PERT Problem

Analyze the same problem with probabilistic activity times given.

Activity	Immediate Predecessors	Most Optimistic Time	Most Likely Time	Most Pessimistic Time	Expected Time (ET)	Variance
A	--	2	3	6
B	A	3	4	5
C	B	1	2	4
D	B	3	5	6
E	C	3	4	5
F	D	3	3	4
G	E,F	1	2	3

Step 1. Calculate the expected time for each activity.

Step 2. Identify the different paths in the network and total activity time on path.

(Use the expected times of each activity for this calculation).

Step 3. Identify the critical path(s) on the network. The critical path is the one having the longest total activity times AND also has no slack.

Estimating the Probability of a Completion Date

Step 1. Calculate the variance of completion times from the most optimistic and most pessimistic completion times and insert in table.

Step 2. Find the total variance for path in the network. The total variance along the path is simply the sum of the individual variances of activities on the path.

Path 1: Total Variance:

Path 2: Total Variance:

Step 3. Find the probability of a scheduled completion date of less than 17 days.

1. Sketch out the project mean and project standard deviation assuming a normal distribution with mean and standard deviation found above. Remember the standard deviation is the square root of the variance!

2. Now, find the z value for a scheduled completion date of day 17 on the critical path using the formula:

z = DT-ETpp2 = ______________ = _______________

Using the z value, a probability value can be found. ______________