cpm process

8/2/2019 Cpm Process

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Project ManagementProject Management

Tuesday, May 9, 2006Tuesday, May 9, 2006

Competing with TimeCompeting with Time


nn Management complex projectsManagement complex projects

nn Many parallel tasksMany parallel tasks

nn Deadlines and milestones must be metDeadlines and milestones must be met

nn Difficult to knowDifficult to know ““what to do firstwhat to do first””

nn Difficult to know when project is in troubleDifficult to know when project is in trouble

nn Often have competition for limited resourcesOften have competition for limited resources

W hen to use:


ExamplesExamples

nn Building a new airportBuilding a new airport

nn Designing a new computer productDesigning a new computer product

nn Launching an advertising campaignLaunching an advertising campaign

nn Construction projects of all typesConstruction projects of all types

nn Maintenance projectsMaintenance projects

nn Community service projectsCommunity service projects


TechniquesTechniques

nn Critical Path Method (CPM)Critical Path Method (CPM)–– Developed by DuPont (1950Developed by DuPont (1950’’s)s)

–– Plan and control maintenance of chemical plantsPlan and control maintenance of chemical plants

–– Credited with reducing length of maintenance shutdownCredited with reducing length of maintenance shutdown

by 40%by 40%

nn Project Evaluation and Review TechniqueProject Evaluation and Review Technique

(PERT)(PERT)

–– Developed by Navy (early 1960Developed by Navy (early 1960’’s)s)–– Plan and control the Polaris missile projectPlan and control the Polaris missile project

–– Credited with speeding up project by 2 yearsCredited with speeding up project by 2 years

Critical PathCritical PathMethodMethod

(CPM)(CPM)


Critical Path Method (CPM)Critical Path Method (CPM)

nn Graphical method of portraying relationship of Graphical method of portraying relationship of

projectproject activities activities

nn AnAn activity activity is any discrete part or task of a projectis any discrete part or task of a project

which takeswhich takes resources and time resources and time to completeto complete

nn Activities exhibitActivities exhibit precedence relations precedence relations (some must(some must

be completed before others can start)be completed before others can start)

nn Activities with their precedence relations form aActivities with their precedence relations form a

project network project network

nn Critical Path Method Critical Path Method finds thefinds the longest pathlongest path

through the resulting project networkthrough the resulting project network


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Critical Path MethodCritical Path Method

Precedence RelationsPrecedence Relations

Activity Immediate Predecessor Duration (days)

A

B

C

D


Simple Project NetworkSimple Project Network

AA

BB

CC

DD


Precedence RelationsPrecedence Relations

Activity Immediate Predecessor Duration (days)

A (Start) 4

B A 3

C A 5

D B,C 2



AA

BB

CC

DD

Project Network


Activity Start/Finish TimesActivity Start/Finish Times

ES

LS

EF

LF


Activity Start/Finish TimesActivity Start/Finish Times

ES

LS

EF

LF

ActivityName

Activity

Duration

Early

Finish

Time

Late

Finish

Time

Early

Start

Time

Late

Start

Time




Finding the Critical PathFinding the Critical Path

A D

C

B

4

3

5

2

0

Start at

time t=0



A D

C

B

4

3

5

2

0 4

4

4

7

9

9 11

119

9

9

6

4

4



A D

C

B

4

3

5

2

0 4

4

4

7

9

9 11

119

9

9

6

4

40

S=0-0=4-4=0

Activity Slack: S = EFT-EST = LFT-EFT



A D

C

B

4

3

5

2

0 4

4

4

7

9

9 11

119

9

9

6

4

40

S=0 S=0

S=0

S=2

Critical Path: Path with zero activity slacks

CPM TerminologyCPM Terminology

nn Critical PathCritical Path:: the chain of act ivitie s along which the the chain of act ivitie s along which the

delay of any activity will delay the project delay of any activity will delay the project

nn Early Start Time (ES)Early Start Time (ES):: the ear lies t that an activity could the ear lies t that an activity could

possibly start, given precedence relations possibly start, given precedence relations

nn Late Start Time (LS)Late Start Time (LS):: the la test that an activity could the la test that an activity could

possibly s tart without delaying the project possibly s tart without delaying the project

nn Early Finish Time (EF)Early Finish Time (EF) :: the earliest that an activity the earliest that an activity

could possibly finish could possibly finish

nn Late Finish Time (LF)Late Finish Time (LF) :: the lat est that an act ivity could the lat est that an act ivity could

possib ly finish without delaying the pro ject possib ly finish without delaying the pro ject

nn Activity SlackActivity Slack:: the amount of the amount of “ “ play play” ” in the timing of thein the timing of the

activity; activity; slack = EFT slack = EFT -- EST = LFT EST = LFT -- EFT EFT


ExampleExampleSuppose you a re an advertising manager responsible for

the launch of a new m edia advertising campaign. Thecampaign (project) has the follow ing activ ities:

