Pert/CPM Analysis

8/8/2019 Pert/CPM Analysis

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Project Management - CPM/PERT


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Project Network

2

` Use of nodes and arrows

Arrows An arrow leads from tail to head directionally

` Indicate ACTIVITY, a time consuming effort that is required to perform apart of the work.

Nodes A node is represented by a circle- Indicate EVENT, a point in time where one or more activities start and/or

finish.

Network analysis is the general name given to certain specific techniques which can beused for the planning, management and control of projects

Activity

A task or a certain amount of work required in the project Requires time to complete

Represented by an arrow

Dummy Activity

Indicates only precedence relationships

Does not require any time of effort


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3

` Event`

Signals the beginning or ending of an activity` Designates a point in time` Represented by a circle (node)

` Network` Shows the sequential relationships among activities using nodes

and arrows

Activity-on-node (AON)

nodes represent activities, and arrows show precedence relationships

Activity-on-arrow (AOA)arrows represent activities and nodes are events for points in time

Project Network


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A A Pro ect Networ or House

4

3

2 0

1

3

1 1

11 2 4 6 7

3

5

Lay

foundation

Design house

and obtain

financing

Order and

receive

materials

Dummy

Finishwork

Select

carpet

Select

paint

Buildhouse

AON Project Network for House

13

2

2

4

3

31 5

1

61

71Start

Design house

and obtain

financing

Order and receivematerials

Select paint

Select carpet

Lay foundations Build house

Finish work


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Situations in network diagram

5

AB

C

A must finish before either B or C can start

A

B

C both A and B must finish before C can start

D

C

B

Aboth A and C must finish before either of B or D can

start

A

C

B

D

Dummy

A must finish before B can start

both A and C must finish before D can start


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Concurrent Activities

6

2 3

Lay foundationLay foundation

Order materialOrder material

(a)(a) Incorrect precedenceIncorrect precedence

relationshiprelationship

(b)(b) Correct precedenceCorrect precedence

relationshiprelationship

3

42

DummyDummyLayLay

foundationfoundation

Order materialOrder material

11

22 00


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Network example

7

Illustration of network analysis of a minor redesign of a product and its associated packaging.

The key question is: How long will it take to complete this project ?


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8

For clarity, this list is kept to a minimum by specifying only immediate relationships, that is

relationships involving activities that "occur near to each other in time".


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uest ons to prepare act v ty networ

9

` Is this a Start Activity?

` Is this a Finish Activity?

` What Activity Precedes this?` What Activity Follows this?

` What Activity is Concurrent with this?


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CPM calculation

10

`

Path` A connected sequence of activities leading from the starting

event to the ending event

` Critical Path

` The longest path (time); determines the project duration

` Critical Activities

` All of the activities that make up the critical path


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Forwar Pass

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` Earliest Start Time (ES)` earliest time an activity can start

` ES = maximum EF of immediate predecessors` Earliest finish time (EF)

` earliest time an activity can finish` earliest start time plus activity time

EF= ES + t

Latest Start Time (LS)

Latest time an activity can start without delaying critical path time

LS= LF - t

Latest finish time (LF)latest time an activity can be completed without delaying critical path time

LS = minimum LS of immediate predecessors

Backward Pass


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CPM analysis

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` Draw the CPM network

` Analyze the paths through the network

` Determine the float for each activity

` Compute the activitys float

float = LS - ES = LF - EF

` Float is the maximum amount of time that this activity can be

delay in its completion before it becomes a critical activity, i.e.,

delays completion of the project

` Find the critical path is that the sequence of activities and events

where there is no slack i.e.. Zero slack` Longest path through a network

` Find the project duration is minimum project completion time


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CPM Example:

13

` CPMNetwork

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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CPM Example

14

` ES 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 Example

15

` ES 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 Example

16

` ES 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 Example

17

` LS 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 21

21 33

6 23

21 30

23 29

6 21

21 33

27 33

24 33


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CPM ExampleCPM Example

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`

LS 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 21

21 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 Example

20

`

Critical 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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PERT Example

21

Immed. Optimistic Most Likely Pessimistic

Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.)

