 9)
(ES = 5, EF = 5)
Early Start and Finish Times
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Late TimesLate TimesLSLS - latest time activity can start & - latest time activity can start &
not delay projectnot delay projectBackward pass starts at end of Backward pass starts at end of
CPM/PERT network to determine CPM/PERT network to determine LSLS timestimes
LF = LS + LF = LS + activity timeactivity timeLSLSijij == LFLFijij -- ttijij
LFLFijij = minimum (LS= minimum (LSjj))
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Computing Computing Late TimesLate Times
LFLF6767 = 9 months = 9 monthsLSLS6767 = LF = LF6767 - - tt67 67 = 9 - 1 = 8 months= 9 - 1 = 8 monthsLFLF5656 = minimum (LS = minimum (LS66) = 8 months) = 8 monthsLSLS5656 = LF = LF5656 - - tt56 56 = 8 - 1 = 7 months= 8 - 1 = 7 monthsLFLF2424 = minimum (LS = minimum (LS44) = min(5, 6) ) = min(5, 6)
= 5 months= 5 monthsLSLS2424 = LF = LF2424 - - tt24 24 = 5 - 1 = 4 months= 5 - 1 = 4 months
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
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Computing Computing Late TimesLate Times
LFLF6767 = 9 months = 9 monthsLSLS6767 = LF = LF6767 - - tt67 67 = 9 - 1 = 8 months= 9 - 1 = 8 monthsLFLF5656 = minimum (LS = minimum (LS66) = 8 months) = 8 monthsLSLS5656 = LF = LF5656 - - tt56 56 = 8 - 1 = 7 months= 8 - 1 = 7 monthsLFLF2424 = minimum (LS = minimum (LS44) = min(5, 6) ) = min(5, 6)
= 5 months= 5 monthsLSLS2424 = LF = LF2424 - - tt24 24 = 5 - 1 = 4 months= 5 - 1 = 4 months
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
1 2 4 6 7
3
5
3
2 0
1
3
1 1
1
ES = 3, EF = 5LS = 3, LF = 5( )
ES = 5, EF = 8LS = 5, LF = 8( )
ES = 3, EF = 4LS = 4, LF = 5( )ES = 0, EF = 3
LS = 0, LF = 3( )
ES = 5, EF = 5LS = 5, LF = 5( )
ES = 5, EF = 6LS = 6, LF = 7( )
ES = 8, EF = 9LS = 8, LF = 9( )
ES = 6, EF = 7LS =7, LF = 8( )
Early and Late Start and Finish Times
Figure 6.9
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Activity SlackActivity SlackActivities on critical path have Activities on critical path have
ES = LSES = LS & & EF = LFEF = LFActivities not on critical path have Activities not on critical path have
slackslack SSijij = LS = LSijij - ES - ESijij
SSijij = LF = LFijij - EF - EFijij
SS24 24 = LS= LS2424 - ES - ES24 24 = 4 - 3 = 1 month= 4 - 3 = 1 month
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Activity Slack Activity Slack DataData
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
ActivityActivity LSLS ESES LFLF EFEF SlacksSlacks
*1-2*1-2 00 00 33 33 00*2-3*2-3 33 33 55 55 002-42-4 44 33 55 44 11
*3-4*3-4 55 55 55 55 004-54-5 66 55 77 66 11
*4-6*4-6 55 55 88 88 005-65-6 77 66 88 77 11
*6-7*6-7 88 88 99 99 00* Critical path* Critical path
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Activity Slack Activity Slack DataData
33
22 00
11
33
11 11
111 2 4 6 7
3
5
Lay Lay foundationfoundation
Design house Design house and obtain and obtain financingfinancing
Order and Order and receive receive materialsmaterials
DummyDummy
Finish Finish workwork
Select Select carpetcarpet
Select Select paintpaint
Build Build househouse
ActivityActivity LSLS ESES LFLF EFEF SlacksSlacks
*1-2*1-2 00 00 33 33 00*2-3*2-3 33 33 55 55 002-42-4 44 33 55 44 11
*3-4*3-4 55 55 55 55 004-54-5 66 55 77 66 11
*4-6*4-6 55 55 88 88 005-65-6 77 66 88 77 11