Activity Predecessors Time

A. Media b ids none 2 wks

B. Ad concep t none 6

C. Pilot layouts B 3

D. Select media A 8

E. Client ch eckoff A,C 6

F. Pre-p rod u ction B 8

G. Fin al p rod uction E,F 5

H. Launch campaign D,G 0



CPM AnalysisCPM Analysis

Example Project NetworkExample Project Network

A

2

A

2

B

6

B

6

F8

F8

D

8

D

8

C3

C3

E6

E6

G5

G5

H0

H0StartStart

Program EvaluationProgram Evaluation

andandReview TechniqueReview Technique

(PERT)(PERT)


Project Evaluation and ReviewProject Evaluation and Review

Technique (PERT)Technique (PERT)

nn Similar to Critical Path Method (CPM)Similar to Critical Path Method (CPM)

nn Accounts forAccounts for uncertaintyuncertaintyin activityin activityduration estimatesduration estimates

nn Provides estimates of project durationProvides estimates of project duration probabilities probabilities

nn Best used for highly uncertain projectsBest used for highly uncertain projects–– new product developmentnew product development

–– unique or firstunique or first--time projectstime projects–– research and developmentresearch and development

PERT AnalysisPERT Analysis


AA

BB

CC

DD


A Simple ExampleA Simple Example

Most

Optimistic

Most

Likely

Most

PessimisticActivity

2 3 10A

1 7B

4 6C

0.5 5.5D

2.5

5

1.5

m a b


Beta Distribution AssumptionBeta Distribution Assumption

Assume a “Beta” distribution

activity

duration

d e n s i t y

m a b




Expected Time and VarianceExpected Time and Variance

Expected Time =

Variance =

a + 4m + b6

(b - a) 2

36


Beta Distribution AssumptionBeta Distribution Assumption

activity

duration

d e n s i t y

m a b

expected duration


Expected Time and VarianceExpected Time and Variance

Activity A Activity A

ET =

Var =

a + 4m + b6

(b - a) 2

36

=

=

2+4(3)+106

= 4.0

(10-2) 2

36

= 1.778


Time and Variance ExampleTime and Variance Example

Expected

TimeVariance

Critical

Path?Activity

4 1.778AB

C

D


Time and Variance ExampleTime and Variance Example

Expected

TimeVariance

Critical

Path?Activity

4 1.778A

3 1.0B

5 0.111C

2 0.694D


Probability of CompletionProbability of Completion

W hat is t he probability that a project w ill be completed

by a specified due date?

Due Date - Expected Completion Date

Sum of the Variances on the Critical Path

z=

Normal Distribution

z



12 - 11

1.778 + 0.111 + 0.694


Completion Probability ExampleCompletion Probability Example

What is the probability of completing the project w ithin

12 days ?

z = = 0.622




12 days?

z = 0.622

Probability of completion = 0.7324

From a Z-table for standard Normal distributions:




12 days ?

z = 0.622

Probability of completion = 0.732

Conclusion:

There is about a 73% chance of completing the project in 12 days or less


Larger ExampleLarger Example

Suppose the duration of the activit ies of the ad

campaign are, in fact, uncertain:(a) (m) (b)

Act iv it y Pred s O p ti mi st ic Li k el y P essi mi st ic

A. none 1 2 3 wks

B. none 4 6 8

C. B 3 3 3

D. A 2 8 10

E. A,C 3 6 9

F. B 1 8 15

G. E,F 4 5 6

H. D,G 0 0 0


Larger ExampleLarger Example

Suppose the duration of t he activ iti es of the ad

campaign are, in fact , uncertain:(a) (m) (b)

Act iv it y Pred s O p ti mi st ic Li k el y Pes sim is ti c

A. none 1 2 3 wks

B. none 4 6 8

C. B 3 3 3

D. A 2 8 10E. A,C 3 6 9

F. B 1 8 15

G. E,F 4 5 6

H. D,G 0 0 0


Activity StatisticsActivity Statistics

Activity D Activity D

Expect ed Activ it y Durat ion for “D”:

ET = a + 4m + b

6 =

2+4(8)+106

= 7.33




Activity StatisticsActivity Statistics

Activity D Activity D

Variance of A ctiv ity Duration for “D”:

