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Critical Path Method (CPM)

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Network Diagram / Arrow Diagram / Node diagram

1

2

3

4

5

6

7

8

Source /

Start

Sink /

End

Nodes

3A

3G

7B

5C

9D

6E

7F 3

I

2H

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Activity

Smallest subdivision of the work is called a job or activity

1 2Tail Event /

Starting Event

Head Event /

End Event

Fix up the chief guest (A)

Activity Activity Label

5 Days

Duration

Event Label

Hunt for chief guest begins Hunt for chief guest ends

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Tips for drawing a network diagram

Correct ways to represent an activity:

1

2

2

2

1

1

A

A

A

5

5

5

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Tips for drawing a network diagram . . . contd

Incorrect ways to represent an activity:

A

521

1) Gaps not allowed

A

5

2) Labeling of events

2A

5

3) Should have a definite start

1

4) Should have a definite end

? ?

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Tips for drawing a network diagram . . . contd

Incorrect ways to represent an activity:

A

511

5) Equal event labels not allowed

21

6) Extra activity not allowed

A

5

12

7) Tail event label smaller than

head event label

A

5

81

8) Arrow is in centre of line

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Tips for drawing a network diagram . . . contd

A, B, & C start together (parallel events)

1

2

3

4

3A

7B

5C

1

1

1

2

3

4

3A

7B

5C

Correct Method Incorrect Method

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Tips for drawing a network diagram . . . contd

Series events:

1 2 37A

6B

B starts after A

1

2

3

3A

5B

4

8C

3D

52

E

A & B start together

C start after A

D start after B

E start after C & D

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Problem - 1

Succeeding activityP Q R S T U V

Preceding activity

- P P Q R S,T UDraw Network Diagram

P

Q

R

S

T

U V765

4

3

21

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Problem - 2

ActivityA B C D E F G H I

Preceding activity

- A A B B C E D,F G,HDraw Network Diagram

A

B

C

E

D

F

G

H I 876

5

4

3

21

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Problem - 3

1 2 1 3 2 4 3 4 3 5 4 5 5 - 6Activity

Draw Network Diagram and identify different paths

65

4

2

3

1

1 3 5 6

1 2 4 5 6

1 3 4 5 - 6

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Problem 4 (Practice)

Activity A B C D E F G H I J K

Draw Network Diagram and identify different paths

4

3

2

1

5

96

7

8K

J

A

H

G

F

E

D

C

B

A

1-2-5-8-9 1-3-6-8-9

1-3-7-9 1-4-7-9

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Problem 5

a) A,C & D can start immediately b) E > B,C c) F,G > D

d) H,I > E,F e) J > I,G f) K > H g) B > A

1-2-3-5-7-8 1-2-3-5-6-

81-3-5-7-8 1-3-5-6-8

1-4-5-7-8 1-4-5-6-8

1-4-6-8

2

1

K

J

I

G

H

F

E

D

C

BA

8

7

6

5

4

3

Draw Network Diagram and identify different paths

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Problem 6 (Practice)

a) A & B are start jobs b) A controls C, D & E c) B controls F & K

d) G depends on C e) H depends on E f) F control I

g) D controls J h) G, H, I , J & K are last activities

Draw Network Diagram and identify different paths

1-2-3-8 1-2-4-8

1-2-5-8 1-6-7-8

1-6-8

5

4

3

2

1

I

H

J

G

F

E

D

C

B

A8

76

K

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Dummy Activity

A & B start together. C starts after A & B. Here two activities start together and alsoend together.

1 2B

A

Incorrect way

3C

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Dummy Activity

A & B start together. C starts after A & B. Here two activities start together and

also end together. In this case insert a new activity called DUMMY activity. This

activity is inserted just for representation purpose with duration mentioned as = 0

1

2

3

3A

5B

42

C

1

3

2

3A

5B

42

C

00

D0 D0

Correct ways

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Problem - 7

ActivityA B C D E F G

- A B B C C,D E,FPreceding activityDraw Network Diagram and identify different

paths

A B

D

CE

D0

F

G6

5

4

3217

1 2 3 - 4 6 7 1 2 3 5 6 - 7

1 2 3 4 5 6 - 7

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Problem 8 (Practice)

Activity A B C D E F G H

Preceding activity - - A A B,C B,C D,E,F F

H

5

643

2

1

G

F

E

D

C

B

A

D0

1-2-5-6 1-2-3-5-6

1-2-3-4-6 1-2-3-4-5-6

1-3-5-6 1-3-4-6

1-3-4-5-6

Draw Network Diagram and identify different

paths

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Critical Path

Critical Path is the path having longest duration

All the activities covered in critical path are called critical

activities

The duration to complete the critical path is called Project

Duration

Any delay in critical path will cause delay in the entire

project

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Problem - 9

Activity 1-2 1-3 1-4 2-3 2-6 3-5 3-6 4-5 5-6 5-7 6-7Duration

7

6

4

3

2

1

5

7

68

3

12

6

8

40

8

6

1-2-6-7 = 8 + 8 + 8 = 24

1-2-3-6-7 = 8 + 6 + 4 + 8 = 26

1-2-3-5-7 = 8 + 6 + 6 + 6 = 26

1-2-3-5-6-7 = 8 + 6 + 6 + 0 + 8 = 28

1-3-6-7 = 7 + 4 + 8 = 19

1-3-5-7 = 7 + 6 + 6 = 19

1-3-5-6-7 = 7 + 6 + 0 + 8 = 21

1-4-5-7 = 3 + 12 + 6 = 21

1-4-5-6-7 = 3 + 12 + 0 + 8 = 23

Draw Network Diagram, find Critical

path & Project Duration

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Problem 10 (Practice)

Activity A B C D E F G H J K L M N O

Preceding

Duration

Draw Network Diagram, find Critical path & Project Duration

5

4

3

2

1

O

N

M

L

K

J

H

G

F

E

D

C

B

A

1

1 2

3

3

45

1211

10

9

8

7

6

5

4

3

2

1

0

D0

66 D1

0

1-2-4-6-10-11-12 = 1+5+4+4+5+6 = 25

1-2-4-6-7-10-11-12 = 1+5+4+0+3+5+6 = 24

1-2-4-7-10-11-12 = 1+5+2+3+5+6 = 22

1-3-5-8-11-12 = 3+3+1+1+6 = 14

1-3-5-8-9-11-12 = 3+3+1+0+2+6 = 15

1-3-5-9-11-12 = 3+3+6+2+6 = 20