*6-7*6-7 88 88 99 99 00* Critical path* Critical path
1 2 4 6 7
3
5
3
2 0
1
3
1 1
1
Figure 6.10
Activity Slack
S = 0
S = 1S = 1
S = 1
S = 0 S = 0
S = 0
S = 0
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Probabilistic Time Probabilistic Time EstimatesEstimates
Reflect uncertainty of activity timesReflect uncertainty of activity timesBeta distribution is used in PERTBeta distribution is used in PERT
aa = optimistic estimate = optimistic estimatemm = most likely time estimate = most likely time estimatebb = pessimistic time estimate= pessimistic time estimate
wherewhere
Mean (expected time):Mean (expected time): tt = =aa + 4 + 4mm + + bb
66
Variance:Variance: 22 = =bb - - aa
66
22
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Example Beta DistributionsExample Beta Distributions
PP(t
ime)
(tim
e)
PP(t
ime)
(tim
e)
PP(t
ime)
(tim
e)
TimeTimeaa mmtt bbaa mm tt bb
m m = = tt
TimeTime
TimeTimebbaa
Figure 6.11Figure 6.11
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Southern Textile CompanySouthern Textile Company
System System changeover changeover
2
4
6
1 73 5 9
8
Manual Manual TestingTesting
DummyDummy
System System TrainingTraining
DummyDummySystem System TestingTesting
OrientationOrientation
Position Position recruitingrecruiting
System System developmentdevelopment
Equipment Equipment installationinstallation
Equipment testing Equipment testing and modificationand modification
Final Final debuggingdebugging
Job Job trainingtraining
aa
bb
cc
dd
ee
ff
gg
hh
ii
jj kk
ll
mm
Example 6.1Example 6.1
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Activity EstimatesActivity Estimates
1 - 21 - 2 66 88 1010 88 0.440.441 - 31 - 3 33 66 99 66 1.001.001 - 41 - 4 11 33 55 33 0.440.442 - 52 - 5 00 00 00 00 0.000.002 - 6 2 - 6 22 44 1212 55 2.782.783 - 5 3 - 5 22 33 44 33 0.110.114 - 54 - 5 33 44 55 44 0.110.114 - 84 - 8 22 22 22 22 0.000.005 - 75 - 7 33 77 1111 77 1.781.785 - 85 - 8 22 44 66 44 0.440.447 - 87 - 8 00 00 00 00 0.000.006 - 96 - 9 11 44 77 44 1.001.007 - 97 - 9 11 1010 1313 99 4.004.00
TIME ESTIMATES (WKS)TIME ESTIMATES (WKS) MEAN TIMEMEAN TIME VARIANCEVARIANCE
ACTIVITYACTIVITY aa mm bb tt 22
2
4
6
1 73 5 9
8
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2
4
6
1 73 5 9
8
Early and Late TimesEarly and Late Times
For Activity 1-2For Activity 1-2
aa = 6,= 6, m m = 8, = 8, bb = 10 = 10
t t = = = 8 weeks= = = 8 weeksaa + 4 + 4mm + + bb
666 + 4(8) + 106 + 4(8) + 10
66
22 = = = week = = = weekbb - - aa
66
2210 - 610 - 6
66
224499
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2
4
6
1 73 5 9
8
Early and Late TimesEarly and Late Times
ACTIVITYACTIVITY tt ESES EFEF LSLS LFLF SS
1 - 21 - 2 88 0.440.44 00 88 11 99 111 - 31 - 3 66 1.001.00 00 66 00 66 001 - 41 - 4 33 0.440.44 00 33 22 55 222 - 52 - 5 00 0.000.00 88 88 99 99 112 - 6 2 - 6 55 2.782.78 88 1313 1616 2121 883 - 5 3 - 5 33 0.110.11 66 99 66 99 004 - 54 - 5 44 0.110.11 33 77 55 99 224 - 84 - 8 22 0.000.00 33 55 1414 1616 11115 - 75 - 7 77 1.781.78 99 1616 99 1616 005 - 85 - 8 44 0.440.44 99 1313 1212 1616 337 - 87 - 8 00 0.000.00 1313 1313 1616 1616 336 - 96 - 9 44 1.001.00 1313 1717 2121 2525 887 - 97 - 9 99 4.004.00 1616 2525 1616 2525 00
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Southern Textile CompanySouthern Textile Company
Example 6.1Example 6.1
2
4
6