Var =(b - a) 2

36 =

(10-2) 2

36 = 1.78

Expected Activ it y Durat ion for “D”:

ET = a + 4m + b

6 =

2+4(8)+106

= 7.33


Project Duration StatisticsProject Duration Statistics

Activity Critical? M ean Var C.P. Var

A. 2 0.11B. 6 0.44

C. 3 0.00

D. 7.33 1.78

E. 6 1.00

F. 8 5.44

G. 5 0.11

H. 0 0.00



A2

A2

B

6

B

6

F8

F8

D

7.33

D

7.33

C3

C3

E6

E6

G5

G5

H0

H0StartStart



A2

A2

B

6

B

6

F8

F8

D

7.33

D

7.33

C3

C3

E6

E6

G5

G5

H0

H0StartStart



A2

A2

B

6

B

6

F8

F8

D

7.33

D

7.33

C3

C3

E6

E6

G5

G5

H0

H0StartStart

Critical Path Duration = 20 days


Project Duration StatisticsProject Duration Statistics

Activity Critical? M ean Var C.P. Var

A. 2 0.11

B. Yes 6 0.44 0.44

C. Yes 3 0.00 0.00

D. 7.33 1.78

E. Yes 6 1.00 1.00

F. 8 5.44

G. Yes 5 0.11 0.11

H. Yes 0 0.00 0.00

Critical Path Variance =σ 2 = 1.55




Using Project StatisticsUsing Project Statistics

What is the probability that the ad campaign

can be completed in 18 w eeks? 20? 24?

18 weeks: Z = x - µ

σ

18 - 20

sqrt(1.55)= = -1.61

Prob(x<18) = 1- 0.9463 = 0.054 or 5.4%





18 weeks: Z = -1.61 Prob(x<18) = 5.4%

20 weeks: Z = 0.00 Prob(x<20) = 50%

24 weeks: Z = = 3.21

Prob(x<24) = 0.993 or 99.3%

24 - 20

sqrt(1.55)





18 weeks: Z = -1.61 Prob(x<18) = 5.4%

20 weeks: Z = 0.00 Prob(x<20) = 50%

24 weeks: Z = 3.21 Prob(x<24) = 99.3%

Critical PathCritical Path

nn Slack times along the critical path are equal toSlack times along the critical path are equal to

zero. Slack = LFzero. Slack = LF -- EF = LSEF = LS -- ESES

nn The critical path is the path with the longestThe critical path is the path with the longest

duration in the networkduration in the network

nn Project cannot be completed in less than theProject cannot be completed in less than the

time of the critical pathtime of the critical path

nn Managerial implications?Managerial implications?

Project CrashingProject Crashing

nn CrashingCrashing reduces project time by expendingreduces project time by expending

additional resourcesadditional resources

nn Crash timeCrash time is the amount of time an activity isis the amount of time an activity is

reducedreduced

nn Crash costCrash cost is the cost of reducing an activityis the cost of reducing an activity’’ss

timetime

nn The goal of crashing is to reduce a projectThe goal of crashing is to reduce a project’’ss

duration at minimum costduration at minimum cost

Project CrashingProject Crashing

nn Would you ever crash (i.e. spend money on shortening) aWould you ever crash (i.e. spend money on shortening) a

nonnon--critical activity? Why?critical activity? Why?

nn If you had several critical activities that you could crash,If you had several critical activities that you could crash,

how would you decide which one, if any, to select?how would you decide which one, if any, to select?

nn What can happen with your nonWhat can happen with your non--critical activities andcritical activities and

their slack times as you crash activities along the criticaltheir slack times as you crash activities along the critical

path?path?



Crashing ExampleCrashing Example

A

5

B 60

F 45

C 65

D 10

G 100

E

20

170

Critical activities AFGE

Crashing G by 20 daysCrashing G by 20 days

A

5

B 60

F 45

C 65

D 10

G 80

E

20

150

Critical activities ABFCGE

Crashing E by 13 daysCrashing E by 13 days

A

5

B 60

F 45

C 65

D 10

G 80

E

7

137


Crashing A by 3 daysCrashing A by 3 days

A

2

B 60

F 45

C 65

D 10

G 80

E

7

134


Crashing B&G by 15 daysCrashing B&G by 15 days

A

2

B 45

F 45

C 65

D 10

G 65

E

7

119


Crashing C&G by 10 daysCrashing C&G by 10 days

A

2

B 45

F 45

C 55

D 10

G 55

E

7

109




Crashing C&F by 20 daysCrashing C&F by 20 days

A

2

B 45

F 25

C 35

D 10

G 55

E

7

89


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