Page 238 - DMGT521_PROJECT_MANAGEMENT

Unit 13: PERT, CPM and Time Estimation

In Activity 1-3, the time estimates are 3,12 and 21. Using our PERT formula, we get: Notes



3 (4 12) 21 72
t    12
e
6 6
(21 3) 18

s    3
1
6 6
The Standard Deviation (s.d.) for this activity is also calculated using the PERT formula.
We calculate the PERT event times and other details as below for each activity:

Event to tm tp te ES EF LS LF TF s.d. Var.
1-3 3 12 21 12 0 12 0 12 0 3 9
3-5 6 15 30 16 12 28 12 28 0 4 16
1-2 2 5 14 6 0 6 5 11 5 2 4
2-4 5 14 17 13 6 19 11 24 5 2 4
3-4 2 5 8 5 12 17 19 24 7 1 1
4-5 1 4 7 4 19 23 24 28 5 1 1

Estimating Risk

Having calculated the S.D. and the Variance, we are ready to do some risk analysis. Before that
we should be aware of two of the most important assumptions made by PERT.
1. The Beta distribution is appropriate for calculation of activity durations.
2. Activities are independent, and the time required to complete one activity has no bearing
on the completion times of its successor activities in the network. The validity of this
assumption is questionable when we consider that in practice, many activities have
dependencies.

!
Caution PERT assumes that the expected length of a project (or a sequence of independent
activities) is simply the sum of their separate expected lengths.
Expected Length of a Project

PERT assumes that the expected length of a project (or a sequence of independent activities) is
simply the sum of their separate expected lengths.
Thus the summation of all the t ’s along the critical path gives us the length of the project.
e
Similarly the variance of a sum of independent activity times is equal to the sum of their
individual variances.
In our example, the sum of the variance of the activity times along the critical path, VT is found
to be equal to (9+16) = 25.
The square root VT gives us the standard deviation of the project length. Thus, ST=Ö 25=5. The
higher the standard deviation, the greater the uncertainty that the project will be completed on
the due date.

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