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Quantitative analysis:PERT and CPM.

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Problem 1 - Crashing

Development of a new deluxe version of a particular software product is being considered. The activities necessary for the completion of this are listed in the table below.

Activity Normal Time Crash Time Normal Cost Crash Cost Immediate
Predecessor
A 4 3 2000 2600 -
B 2 1 2200 2800 -
C 3 3 500 500 -
D 8 4 2300 2600 A
E 6 3 900 1200 B
F 3 2 3000 4200 C
G 4 2 1400 2000 D,E

Indirect costs = \$200/week
Penalty (one time) = \$4000 after week 12 (penalty is in effect at week 13)
Bonus (one time) = \$2500 at week 10

1) What is the expected completion time for the project (before crashing)?
2) What is the critical path?
3) What activities will you crash?
4) What is the optimal time for the project?
5) What is the total cost of the project after crashing?

Problem 2 - Crashing

Activity Pred Normal Time Normal Cost Crash Cost/wk Max Crash
A -- 4 7,000 1,000 1
B A 6 5,000 2,500 2
C B 10 13,400 3,800 1
D C 12 9,500 ------- 0
E A 23 17,700 3,600 3
F E 4 4,400 2,000 1

Indirect Costs = \$2000/wk
Penalty = \$1600/wk after week 28
Bonus = \$5000 at week 22

1) What is the expected time of completion for the project?
2) What is the critical path?
3) What is the first activity you will crash?
4) What is the second activity you will crash?
5) What is the total cost of the project after crashing?
6) What is the optimal time of completion for the project?

A different version of the software product (from last week's problems) is also being considered. The activities necessary for the completion of this are listed in the table below.

Activity Normal Time Crash Time Normal Cost Crash Cost/wk Immediate
Predecessor

A 4 3 2,000 400 -
B 5 3 2,200 300 A
C 3 3 500 ----- -
D 8 4 2,400 50 A
E 6 3 900 150 B
F 3 2 3,000 600 C
G 4 2 1,700 700 D,E

Indirect costs = \$450/week
Penalty = \$100/week after week 12 (penalty is in effect at week 13)
Bonus (one time) = \$2500 at week 8

(a) What is the expected completion time for the project?
(b) What is the critical path?
(c) What is the critical path after crashing?
(d) What is the optimal time for the project?
(e) What is the total cost of the project after crashing?

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Solution Summary

The problem set deal questions in Program evaluation and Review techniques (PERT) and Critical path Method (CPM) used for project scheduling and evaluation.

\$2.19

Quantitative Analysis: PERT/CPM Analysis

A construction project is broken down into the following 10 activities:

Activity Immediate Predecessor Time (Weeks)
1 -- 4
2 1 2
3 1 4
4 1 3
5 2, 3 5
6 3 6
7 4 2
8 5 3
9 6, 7 5
10 8, 9 7

a. Find the critical path.

b. If activities 1 and 10 can't be shortened, but activities 2 through 9 can be shortened to a minimum of one
week each at a cost \$10,000 per week, which activities would you shorten to cut the project by four weeks?

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