1 73 5 9
8
ES = 9, EF = 16ES = 9, EF = 16LS = 9, LF = 16LS = 9, LF = 16
ES = 0, EF = 8ES = 0, EF = 8LS = 1, LF = 9LS = 1, LF = 9
ES = 0, EF = 6ES = 0, EF = 6LS = 0, LF = 6LS = 0, LF = 6
ES = 6, EF = 9ES = 6, EF = 9LS = 6, LF = 9LS = 6, LF = 9
ES = 0, EF = 3ES = 0, EF = 3LS = 2, LF = 5LS = 2, LF = 5
ES = 3, EF = 7ES = 3, EF = 7LS = 5, LF = 9LS = 5, LF = 9
ES = 9, EF = 13ES = 9, EF = 13LS = 12, LF = 16LS = 12, LF = 16
ES = 8, EF = 8ES = 8, EF = 8LS = 9, LF = 9LS = 9, LF = 9
ES = 13, EF = 13ES = 13, EF = 13LS = 16, LF = 16LS = 16, LF = 16
ES = 3, EF = 5ES = 3, EF = 5LS = 14, LF = 16LS = 14, LF = 16
ES = 16, EF = 25ES = 16, EF = 25LS = 21, LF = 25LS = 21, LF = 25
ES = 13, EF = 17ES = 13, EF = 17LS = 21, LF = 25LS = 21, LF = 25
ES = 8, EF = 13ES = 8, EF = 13LS = 16, LF = 21LS = 16, LF = 21
88
55
44
66 33 77
99
33
22
44 00
00
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Southern Textile CompanySouthern Textile Company
Example 6.1Example 6.1
2
4
6
1 73 5 9
8
ES = 9, EF = 16ES = 9, EF = 16LS = 9, LF = 16LS = 9, LF = 16
ES = 0, EF = 8ES = 0, EF = 8LS = 1, LF = 9LS = 1, LF = 9
ES = 0, EF = 6ES = 0, EF = 6LS = 0, LF = 6LS = 0, LF = 6
ES = 6, EF = 9ES = 6, EF = 9LS = 6, LF = 9LS = 6, LF = 9
ES = 0, EF = 3ES = 0, EF = 3LS = 2, LF = 5LS = 2, LF = 5
ES = 3, EF = 7ES = 3, EF = 7LS = 5, LF = 9LS = 5, LF = 9
ES = 9, EF = 13ES = 9, EF = 13LS = 12, LF = 16LS = 12, LF = 16
ES = 8, EF = 8ES = 8, EF = 8LS = 9, LF = 9LS = 9, LF = 9
ES = 13, EF = 13ES = 13, EF = 13LS = 16, LF = 16LS = 16, LF = 16
ES = 3, EF = 5ES = 3, EF = 5LS = 14, LF = 16LS = 14, LF = 16
ES = 16, EF = 25ES = 16, EF = 25LS = 21, LF = 25LS = 21, LF = 25
ES = 13, EF = 17ES = 13, EF = 17LS = 21, LF = 25LS = 21, LF = 25
ES = 8, EF = 13ES = 8, EF = 13LS = 16, LF = 21LS = 16, LF = 21
88
55
44
66 33 77
99
33
22
44 00
00
2 = 2 + 2 + 2 + 2
= 1.00 + 0.11 + 1.78 + 4.00
= 6.89 weeks
13 35 57 79
Total project variance
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Probabilistic Network Probabilistic Network AnalysisAnalysis
Determine probability that project is Determine probability that project is completed within specified timecompleted within specified time
wherewhere == ttpp = project mean time = project mean time
== project standard deviationproject standard deviationx x == proposed project timeproposed project timeZZ = = number of standard deviations number of standard deviations xx
is from meanis from mean
ZZ = =xx - -
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Normal Distribution Of Normal Distribution Of Project TimeProject Time
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Normal Distribution Of Normal Distribution Of Project TimeProject Time
= = ttpp TimeTimexx
Z
ProbabilityProbability
Figure 6.12Figure 6.12
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Southern Textile ExampleSouthern Textile Example
What is the probability that the project What is the probability that the project is completed within 30 weeks?is completed within 30 weeks?
Example 6.2Example 6.2
= 25= 25 Time (weeks)Time (weeks)xx = 30 = 30
PP((xx 30 weeks) 30 weeks)
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Southern Textile ExampleSouthern Textile Example
What is the probability that the project What is the probability that the project is completed within 30 weeks?is completed within 30 weeks?
