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PROJECT SCHEDULING WITH UNCERTAIN ACTIVITY TIMES 383
Figure 9.9 Porta-Vac Cordless Vacuum Cleaner Project Network
F
C Cost
Routing
Estimates
A J
Prepare D G Final Finish
Design Prototype Testing Report
E H I
Start Marketing Market Pricing and
Brochure Survey Forecast
B
Plan Market
Research
Figure 9.10 Porta-Vac Project Network with Activity Times
C 5 8 F 8 10
3 8.5 11.5 2 11.5 13.5
A 0 5 D 5 9 G 9 12 J 13.5 15.5
Finish
5 0 5 4 5.5 9.5 3 9.5 13.5 2 13.5 15.5
E 5 8 H 8 11.5 I 11.5 13.5
Start
3 5 8 3.5 8 11.5 2 11.5 13.5
B 0 1.5
1.5 0 8
values rather than by one specific time estimate. In these instances, the uncertain
activity times are treated as random variables with associated probability distribu-
tions. As a result, probability statements will be provided about the ability to meet a
specific project completion date.
To incorporate uncertain activity times into the analysis, we need to obtain three
time estimates for each activity:
Optimistic time a ¼ the minimum activity time if everything progresses ideally
Most probable time m ¼ the most probable activity time under normal conditions
Pessimistic time b ¼ the maximum activity time if significant delays are encountered
To illustrate the PERT/CPM procedure with uncertain activity times, let us con-
sider the optimistic, most probable and pessimistic time estimates for the Porta-Vac
activities as presented in Table 9.4. Using activity A as an example, we see that the
most probable time is five weeks with a range from four weeks (optimistic) to 12
weeks (pessimistic). If the activity could be repeated a large number of times, what is
the average time for the activity? This average or expected time (t)isas follows:
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