Operations and Supply Chain Management The Core

PROJECTS chapter 5 143
CPM Network for Computer Design Project
exhibit 5.7
21
28
28
36
0 21
A(21)
0 21
21
21
21
C(7)
F(8)
28
28
26
26
28
28
B(5) D(2) E(5)
26
26 28
31
36
33
36
36
36
G(2)
38
38
Slack Calculations and Critical Path Determinations
Activity LS–ES Slack On Critical Path
A
B
C
D
E
F
G
0–0
21–21
21–21
26–26
31–28
28–28
36–36
0
0
0
0
3
0
0
of completing the project by particular times can be estimated. (Note that the probability
calculations are a distinguishing feature of the classic PERT approach.)
Example 5.3: Three Time Estimates
We use the same information as in Example 5.2, with the exception that activities have three time
estimates.
SOLUTION
1. Identify each activity to be done in the project.
2. Determine the sequence of activities and construct a network reflecting the precedence
relationships.
3. The three estimates for an activity time are:
a = Optimistic time: the minimum reasonable period of time in which the activity can be
completed. (There is only a small probability, typically assumed to be 1 percent, that the
activity can be completed in less time.)
m = Most likely time: the best guess of the time required. Since m would be the time thought
most likely to appear, it is also the mode of the beta distribution discussed in step 4.
b = Pessimistic time: the maximum reasonable period of time the activity would take to be
completed. (There is only a small probability, typically assumed to be 1 percent, that it
would take longer.)
Typically, this information is gathered from those people who are to perform the activity.
4. Calculate the expected time (ET) for each activity. The formula for this calculation is
ET = ________ a + 4m + b
​ ​ [5.1]
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