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PROJECT SCHEDULING WITH UNCERTAIN ACTIVITY TIMES 387

Table 9.6 Activity Schedule for the Porta-Vac Project
Earliest Latest Earliest Latest
Start Start Finish Finish Slack Critical
Activity (ES) (LS) (EF) (LF) (LS – ES) Path?
A 0 0 6 6 0 Yes
B 0 7 2 9 7
C 6 10 9 13 4
D 6 7 11 12 1
E 6 6 9 9 0 Yes
F 9 13 11 15 4
G 11 12 14 15 1
H 9 9 13 13 0 Yes
I 13 13 15 15 0 Yes
J 15 15 17 17 0 Yes

Assuming that the distribution of the project completion time T follows a
3
normal or bell-shaped distribution allows us to draw the distribution shown in
Figure 9.13. With this distribution, we can calculate the probability of meeting a
specified project completion date. For example, suppose that management allotted
20 weeks for the Porta-Vac project. What is the probability that we will meet the
20-week deadline? Using the normal probability distribution shown in Figure 9.14,
we are asking for the probability that T 20; this probability is shown graphically as
the shaded area in the figure. The z value for the normal probability distribution at
T ¼ 20 is:
20 17
z ¼ ¼ 1:82
1:65

Figure 9.13 Normal Distribution of the Project Completion Time for the Porta-Vac
Project

The normal distribution
tends to be a better
approximation of the
distribution of total time
for larger projects where σ = 1.65 weeks
the critical path has
many activities. Expected
completion time

T
17
Time (weeks)

3
Use of the normal distribution as an approximation is based on the central limit theorem, which indicates that
the sum of independent random variables (activity times) follows a normal distribution as the number of
random variables becomes large.

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