The document discusses the Program Evaluation and Review Technique (PERT) which is a management tool used to define and integrate project events. PERT uses optimistic, pessimistic, and most likely time estimates to calculate the expected time for tasks. It is event-oriented and models the logical order and dependencies of activities. Variance and standard deviation are also calculated to measure uncertainty. An example project is provided showing how to determine activity times, critical paths, and the probability of meeting a deadline.

1. ENGINEERING MANAGEMENT
MS-322
Lec # 10
Program Evaluation & Review Technique
(PERT)

2. Introduction
A management tool for defining and integrating events; a process which must be
accomplished in time to assure completing project objectives on schedule.
Initially PERT was developed to manage the Polaris missile project. It Helps to
forecast the project completion date or one may use this technique to calculate the
expected time or to handle uncertain activity times for a task.
PERT is a technique that uses Optimistic time (O), Pessimistic time (P) and
Most likely/ Realistic Time (R) estimates to calculate the Expected Time (ET)
or a particular task.
The Optimistic time (to) reflects the maximum possible periods of time for an
activity to be completed OR it is a duration of the activity when everything goes
well. It is assumed that such performance can be improved only in about 1% of
the cases. While the Pessimistic time (tp) is the longest duration expected under
the assumption that every thing goes wrong. There is only 1 % chance that the
activity will extend beyond this value.

3. Introduction
The Realistic time (R) OR the Most likely time (tm) reflects the Project
manager’s Best Guess of the amount of time required for a task completion.
It is a normal time for the activity which would occur most often if the activity
was to be repeated several times under the same conditions.
The result of analysis are expressed in terms of events. PERT is hence said to be
Event oriented.

4. PERT Network
 Events must take place in a logical order.
 Activities represent the time and the work it takes to get from one event to
another.
 No event can be considered reached until all activities leading to the event are
completed.
 No activity may be begun until the event preceding it has been reached.

5. Compute Expected Completion Time (ET)/ Mean Completion Time
The expected Completion time should be closer to the realistic time (r), it is
typically weighed Four times more than the Optimistic time (o) and the
Pessimistic time (p). Once these values are added together , it must be divided by
6 to determine the Expected Time for a task.
ET = O + 4r + p
6

6. Compute Expected Completion Time (ET)/ Mean Completion Time
The above equation is a weighted average where the Most Likely/ Realistic Time
estimate is weighted 4 times more heavily than the optimistic and pessimistic
estimations.
Example:
A project manager estimate that the most likely time to complete a project is 12
days, where as the optimistic duration is 10 days, and pessimistic duration is 17
days.
ET = O + 4r + p
6
ET = 10 + 4(12) + 17
6
= 12.5 days

7. Variance (σ ) and Standard Deviation
Variance
In order to measure the degree of uncertainty, need to calculate the variance. The
variance is a descriptive measure of the uncertainty associated with an activity
time distribution.
It is also known as the Estimation of the Probability of Completion Dates.
i.e. a large variance indicates great uncertainty, a small variance indicates a more
accurate estimate. The symbol used to denote variance is σ (sigma) and its value
is compiled as….

8. Variance (σ ) and Standard Deviation
Standard Deviation
The standard deviation is the square root of the variance given as….
Where N is the quantity of the numbers
μ is the mean
xi is the individual numbers
Steps to calculate the variance
1. First find the mean of given numbers
2. For each number subtract the mean and square the result
3. Go for the average of those squared differences
4. Finally go for SD

9. Variance (σ ) and Standard Deviation
Example: 1
There is a group of flowers having specific numbers like
9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
Find the standard deviation…
Sol:
Step 1: Find the mean.
(9+2+5+4+12+7+8+11+9+3+7+4+12+5+4+10+9+6+9+4) 140
20 20
Step 2: Subtract the mean from each number and square the results
(9 - 7)2 = (2)2 = 4
(2 - 7)2 = (-5)2 = 25 and so on
Step 3: now go for average/ mean of those squared difference values
(4+25+4+9+25+0+1+16+4+16+0+9+25+4+9+9+4+1+4+9) = 178
= = 7

10. Variance (σ ) and Standard Deviation
Example: 1 Cont…
Now 178 x 1/N or 1/20 = 8.9 Hence the variance has obtained
Step 4: Now go for standard deviation, just take the square root of obtained value
σ = √(8.9) = 2.983

11. Variance (σ ) and Standard Deviation
Example: 2 In below fig. just consider the height of pets in mm
as 600mm, 470mm, 170mm, 430mm and 300mm
Now find out the Mean, the Variance, and the Standard Deviation.

12. Variance (σ ) and Standard Deviation
Example: 2 as the mean (average) height is 394 mm as shown in below fig.
Now calculate the each pets difference from the mean
It is obtained as 206, 76, -224, 36 and -94

13. Variance (σ ) and Standard Deviation
Example: 2
Now for variance take each difference, square it, and then average the result
Now the SD is computed as
Hence the variance has obtained

14. Variance (σ ) and Standard Deviation
Example: 2
It shows which heights are within one Standard Deviation (147mm) of the Mean
Here the Standard Deviation shows having a "standard" way of knowing what is
normal, and what is extra large or extra small.

15. Working project example
Activity predecessor Optimistic Most Likely Pessimistic
A -- 4 6 8
B -- 1 4.5 5
C A 3 3 3
D A 4 5 6
E A 0.5 1 1.5
F B, C 3 4 5
G B, C 1 1.5 5
H E, F 5 6 7
I E, F 2 5 8
J D, H 2.5 2.75 4.5
K G, I 3 5 7

16. Working project example Cont…
• What is the expected time to complete the project..?
• Compute the variance.
• Go for ES, EF and LS, LF time for each activity.
• Determine the critical path and project completion time..?
• If the management has set a completion deadline for 24 days, what is the
probability that they will meet this deadline…?

17. Working project example Cont…
Sol: 1. The expected time
2. The variance
ET = O + 4r + p
6
Activity ET Variance (σ2)
A 6 4/9
B 4 4/9
C 3 0
D 5 1/9
E 1 1/36
F 4 1/9
G 2 4/9
H 6 1/9
I 5 1
J 3 1/9
K 5 4/9
3. The ES, EF and LS, LF with slack
Activity ES EF LS LF Slack
A 0 6 0 6 0
B 0 4 5 9 5
C 6 9 6 9 0
D 6 11 15 20 9
E 6 7 12 13 6
F 9 13 9 13 0
G 9 11 16 18 7
H 13 19 14 20 1
I 13 18 13 18 0
J 19 22 20 23 1
K 18 23 18 23 0

18. Working project example Cont…
4. The Critical path and project completion time
5. As the given deadline is 24 days so the variance or the mean completion
time is
2 = 2
A + 2
C + 2
F + 2
I + 2
K
= 4/9 + 0 + 1/9 + 1 + 4/9
= 2
 = 1.414
Hence A – C – F – I – K is a critical path and the project completion
Time will be 6+3+4+5+5 = 23 Days

19. Working project example Cont…
5. According to the central limit theorem, which indicates that the sum of
independent random variables can be approximately represented by a nor-
mal distribution as the number of random variables becomes larger, the
project completion is approximated by a normal distribution. So it is given
as
Now from Standard Normal Distribution table it is given as
= 0.76115
Thus there is a 76.12% chance that the project will meet its deadline
z
T E T
=

=

=
( )
.
.

24 23
1414
071

20. The End