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398 CHAPTER 9 PROJECT SCHEDULING: PERT/CPM

13 The Daugherty Porta-Vac project discussed in Section 9.2 has an expected project
completion time of 17 weeks. The probability that the project could be completed in
20 weeks or less is 0.9656. The noncritical paths in the Porta-Vac project network are:
A D G J
A C F J
B H I J
a. Use the information in Table 9.5 to compute the expected time and variance for each
path shown.
b. Calculate the probability that each path will be completed in the desired 20-week
period.
c. Why is the calculation of the probability of completing a project on time based on the
analysis of the critical path? In what case, if any, would making the probability
computation for a noncritical path be desirable?
14 The manager of the Oak Hills Swimming Club is planning the club’s swimming
team programme. The first team practice is scheduled for May 1. The activities,
their immediate predecessors, and the activity time estimates (in weeks) are as follows.

Immediate Time (weeks)
Activity Description Predecessor Optimistic Most Probable Pessimistic
A Meet with board — 1 1 2
B Hire coaches A 4 6 8
C Reserve pool A 2 4 6
D Announce programme B, C 1 2 3
E Meet with coaches B 2 3 4
F Order team suits A 1 2 3
G Register swimmers D 1 2 3
H Collect fees G 1 2 3
I Plan first practice E, H, F 1 1 1

a. Draw a project network.
b. Develop an activity schedule.
c. What are the critical activities, and what is the expected project completion time?
d. If the club manager plans to start the project on February 1, what is the probability the
swimming programme will be ready by the scheduled May 1 date (13 weeks)? Should
the manager begin planning the swimming programme before February 1?

15 The product development group at Landon Corporation has been working on a new
computer software product that has the potential to capture a large market share.
Through outside sources, Landon’s management learned that a competitor is working
to introduce a similar product. As a result, Landon’s top management increased its
pressure on the product development group. The group’s leader turned to PERT/CPM
as an aid to scheduling the activities remaining before the new product can be brought
to the market. The project network is as follows.

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