Example 6.2Example 6.2
= 25= 25 Time (weeks)Time (weeks)xx = 30 = 30
PP((xx 30 weeks) 30 weeks)
22 = 6.89 weeks= 6.89 weeks
= 6.89= 6.89
= 2.62 weeks= 2.62 weeks
ZZ ==
==
= 1.91= 1.91
xx - -
30 - 2530 - 252.622.62
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Southern Textile ExampleSouthern Textile Example
What is the probability that the project What is the probability that the project is completed within 30 weeks?is completed within 30 weeks?
Example 6.2Example 6.2
= 25= 25 Time (weeks)Time (weeks)xx = 30 = 30
PP((xx 30 weeks) 30 weeks)
22 = 6.89 weeks= 6.89 weeks
= 6.89= 6.89
= 2.62 weeks= 2.62 weeks
ZZ ==
==
= 1.91= 1.91
xx - -
30 - 2530 - 252.622.62
From Table A.1, a From Table A.1, a ZZ score of 1.91 score of 1.91 corresponds to a probability of 0.4719.corresponds to a probability of 0.4719.Thus Thus PP(30) = 0.4719 + 0.5000 = 0.9719(30) = 0.4719 + 0.5000 = 0.9719
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Southern Textile ExampleSouthern Textile Example
What is the probability that the project What is the probability that the project is completed within 22 weeks?is completed within 22 weeks?
Example 6.3Example 6.3
= 25= 25 Time (weeks)Time (weeks)xx = 22 = 22
PP((xx 22 weeks) 22 weeks)
0.3729
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Southern Textile ExampleSouthern Textile Example
What is the probability that the project What is the probability that the project is completed within 22 weeks?is completed within 22 weeks?
Example 6.3Example 6.3
22 = 6.89 weeks= 6.89 weeks
= 6.89= 6.89
= 2.62 weeks= 2.62 weeks
ZZ ==
==
= -1.14= -1.14
xx - -
22 - 2522 - 252.622.62
= 25= 25 Time (weeks)Time (weeks)xx = 22 = 22
PP((xx 22 weeks) 22 weeks)
0.3729
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Southern Textile ExampleSouthern Textile Example
What is the probability that the project What is the probability that the project is completed within 22 weeks?is completed within 22 weeks?
Example 6.3Example 6.3
22 = 6.89 weeks= 6.89 weeks
= 6.89= 6.89
= 2.62 weeks= 2.62 weeks
ZZ ==
==
= -1.14= -1.14
xx - -
22 - 2522 - 252.622.62
From Table A.1, a From Table A.1, a ZZ score of -1.14 score of -1.14 corresponds to a probability of 0.3729.corresponds to a probability of 0.3729.Thus Thus PP(22) = 0.5000 - 0.3729 = 0.1271(22) = 0.5000 - 0.3729 = 0.1271
= 25= 25 Time (weeks)Time (weeks)xx = 22 = 22
PP((xx 22 weeks) 22 weeks)
0.3729
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Project CrashingProject CrashingCrashing is reducing project time Crashing is reducing project time
by expending additional resourcesby expending additional resourcesCrash time is an amount of time an Crash time is an amount of time an
activity is reducedactivity is reducedCrash cost is the cost of reducing Crash cost is the cost of reducing
the activity timethe activity timeGoal is to reduce project duration Goal is to reduce project duration
at minimum costat minimum cost
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Housebuilding NetworkHousebuilding Network
121288 00
44 1212
44 44
441 2 4 6 7
3
5
Figure 6.15Figure 6.15
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121288 00
44 1212
44 44
441 2 4 6 7
3
5
Housebuilding NetworkHousebuilding Network
$7,000 –
$6,000 –
$5,000 –
$4,000 –
$3,000 –
$2,000 –
$1,000 –
–| | | | | | |
0 2 4 6 8 10 12 14 Weeks
Normal activity
