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388 CHAPTER 9 PROJECT SCHEDULING: PERT/CPM

Figure 9.14 Probability the Porta-Vac Project Will Meet the 20-Week Deadline

at T = 20
= 1.65 weeks z = 20 – 17 = 1.82
1.65

P(T 20)

T
17 20
Time (weeks)

Using z ¼ 1.82 and the table for the normal distribution (see Appendix A), we find
that the probability of the project meeting the 20-week deadline is
0.4656 + 0.5000 ¼ 0.9656. Thus, even though activity time variability may cause
the completion time to exceed 17 weeks, calculations indicate a high probability
that the project will be completed before the 20-week deadline. Similar probability
calculations can be made for other project deadline alternatives.

NOTES AND COMMENTS

or projects involving uncertain activity times, the critical activities may cause an original noncritical
F probability that the project can be completed activity to become critical and hence increase the time
within a specified amount of time is helpful manage- required to complete the project. By frequently mon-
rial information. However, remember that this pro- itoring the progress of the project to make sure all
bability estimate is based only on the critical activities are on schedule, the project manager will be
activities. When uncertain activity times exist, longer- better prepared to take corrective action if a noncritical
than-expected completion times for one or more non- activity begins to lengthen the duration of the project.

9.3 Considering Time–Cost Trade-Offs

The original developers of CPM provided the project manager with the option of
adding resources to selected activities to reduce project completion time. Added
resources (such as more workers, overtime and so on) generally increase project
costs, so the decision to reduce activity times must take into consideration the
additional cost involved. In effect, the project manager must make a decision that
Using more resources to involves trading reduced activity time for additional project cost.
reduce activity times was Consider a scenario in a hospital. In one of the surgical clinics, two specialist
proposed by the machines periodically have to undergo routine maintenance. While this is being
developers of CPM. The
shortening of activity done, medical operations are halted and clearly the hospital manager is keen for the
times is referred to as time needed for maintenance to be as short as possible. Table 9.7 summarizes the
crashing. key activities involved in this project. Because management has had substantial

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