Cpm Pert

CPM / PERT

Introduction  Developed

in 1950s

 To

aid in the planning and scheduling of large projects

 Basic

concepts of CPM / PERT, such as activities, events and predecessors have become regular part of the language of Project Managers 2

CPM / PERT  CPM

– Critical Path Method

 PERT

– Project Evaluation and Review Techniques

3

What is a project  The

project consists of a well-defined collection of jobs, or activities, which when completed marks the end of the project  The jobs may be started or stopped independently of each other, within a given sequence  The jobs are ordered, i.e. they must be performed in technological sequence

4

Network Diagram 1

Start Node / End Node Connector indicating two nodes

Name of the activity Duration

5

Draw Network Diagram … 1 Activity

Start Node

End Node

Description

Duration (in Days)

A

1

2

Forecasting unit sales

14

B

2

4

Pricing sales

3

C

2

3

Preparing production schedule

7

D

3

4

Costing the production

4

E

4

5

Preparing the budget

10

6

14 days A

2

4 10

B 7

4d a ys D

1

3 da ys

ys da

C

3

E

da y

s

5

7

Draw Network Diagram … 2 Activity

Immediate Predecessor

Duration (in Days)

A

-

14

B

-

3

C

A

7

D

A, B

3

E

C

4

F

D, E

10

8

Dummy Activities  Every

project preferably should have one start node and one end node  We require dummy activities when a project contains groups of two or more jobs which have some, but not all, of their immediate predecessors in common  These dummy activities have duration of 0 units of time

9

Draw Network Diagram … 2 Activity Start Node End Node

Immediate Predecessor

Duration (in Days)

A

1

3

-

14

B

1

2

-

3

C

1

4

-

7

F

2

3

B

0

G

2

4

B

0

D

3

5

A, B

4

E

4

5

B, C

10

10

Critical Path … 1 Activity

Immediate Predecessor

Duration (in Days)

A

-

8

B

A

2

C

B

3

D

-

5

E

D

2

F

E

3

11

Critical Path … 1 Activity

Start Node

End Node

Immediate Predecessor

Duration (in Days)

A

1

2

-

8

B

2

3

A

2

C

3

6

B

3

D

1

4

-

5

E

4

5

D

2

F

5

6

E

3

12

How many different paths?  From

start node to end node, we can have more than one paths  Summing up durations of the activities on a particular path gives the total duration of that path, called as “Project Path”  A path is called a “Critical Path” if it is the longest project path in a project network  Activities on the critical path are called as “Critical Activities” 13

Find Critical paths Activity

Start Node

End Node

Duration (in Days)

A

1

2

2

B

1

3

4

C

2

5

3

D

3

4

2

E

3

5

5

F

3

6

5

G

4

6

2

H

4

7

3

I

5

8

4

J

6

7

6

K

7

8

1

14

Different Critical paths are …  A:

1-2-5-8 (9 Days)

 B:

1-3-5-8 (13 Days)

 C:

1-3-6-7-8 (16 Days) .. Critical Path

 D:

1-3-4-6-7-8 (15 Days)

 E:

1-3-4-7-8 (10 Days)

15

Why Critical Path?  If

we want to complete the project, even within the less duration than that of the total project duration, then we need to shorten the duration of the critical activities

 If

we shorten the duration of non-critical activities, the total project duration will not reduce, hence will not be of any use 16

What do we then?  For

complex projects, we will have to find all possible project paths

 We

use a mathematical algorithm to find out critical path

17

Multiple Critical Paths  In

case, if we have more than one critical paths, then we cannot shorten any critical activity to reduce the total project duration

 We

have to shorten those critical activities which are common to all the critical paths

