Homework Solutions – Chapter 3

1. The following activities are part of a project to be scheduled using CPM:

Activity Immediate Predecessor Time (wks)
A – 6

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C A 7
D C 2
E B,D 4
F D 3
G E,F 7

a. Draw the network
b. What is the critical path?
c. How many weeks will it take to complete the project?
d. How much slack does activity B have?

Solution

b. A-C-D-E-G, also shown in the network above as the bold path.
c. 26 weeks, 6+7+2+4+7.
d. 6 weeks, 15-9.

2. For the project with the following information,
a. Determine the critical path and the early completion time in weeks.
b. Reduce the project completion time by three weeks. Assume a linear cost per
week shortened, and show, step by step, how you arrived at your schedule.

Solution
a. A-B-D-G, 25 weeks, 5+10+6+4.

b. First, reduce D (lowest cost activity on the critical path) by one week. This adds an additional
critical path with activities C and E in it. Second, crash activity G by one week. Critical paths
remain the same. Third, crash activity A by one week at a cost of $3,000, which is the least
expensive.

Summary of activities crashed:
Step Activity Cost to crash Weeks reduced
1 D $1,000 1
2 G 2,000 1
3 A 3,000 1
Total cost $6,000

 

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