The document discusses the Critical Path Method (CPM) for project scheduling. It was developed by Du Pont to aid in trade-offs between project costs and completion time. CPM uses activity-on-node network diagrams to show precedence relationships between tasks. The document provides examples and illustrations of how to determine the critical path of a project and how crashing the schedule by reducing task durations can impact overall project time and costs.

1. 4/11/2013
Critical Path Method (CPM)
• Critical Path Method was developed by Du Pont
• In Critical Path Method (CPM) the emphasis is on the
Critical Path Methods trade-off between
– the cost of the project and
– its overall completion time
Presented by: • e.g.
Anupam Kumar – For certain activities it may be possible to decrease their
completion times by spending more money
Reader
– How does this affect the overall completion time of the
SMS Varanasi project?
Critical Path Method Illustration 1
• In Critical Path Method (CPM) activities are shown as • A leading company has decided to bring about certain changes in its
product design for which the time estimates are as follows.
– a network of precedence relationships using • Estimate the time it would take to get the new design implemented.
– activity-on-node network construction. • The activity precedence detail is: Activity number Activity number
• CPM is used in Production management must finish before can start
1 3
– for the jobs of repetitive in nature where the activity time
2 4
estimates can be predicted with considerable certainty due
3 5
to the existence of past experience.
4 6
• CPM has 5,6 7
– Single estimate of activity time 7 8
– Deterministic activity times 8 9
8 10
9,10 11
Illustration 1 (Contd.) Illustration 2
Activity Activity Time
No. (in Weeks)
• The time estimates for completing the plant
1 Redesign Product 6
2 Redesign Packaging 2
construction project is as shown.
3 Order & receive component for redesigned product 3 – Determine the critical path.
4 Order & receive component for redesigned packaging 2 – How much slack time is available in the non critical path?
5 Assemble Product 4
6 Make up packaging 1
7 Package redesign product 1 3
8 Test Market redesigned product 6
5
9 Revise redesigned product 3
10 Revise redesigned packaging 1 12 4 6
1 2 4 7 8
11 Present result to Board 1
6
© Copyright 2013 Anupam Kumar 1

2. 4/11/2013
Crashing CPM Networks Illustration 3
Activity Time in Weeks Cost (Rs.)
• Project Timelines are crashed for due to • The network details for
Normal Crash Normal Crash
urgent or contingent conditions. a small project is as
1-2 6 4 10,000 14,000
given.
• Crashing of CPM Networks is 1-3 4 3 5,000 8,000
– Draw a network diagram
2-4 3 2 4,000 5,000
– The process to reduce the normal project duration 3-5 8 6 9,000 12,000 with the normal times.
– to the desired shorter duration 4-5 7 4 7,000 8,000 – What would be the cost
Total Cost: 35,000 47,000 of the project if the non-
– activities on the critical path are crashed critical path is to be
– by the use of additional resources / expenses. converted to the critical
Time-cost ratio = Increase in cost / Decrease in time path through project
= (crash cost – normal cost) / (normal time – crash time) time crashing?
Illustration 4 Illustration 4 (Contd.)
Activity Normal Time Normal Cost Crash time Crash cost Immediate
• A company received an order from a reputed Predecessor
customer. A 4 1000 3 1300 None
– As per the contract, from the day 15th the company will B 7 1400 4 2000 None
have to pay a penalty of Rs. 10 per day until job is C 5 2000 4 2700 None
completed. D 6 1200 5 1400 A
– Indirect project costs per day is Rs. 200. E 3 900 2 1100 B
F 11 2500 6 4000 C
– The data on direct cost and activities are as follows.
G 4 800 3 1500 D, E
• Draw project network diagram. H 3 300 1 500 F, G
• What completion date would you recommend?
• Compute project cost after crashing.
© Copyright 2013 Anupam Kumar 2