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CONSIDERING TIME–COST TRADE-OFFS 389

Table 9.7 Activity List for the Two-Machine Maintenance Project
Activity Description Immediate Predecessor Expected Time (days)
A Overhaul machine I — 7
B Calibrate machine I A 3
C Overhaul machine II — 6
D Calibrate machine II C 3
E Test system B, D 2

experience with similar projects, the times for maintenance activities are considered
to be known; hence, a single time estimate is given for each activity. The project
network is shown in Figure 9.15.
The procedure for making critical path calculations for the maintenance project
network is the same one used to find the critical path in the networks for both
the Souk al Bustan Shopping Centre expansion project and the Porta-Vac project.
Making the forward pass and backward pass calculations for the network in
Figure 9.15, we obtained the activity schedule shown in Table 9.8. The zero slack
times, and also the critical path, are associated with activities A–B–E. The length
of the critical path, and thus the total time required to complete the project, is
12 days.

Crashing Activity Times
Suppose now the hospital manager insists that the maintenance must be completed
within ten days, given the effect on patient treatment. By looking at the length of the
critical path of the network (12 days), we realize that meeting the desired project
completion time is impossible unless we can shorten some activity times. This
shortening of activity times, which usually can be achieved by adding resources, is
referred to as crashing. However, the added resources associated with crashing
activity times usually result in added project costs, so we will want to identify the
activities that cost the least to crash and then crash those activities only the amount
necessary to meet the desired project completion time.
For example, we know that Activity A, on the critical path, is expected to take
seven days. However, suppose that by paying the staff involved a bonus of E300 we
could reduce this to four days. Given that Activity A is critical we know that a
reduction in activity time, other things being equal, will lead to a reduction in overall

Figure 9.15 Two-Machine Maintenance Project Network

A 0 7 B 7 10
7 0 7 3 7 10

E 10 12
Start Finish
2 10 12
C 0 6 D 6 9
6 0 7 3 7 10

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