18

Can Critical Path Change?  After

shortening the project duration, there may be change in critical path

 Therefore,

after every unit change of duration, we need to find out critical path again

19

Forward Pass / Backward Pass i

j

Duration

1

2

14

1

3

3

2

3

0

2

4

7

3

5

3

4

5

4

5

6

10

Ei

Ej

Li

Lj

Slack

20

Forward Pass / Backward Pass i

j

Duration

Ei

Ej

1

2

14

0

14

1

3

3

0

3

2

3

0

14

14

2

4

7

14

21

3

5

3

14

17

4

5

4

21

25

5

6

10

25

35

Li

Lj

Slack

21

Forward Pass / Backward Pass i

j

Duration

Ei

Ej

Li

Lj

1

2

14

0

14

0

14

1

3

3

0

3

19

22

2

3

0

14

14

22

22

2

4

7

14

21

14

21

3

5

3

14

17

22

25

4

5

4

21

25

21

25

5

6

10

25

35

25

35

Slack

22

Forward Pass / Backward Pass i

j

Duration

Ei

Ej

Li

Lj

Slack

1

2

14

0

14

0

14

-

1

3

3

0

3

19

22

19

2

3

0

14

14

22

22

8

2

4

7

14

21

14

21

-

3

5

3

14

17

22

25

8

4

5

4

21

25

21

25

-

5

6

10

25

35

25

35

23

Forward Pass / Backward Pass i

j

Duration

Ei

Ej

Li

Lj

Slack

1

2

14

0

14

0

14

-

1

3

3

0

3

19

22

19

2

3

0

14

14

22

22

8

2

4

7

14

21

14

21

-

3

5

3

14

17

22

25

8

4

5

4

21

25

21

25

-

5

6

10

25

35

25

35

24

Job

I

J

A B C D E F G H I J

1 2 2 3 3 4 4 5 6 7

2 3 4 5 6 6 7 8 8 8

Example … 2 Duration

2 3 5 4 1 6 2 8 7 4

Ei

Ej

Li

Lj

Slack

25

Job

I

J

A B C D E F G H I J

1 2 2 3 3 4 4 5 6 7

2 3 4 5 6 6 7 8 8 8

Example … 2 Duration

Ei

Ej

2 3 5 4 1 6 2 8 7 4

0 2 2 5 5 7 7 9 13 9

2 5 7 9 6 13 9 17 20 13

Li

Lj

Slack

26

Job

I

J

A B C D E F G H I J

1 2 2 3 3 4 4 5 6 7

2 3 4 5 6 6 7 8 8 8

Example … 2 Duration

Ei

Ej

Li

Lj

2 3 5 4 1 6 2 8 7 4

0 2 2 5 5 7 7 9 13 9

2 5 7 9 6 13 9 17 20 13

0 5 2 8 12 7 14 12 13 16

2 8 7 12 13 13 16 20 20 20

Slack

27

Job

I

J

A B C D E F G H I J

1 2 2 3 3 4 4 5 6 7

2 3 4 5 6 6 7 8 8 8

Example … 2 Duration

Ei

Ej

Li

Lj

Slack

2 3 5 4 1 6 2 8 7 4

0 2 2 5 5 7 7 9 13 9

2 5 7 9 6 13 9 17 20 13

0 5 2 8 12 7 14 12 13 16

2 8 7 12 13 13 16 20 20 20

3 3 7 7 3 7

28

Job

I

J

A B C D E F G H I J

1 2 2 3 3 4 4 5 6 7

2 3 4 5 6 6 7 8 8 8

Example … 2 Duration

Ei

Ej

Li

Lj

Slack

2 3 5 4 1 6 2 8 7 4

0 2 2 5 5 7 7 9 13 9

2 5 7 9 6 13 9 17 20 13

0 5 2 8 12 7 14 12 13 16

2 8 7 12 13 13 16 20 20 20

3 3 7 7 3 7

29

PERT  In

some cases, instead of exact time duration for each activity, 3 estimates are available as follows – to – Optimistic Time – tm – Moderate Time – tp – Pessimistic Time

30

Wt. Average, Std. Dev. & Variance  Weighted

average of these 3 time estimates is calculated as follows – te = (to + 4tm + tp) / 6

 Standard

Deviation for each activity is calculated as follows – st = (tp – to) / 6

 Variance

for each activity is calculated as

– Vt = (St)2 31

PERT Example … 1 Activity

I

J

To

Tm

Tp

A

1

2

2

5

14

B

1

3

3

12

21

C

2

4

5

14

17

D

3

4

2

5

8

E

3

5

6

15

30

f

4

5

1

4

7

Te

St

Vt

32

PERT Example … 1 Activity

I

J

To

Tm

Tp

Te

A

1

2

2

5

14

6

B

1

3

3

12

21

12

C

2

4

5

14

17

13

D

3

4

2

5

8

5

E

3

5

6

15

30

4

f

4

5

1

4

7

16

St

Vt

33

PERT Example … 1 Activity

I

J

To

Tm

Tp

Te

St

A

1

2

2

5

14

6

2

B

1

3

3

12

21

12

3

C

2

4

5

14

17

13

2

D

3

4

2

5

8

5

1

E

3

5

6

15

30

4

1

f

4

5

1

4

7

16

4

Vt

34

PERT Example … 1 Activity

I

J

To

Tm

Tp

Te

St

Vt

A

1

2

2

5

14

6

2

4

B

1

3

3

12

21

12

3

9

C

2

4

5

14

17

13

2

4

D

3

4

2

5

8

5

1

1

E

3

5

6

15

30

4

1

1

f

4

5

1

4

7

16

4

16 35

Variance and SD for the project  Variance

of the project, VT is calculated as the sum of Vt (Variance) for all the activities which are on critical path  Standard Deviation of the project, ST is calculated as square root of the VT  Standard

Normal variable, Z is calculated as

follows – Z = (D – Te) / ST 36

Finding probability of completing the project in given duration  For

the given value of D in the formula, we can find out the probability of completing the project in given duration using “Standard Normal Distribution” table

Z

= (D – Te) / ST

– Where – D is the duration in which we expect the

project to be completed 37

Finding duration of the project for the given probability  For

the given probability, p of completing the project, we can find out the duration, D as follows  P(X = p) to be found out from “Standard Normal Distribution” table  Z = (D – Te) / ST – Where – Z is the value extracted from “Standard Normal Distribution” table for the given probability 38

Questions ???

39