Normal time
Normal cost
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121288 00
44 1212
44 44
441 2 4 6 7
3
5
Housebuilding NetworkHousebuilding Network
$7,000 –
$6,000 –
$5,000 –
$4,000 –
$3,000 –
$2,000 –
$1,000 –
–| | | | | | |
0 2 4 6 8 10 12 14 Weeks
Crash cost
Crashed activity
Normal activity
Normal timeCrash time
Normal cost
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121288 00
44 1212
44 44
441 2 4 6 7
3
5
Housebuilding NetworkHousebuilding Network
$7,000 –
$6,000 –
$5,000 –
$4,000 –
$3,000 –
$2,000 –
$1,000 –
–| | | | | | |
0 2 4 6 8 10 12 14 Weeks
Crash cost
Crashed activity
Normal activity
Normal timeCrash time
Normal cost
Slope = crash cost per week
Total crash cost $2,000Total crash time 5
= = $400 per week
Figure 6.16Figure 6.16
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Normal Activity Normal Activity and Crash Dataand Crash Data
1 2 4 6 7
3
5
TOTALTOTALNORMALNORMAL CRASHCRASH ALLOWABLEALLOWABLE CRASHCRASH
TIMETIME TIMETIME NORMALNORMAL CRASHCRASH CRASH TIMECRASH TIME COST PERCOST PERACTIVITYACTIVITY (WEEKS)(WEEKS) (WEEKS)(WEEKS) COSTCOST COSTCOST (WEEKS)(WEEKS) WEEKWEEK
1-21-2 1212 77 $3,000$3,000 $5,000$5,000 55 $400$400
2-32-3 88 55 2,0002,000 3,5003,500 33 500500
2-42-4 44 33 4,0004,000 7,0007,000 11 3,0003,000
3-43-4 00 00 00 00 00 00
4-54-5 44 11 500500 1,1001,100 33 200200
4-64-6 1212 99 50,00050,000 71,00071,000 33 7,0007,000
5-65-6 44 11 500500 1,1001,100 33 200200
6-76-7 44 33 15,00015,000 22,00022,000 11 7,0007,000
$75,000$75,000 $110,700$110,700
Example 6.4Example 6.4
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Normal Activity Normal Activity and Crash Dataand Crash Data
1 2 4 6 7
3
5
TOTALTOTALNORMALNORMAL CRASHCRASH ALLOWABLEALLOWABLE CRASHCRASH
TIMETIME TIMETIME NORMALNORMAL CRASHCRASH CRASH TIMECRASH TIME COST PERCOST PERACTIVITYACTIVITY (WEEKS)(WEEKS) (WEEKS)(WEEKS) COSTCOST COSTCOST (WEEKS)(WEEKS) WEEKWEEK
1-21-2 1212 77 $3,000$3,000 $5,000$5,000 55 $400$400
2-32-3 88 55 2,0002,000 3,5003,500 33 500500
2-42-4 44 33 4,0004,000 7,0007,000 11 3,0003,000
3-43-4 00 00 00 00 00 00
4-54-5 44 11 500500 1,1001,100 33 200200
4-64-6 1212 99 50,00050,000 71,00071,000 33 7,0007,000
5-65-6 44 11 500500 1,1001,100 33 200200
6-76-7 44 33 15,00015,000 22,00022,000 11 7,0007,000
$75,000$75,000 $110,700$110,700
Example 6.4Example 6.4
12
8 0
4 12
4 4
41 2 4 6 7
3
5
$400
$500
$3,000 $7,000
$200 $200
$7,000
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Normal Activity Normal Activity and Crash Dataand Crash Data
1 2 4 6 7
3
5
TOTALTOTALNORMALNORMAL CRASHCRASH ALLOWABLEALLOWABLE CRASHCRASH
TIMETIME TIMETIME NORMALNORMAL CRASHCRASH CRASH TIMECRASH TIME COST PERCOST PERACTIVITYACTIVITY (WEEKS)(WEEKS) (WEEKS)(WEEKS) COSTCOST COSTCOST (WEEKS)(WEEKS) WEEKWEEK
1-21-2 1212 77 $3,000$3,000 $5,000$5,000 55 $400$400
2-32-3 88 55 2,0002,000 3,5003,500 33 500500
2-42-4 44 33 4,0004,000 7,0007,000 11 3,0003,000
3-43-4 00 00 00 00 00 00
4-54-5 44 11 500500 1,1001,100 33 200200
4-64-6 1212 99 50,00050,000 71,00071,000 33 7,0007,000
5-65-6 44 11 500500 1,1001,100 33 200200
6-76-7 44 33 15,00015,000 22,00022,000 11 7,0007,000
$75,000$75,000 $110,700$110,700
Example 6.4Example 6.4
12
8 0
4 12
4 4
41 2 4 6 7
3
5
$400
$500
$3,000 $7,000
$200 $200
$7,000
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Normal Activity Normal Activity and Crash Dataand Crash Data
