# PROJECT EVALUATION REVIEW TECHNIQUE, PERT - Quantitative Techniques for management

## Project Review Techniques

The project review techniques are

In the critical path method, the time estimates are assumed to be known with certainty. In certain projects like research and development, new product introductions, it is difficult to estimate the time of various activities. Hence PERT is used in such projects with a probabilistic method using three time estimates for an activity, rather than a single estimate, as shown in Figure.

PERT Using Probabilistic Method with 3 Time Estimates

Optimistic time tO:

It is the shortest time taken to complete the activity. It means that if everything goes well then there is more chance of completing the activity within this time.

Most likely time tm:

It is the normal time taken to complete an activity, if the activity were frequently repeated under the same conditions.

Pessimistic time tp:

It is the longest time that an activity would take to complete. It is the worst time estimate that an activity would take if unexpected problems are faced.

Taking all these time estimates into consideration, the expected time of an activity is arrived at.

The average or mean (ta) value of the activity duration is given by,

Ta= t0+4tm+tp/6 .....................(5)

The variance of the activity time is calculated using the formula,

Ta= t0+4tm+tp/6 ...................(6)

Probability for Project Duration

The probability of completing the project within the scheduled time (Ts) or contracted time may be obtained by using the standard normal deviate where Te is the expected
time of project completion.

...............(7)

Probability of completing the project within the scheduled time is,
P (T≤ Ts) = P ( Z≤ Z0 ) (from normal tables) .................(8)

Example : An R & D project has a list of tasks to be performed whose time estimates
are given in the table, as follows.

Time expected for each activity is calculated using the formula (5):

Ta= t0+4tm+tp/6

= 4+4(6)+8/6 = 36/6 = 6 days for activity A

Similarly, the expected time is calculated for all the activities. The variance of activity time is calculated using the formula (6).

Similarly, variances of all the activities are calculated. Construct a network diagram and calculate the time earliest, TE and time Latest TL for all the activities.

Network Diagram

Time Estimates for R & D Project

1. Draw the project network.
2. Find the critical path.
3. Find the probability that the project is completed in 19 days. If the probability is less that 20%, find the probability of completing it in 24 days.

Solution:

Calculate the time average ta and variances of each activity as shown in the following table.

Te & s2 Calculated

From the network diagram Figure, the critical path is identified as 1-4, 4-6, 6-7, with project duration of 22 days. The probability of completing the project within 19 days is given by,

Thus, the probability of completing the R & D project in 19 days is 9.01%. Since the probability of completing the project in 19 days is less than 20%, we find the probability of completing it in 24 days.

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