Problem 

Table shows the activities of a project and their optimistic, pessimistic and most likely times. Develop a network diagram for the project activities. Calculate the probability of finishing the project in 30 days.

Table: Activities and their Optimistic,
Pessimistic and Most Likely Times

Solution

Figure 20.5 shows the network of a project for which the optimistic, pessimistic and expected times of activities are given in Table 20.3.

Now using the optimistic, pessimistic and most likely times given in Table 20.3, we calculate the expected time (t_e) shown in Table 20.4. It is given by the equation

and activity variance is given by the equation

Once, the expected time is computed for each activity, we can find the critical path and the duration of the project. The earliest and the latest times are calculated as described in previous example on CPM. From Figure 20.5, we can see that the critical path includes the activity 1-3-5-6 and the total duration of the project with the expected activity time is equal to 33 days.

Next, we will determine the probability of completing the project within the desired completion period. This step makes use of the following formula:                          

Z = (Desired project period - Expected project period) / (Standard deviation of the critical path activities)

or,

Where,

D     = desired project completion date = 30

E      = earliest expected project completion time = 33

s²_cp = Sum of variance of critical path activities = 12

The probability of completing the project in 30 days is

So the probability of completing the project in 30 days is 0.86.               

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