A -- 4 6 8B -- 1 4.5 5

C A 3 3 3D A 4 5 6E A 0.5 1 1.5F B,C 3 4 5

G B,C1

1

.5 5H E,F 5 6 7I E,F 2 5 8J D,H 2.5 2.75 4.5K G,I 3 5 7


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PERT Example

22

AA

DD

CC

BB

FF

EE

GG

II

HH

KK

JJ

PERT Network


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PROJECT COST


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Cost consideration in project

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` Project managers may have the option or requirement to crash

the project, or accelerate the completion of the project.` This is accomplished by reducing the length of the critical path(s).

` The length of the critical path is reduced by reducing the durationof the activities on the critical path.

` If each activity requires the expenditure of an amount of money

to reduce its duration by one unit of time, then the projectmanager selects the least cost critical activity, reduces it by onetime unit, and traces that change through the remainder of thenetwork.

` As a result of a reduction in an activitys time, a new critical pathmay be created.

` When there is more than one critical path, each of the criticalpaths must be reduced.

` If the length of the project needs to be reduced further, theprocess is repeated.


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Project Crashing

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`

Crashing` reducing project time by expending additional resources

` Crash time

` an amount of time an activity is reduced

` Crash cost` cost of reducing activity time

` Goal

` reduce project duration at minimum cost


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Activity crashing

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Activity time

Crashing activity

Crash time

Crash cost

Normal Activity

Normaltime

Normal

cost

Slope = crash cost per unit time


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Time-Cost Relationship

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Crashing costs increase as project duration decreases

Indirect costs increase as project duration increases

Reduce project length as long as crashing costs are less than indirect costs

Time-Cost Tradeoff

time

Direct cost

Indirect cost

Total project costMin total cost =

optimal project time


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Project Crashing example

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11

1212

22

88

441212

33

44 55

44

66

44

77

44

Project duration = 36


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Time Cost data

29

Activity Normal

time

Normal

cost Rs

Crash

time

Crash

cost Rs

Allowable

crash time

slope

1

2

3

4

5

6

7

12

8

4

12

4

4

4

3000

2000

4000

50000

500

500

1500

7

5

3

9

1

1

3

5000

3500

7000

71000

1100

1100

22000

5

3

1

3

3

3

1

400

500

3000

7000

200

200

7000

75000 110700


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30

1

12

2

8

3

4 5

4

6

4

7

4

R400

R500

R3000

R7000

R200

R200

R70012

4

Project duration = 36

From..

To..

1

7

2

8

3

4 5

4

6

4

7

4

R400

R500

R3000

R7000

R200

R200

R70012

4

Project

duration = 31

Additional cost =

R2000


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Benefits of CPM/PERT

31

Useful at many stages of project management

Mathematically simple

Give critical path and slack time

Provide project documentation

Useful in monitoring costs


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Limitations to CPM/PERT

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Clearly defined, independent and stable activities

Specified precedence relationships

Over emphasis on critical paths

Deterministic CPM model

Activity time estimates are subjective and depend on judgment

PERT assumes a beta distribution for these time estimates, but

the actual distribution may be different

PERT consistently underestimates the expected project

completion time due to alternate paths becoming critical

To overcome the limitation, Monte Carlo simulations can be performed on the network

to eliminate the optimistic bias


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Computer Software

for Project Management

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` Microsoft Project (Microsoft Corp.)

` MacProject (Claris Corp.)

` PowerProject (ASTA Development Inc.)

` Primavera Project Planner (Primavera)

` Project Scheduler (Scitor Corp.)

` Project Workbench (ABT Corp.)


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Practice Example

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A social project manager is faced with a project with the following activities:

Activity Description Duration

Social work team to live in village 5w

Social research team to do survey 12w

Analyse results of survey 5w

Establish mother & child health program 14w

Establish rural credit programme 15w

Carry out immunization of under fives 4w

Draw network diagram and show the critical path. Calculate project duration.


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Practice problem

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Activity Description Duration

1-2 Social work team to live in village 5w

1-3 Social research team to do survey 12w

3-4 Analyse results of survey 5w

2-4 Establish mother & child health program 14w

3-5 Establish rural credit programme 15w4-5 Carry out immunization of under fives 4w

3

1

2

4

5


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Documents

Pert/CPM Analysis