Program Evaluation and Review Technique (PERT)

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The network method discussed so far may be termed as deterministic, since estimated activity times are assumed to be known with certainty. However, in research project or design of gear box or a new machine, various activities are based on judgment. It is difficult to obtain a reliable time estimate due to the changing technology. Time values are subject to change variations. For such cases where the activities are non-deterministic in nature, PERT was developed. Hence, PERT is probabilistic method where the activity time is represented by a probability distribution. This probability distribution of activity times is based upon three different time estimates made for each activity. These are follows.

(i) Optimistic time estimate

(ii) Most likely time estimate

(iii) Pessimistic time estimate

Optimistic time estimate: it is the smallest time taken to complete the activity if everything goes on well. There is very little chance that activity can be done in time less than the optimistic time. It is denoted by or (a).

Most likely time estimate: It refers to the estimate of the normal time the activity would take. This assumes normal delays. It is denoted by or m

Pessimistic time estimate: it is the longest time that an activity would take if everything goes wrong. It is denoted by or b. these three time values are shown in the following figure.

From these time estimates, we have to calculate the expected time of an activity. It is given by the weighted average of the three time estimates

image

The expected length (duration), denoted by to of the entire project is the length of the critical path.

The main objective in the analysis through PERT is to find the completion for a particular event within specified date, given by P (Z ) where

image

Also calculate the expected variance of each activity.

Step 3: Compute the earliest start, earliest finish, latest start, latest finish and total float of each activity.

Step 4: Find the critical path and identify the critical activities.

Step 5: Compute the project length variance which is the sum of the variance of all the critical activities and hence find the standard deviation of the project length .

Step 6: Calculate the standard normal variable Z = / Where is the scheduled time to complete the project.

= normal expected project length duration.

= expected standard deviation of the project length.

Using the normal curve, we can estimate the probability of completing the project within a specified time.

Problems:

1. The following table shows the jobs of a network along with their time estimates.

image

You are required to:

a) Draw the project network.

b) Find the expected duration and variance of each activity.

c) Calculate the early and late occurrence for each event and the expected project length.

d) Calculate the variance and standard deviations of project length.

e) What is the probability that the project will be completed-

(i) 4 weeks earlier than expected.

(ii) Not more than 4 weeks later than expected.

(iii) If the project due date is 19 weeks, what is the probability of meeting the due date.

3. The following table shows the jobs of a network along with their time estimates. The time estimates are in days:

image

(i) Draw the project network.

(ii) Find the critical path.

(iii) Find the probability that the project is completed in 31 days.

4. Assuming that the expected times are normally distributed, find the probability of meeting schedule that as given for the network.

image

Scheduled project completion date is 30 days. Also find the date on which the project manager can complete the project with a probability of 0.90.

Cost consideration in PERT/CPM

Project cost: in order to include the cost aspects in project scheduling we must first define the cost duration relationships for various activities in the project. The total cost of any project comprises direct and indirect costs.

Direct cost: this cost is directly depends upon the amount of resources in the execution of individual activities manpower loading materials consumed etc. the direct cost increase if the activity duration is to be reduced.

Indirect cost: This cost is associated with overhead expenses such as managerial services, indirect supplies, general administration etc. the indirect cost is computed on a paper day, per week, or per month basis. The indirect cost decreases if the activity duration is to be reduces.

The network diagram can be used to identify the activities whose duration should be shortened so that the completion time of the project can be shortened in the most economic manner. The process of reducing the activity duration by putting on extra effort is called crashing the activity. The crash time represents the minimum activity duration time that is possible and any attempts to further crash would only rise the activity cost without reducing the time. The activity cost corresponding to the crash time is called cost  which is the minimum direct cost required to achieve the crash performance time.

The normal cost is equal to the absolute minimum of the direct cost required to perform an activity. The corresponding time duration taken by an activity is known as the normal time .

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