to accompany russell and taylor, operations management, 4th edition, 2003 prentice-hall, inc. all...

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


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


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


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


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


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


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


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


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


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


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


The Project NetworkThe Project Network

Network consists of branches & nodes Network consists of branches & nodes

1 32

BranchBranch

NodeNode



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


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



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



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


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




DummyDummy







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




DummyDummy





The Critical Path

The Critical Path



33

22 00

11

33

11 11

111 2 4 6 7

3

5




DummyDummy





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


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




DummyDummy






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




DummyDummy






Computing Computing Early Early Times Times

33

22 00

11

33

11 11

111 2 4 6 7

3

5




DummyDummy





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


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))


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




DummyDummy






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




DummyDummy





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


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


Activity Slack Activity Slack DataData

33

22 00

11

33

11 11

111 2 4 6 7

3

5




DummyDummy





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


Activity Slack Activity Slack DataData

33

22 00

11

33

11 11

111 2 4 6 7

3

5




DummyDummy





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


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


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



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


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


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


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




2

4

6

1 73 5 9

8

ES = 9, EF = 16ES = 9, EF = 16LS = 9, LF = 16LS = 9, LF = 16













88

55

44

66 33 77

99

33

22

44 00

00




2

4

6

1 73 5 9

8














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


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 - -


Normal Distribution Of Normal Distribution Of Project TimeProject Time


Normal Distribution Of Normal Distribution Of Project TimeProject Time

= = ttpp TimeTimexx

Z

ProbabilityProbability



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?


= 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







22 = 6.89 weeks= 6.89 weeks

= 6.89= 6.89


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







0.3729





22 = 6.89 weeks= 6.89 weeks

= 6.89= 6.89


ZZ ==

==

= -1.14= -1.14

xx - -

22 - 2522 - 252.622.62



0.3729





22 = 6.89 weeks= 6.89 weeks

= 6.89= 6.89


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



0.3729


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


Housebuilding NetworkHousebuilding Network

121288 00

44 1212

44 44

441 2 4 6 7

3

5



121288 00

44 1212

44 44

441 2 4 6 7

3

5


$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


121288 00

44 1212

44 44

441 2 4 6 7

3

5


$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


121288 00

44 1212

44 44

441 2 4 6 7

3

5


$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



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




1 2 4 6 7

3

5



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


12

8 0

4 12

4 4

41 2 4 6 7

3

5

$400

$500

$3,000 $7,000

$200 $200

$7,000



1 2 4 6 7

3

5



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


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



1 2 4 6 7

3

5



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


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


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


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


to accompany russell and taylor, operations management, 4th edition, 2003 prentice-hall, inc. all...

Documents

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project management opim

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elements of project

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