4/11/2013

© Copyright 2013 Anupam Kumar 1

Critical Path Methods

Presented by:

Anupam Kumar

Reader

SMS Varanasi

Critical Path Method (CPM)

• Critical Path Method was developed by Du Pont

• In Critical Path Method (CPM) the emphasis is on the

trade-off between

– the cost of the project and

– its overall completion time

• e.g.

– For certain activities it may be possible to decrease their

completion times by spending more money

– How does this affect the overall completion time of the

project?

Critical Path Method

• In Critical Path Method (CPM) activities are shown as

– a network of precedence relationships using

– activity-on-node network construction.

• CPM is used in Production management

– for the jobs of repetitive in nature where the activity time

estimates can be predicted with considerable certainty due

to the existence of past experience.

• CPM has

– Single estimate of activity time

– Deterministic activity times

Illustration 1

• A leading company has decided to bring about certain changes in its

product design for which the time estimates are as follows.

• Estimate the time it would take to get the new design implemented.

• The activity precedence detail is: Activity number

must finish before

Activity number

can start

1 3

2 4

3 5

4 6

5,6 7

7 8

8 9

8 10

9,10 11

Illustration 1 (Contd.)Activity

No.

Activity Time

(in Weeks)

1 Redesign Product 6

2 Redesign Packaging 2

3 Order & receive component for redesigned product 3

4 Order & receive component for redesigned packaging 2

5 Assemble Product 4

6 Make up packaging 1

7 Package redesign product 1

8 Test Market redesigned product 6

9 Revise redesigned product 3

10 Revise redesigned packaging 1

11 Present result to Board 1

Illustration 2

• The time estimates for completing the plant

construction project is as shown.

– Determine the critical path.

– How much slack time is available in the non critical path?

1 2 4

3

6

5

7 812 4 6

4/11/2013

© Copyright 2013 Anupam Kumar 2

Crashing CPM Networks

• Project Timelines are crashed for due to

urgent or contingent conditions.

• Crashing of CPM Networks is

– The process to reduce the normal project duration

– to the desired shorter duration

– activities on the critical path are crashed

– by the use of additional resources / expenses.

Time-cost ratio = Increase in cost / Decrease in time

= (crash cost – normal cost) / (normal time – crash time)

Illustration 3

Activity Time in Weeks Cost (Rs.)

Normal Crash Normal Crash

1-2 6 4 10,000 14,000

1-3 4 3 5,000 8,000

2-4 3 2 4,000 5,000

3-5 8 6 9,000 12,000

4-5 7 4 7,000 8,000

Total Cost: 35,000 47,000

• The network details for

a small project is as

given.

– Draw a network diagram

with the normal times.

– What would be the cost

of the project if the non-

critical path is to be

converted to the critical

path through project

time crashing?

Illustration 4

• A company received an order from a reputed

customer.

– As per the contract, from the day 15th the company will

have to pay a penalty of Rs. 10 per day until job is

completed.

– Indirect project costs per day is Rs. 200.

– The data on direct cost and activities are as follows.

• Draw project network diagram.

• What completion date would you recommend?

• Compute project cost after crashing.

Illustration 4 (Contd.)

Activity Normal Time Normal Cost Crash time Crash cost Immediate

Predecessor

A 4 1000 3 1300 None

B 7 1400 4 2000 None

C 5 2000 4 2700 None

D 6 1200 5 1400 A

E 3 900 2 1100 B

F 11 2500 6 4000 C

G 4 800 3 1500 D, E

H 3 300 1 500 F, G