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

Activity Immediate Predecessor Time (wks)

A – 6

B A 3

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