1 2 4 6 7
3
5
TOTALTOTALNORMALNORMAL CRASHCRASH ALLOWABLEALLOWABLE CRASHCRASH
TIMETIME TIMETIME NORMALNORMAL CRASHCRASH CRASH TIMECRASH TIME COST PERCOST PERACTIVITYACTIVITY (WEEKS)(WEEKS) (WEEKS)(WEEKS) COSTCOST COSTCOST (WEEKS)(WEEKS) WEEKWEEK
1-21-2 1212 77 $3,000$3,000 $5,000$5,000 55 $400$400
2-32-3 88 55 2,0002,000 3,5003,500 33 500500
2-42-4 44 33 4,0004,000 7,0007,000 11 3,0003,000
3-43-4 00 00 00 00 00 00
4-54-5 44 11 500500 1,1001,100 33 200200
4-64-6 1212 99 50,00050,000 71,00071,000 33 7,0007,000
5-65-6 44 11 500500 1,1001,100 33 200200
6-76-7 44 33 15,00015,000 22,00022,000 11 7,0007,000
$75,000$75,000 $110,700$110,700
Example 6.4Example 6.4
7
8 0
4 12
4 4
41 2 4 6 7
3
5
$500
$3,000 $7,000
$200 $200
$7,000
Crash cost = $2,000
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Normal Activity Normal Activity and Crash Dataand Crash Data
1 2 4 6 7
3
5
TOTALTOTALNORMALNORMAL CRASHCRASH ALLOWABLEALLOWABLE CRASHCRASH
TIMETIME TIMETIME NORMALNORMAL CRASHCRASH CRASH TIMECRASH TIME COST PERCOST PERACTIVITYACTIVITY (WEEKS)(WEEKS) (WEEKS)(WEEKS) COSTCOST COSTCOST (WEEKS)(WEEKS) WEEKWEEK
1-21-2 1212 77 $3,000$3,000 $5,000$5,000 55 $400$400
2-32-3 88 55 2,0002,000 3,5003,500 33 500500
2-42-4 44 33 4,0004,000 7,0007,000 11 3,0003,000
3-43-4 00 00 00 00 00 00
4-54-5 44 11 500500 1,1001,100 33 200200
4-64-6 1212 99 50,00050,000 71,00071,000 33 7,0007,000
5-65-6 44 11 500500 1,1001,100 33 200200
6-76-7 44 33 15,00015,000 22,00022,000 11 7,0007,000
$75,000$75,000 $110,700$110,700
Example 6.4Example 6.4
7
8 0
4 12
4 4
41 2 4 6 7
3
5
$500
$3,000 $7,000
$200 $200
$7,000
Crash cost = $2,000
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Normal Activity Normal Activity and Crash Dataand Crash Data
1 2 4 6 7
3
5
TOTALTOTALNORMALNORMAL CRASHCRASH ALLOWABLEALLOWABLE CRASHCRASH
TIMETIME TIMETIME NORMALNORMAL CRASHCRASH CRASH TIMECRASH TIME COST PERCOST PERACTIVITYACTIVITY (WEEKS)(WEEKS) (WEEKS)(WEEKS) COSTCOST COSTCOST (WEEKS)(WEEKS) WEEKWEEK
1-21-2 1212 77 $3,000$3,000 $5,000$5,000 55 $400$400
2-32-3 88 55 2,0002,000 3,5003,500 33 500500
2-42-4 44 33 4,0004,000 7,0007,000 11 3,0003,000
3-43-4 00 00 00 00 00 00
4-54-5 44 11 500500 1,1001,100 33 200200
4-64-6 1212 99 50,00050,000 71,00071,000 33 7,0007,000
5-65-6 44 11 500500 1,1001,100 33 200200
6-76-7 44 33 15,00015,000 22,00022,000 11 7,0007,000
$75,000$75,000 $110,700$110,700
Example 6.4Example 6.4
7
7 0
4 12
4 4
41 2 4 6 7
3
5
$500
$3,000 $7,000
$200 $200
$7,000
Crash cost = $2,000 + $500 = $2,500
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Crashing costs increase as project Crashing costs increase as project duration decreasesduration decreases
Indirect costs increase as project Indirect costs increase as project duration increasesduration increases
Reduce project length Reduce project length as long as crashing as long as crashing costs are less than costs are less than indirect costsindirect costs
Time-Cost Relationship Time-Cost Relationship
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Time-Cost TradeoffTime-Cost TradeoffC
ost
($)
Co
st (
$)
Project durationProject duration
CrashingCrashing TimeTime
Minimum cost = optimal project timeMinimum cost = optimal project timeTotal project costTotal project cost
Indirect costIndirect cost
Direct costDirect cost
Figure 6.17Figure 6.17