MEHRAN UNIVERSITY OF ENGINEERING & TECHNOLOGY
JAMSHORO
PERT
ENGR. ANEES AHMED VIGHIO
Lecturer,
Department of Civil Engineering
MUET, Jamshoro
PERT
• PERT stands for Program Evaluation and Review Technique.
• PERT can be used to determine the earliest/latest start and finish times
for each activity, the entire project completion time and the
slack(FLOAT) time for each activity.
• PERT and CPM are similar in their basic approach, they do differ in the
way activity times are estimated.
PERT
 PERT is an extension of CPM.
 In reality, activities are usually subjected to uncertainty which
determine the actual durations of the activities.
 It incorporates variabilities in activity duration into project network
analysis.
 The potential uncertainties in activity are accounted for by using
three time estimates for each activity
PERT
• For each PERT activity three times (optimistic, pessimistic and most
likely times) are combined to determine the expected activity completion
time and its variance. Thus, PERT is a probabilistic technique: it allows
us to find the probability of the entire project being completed by any
given date.
• CPM, on the other hand, is called a deterministic approach. It uses two
time estimate, the normal time and the crash time, for each activity
Program Evaluation & Review Technique
a) Optimistic Time
b) Most Likely Time
c) Pessimistic Time
PROJECT EVALUATION REVIEW TECHNIQUE, (PERT)
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.
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,
The variance of the activity time
is calculated using the formula,
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.
Probability of completing the project
within the scheduled time is,
Example
A R & D project has a list of tasks to be performed whose time estimates are given in
the Table 8.11, as follows.
Example
A R & D project has a list of tasks to be performed whose time estimates are
given in the Table 8.11, as follows.
a.Draw the project network.
b.Find the critical path.
c.Find the probability that the project is completed in 19 days.
Time expected for each activity is calculated using the
formula (5): 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.
Solution:
• Expected time of completion of the Project = 24 Days
• Critical Path: B-E-G-J
• Zo(19 Days)= -2.466  Probability= 0.69%
Example no 2 Draw Arrow Network and perform the PERT calculations
for the following schedule of the Project. Also determine the probability
of completion of the project in 37,50 and 57 Days.
Activity
IPA
Optimistic
Pessimistic
5
Most
Likely
6
A
-
B
A
4
5
18
C
A
4
15
20
D
B
3
4
5
E
B, C
5
16
21
F
B, C
10
14
18
G
D,E,F
11
15
19
7
Solution
Activity
IPA
Optimistic
Most Likely
Pessimistic
Expected
Time
Standard
Deviation
Variance
A
-
5
6
7
6
0.33
0.1089
B
A
4
5
18
7
2.33
5.428
C
A
4
15
20
14
2.67
7.1289
D
B
3
4
5
4
0.33
0.1089
E
B, C
5
16
21
15
2.67
7.1289
F
C
10
14
18
14
1.33
1.7689
G
D,E,F
11
15
19
15
1.33
1.7689
Solution:
• Expected Project time = 50 Days
• Critical Activities= A-C-E-G
• Non-Critical Activities= B-D-F
• Z0(37)=-3.23  0.062 %
• Z0(20)=0  50 %
• Zo(57)=1.742= 95.9%
Example no 3 Draw Arrow Network and perform the PERT
calculations for the following schedule of the Project.
Determine probability at 50 days
Activity
IPA
Optimistic
Most Likely
Pessimistic
A
-
1
2
3
B
A
3
6
15
C
A
4
10
16
D
A
2
4
6
E
B
4
7
10
F
B,C
3
5
7
G
C,D
1
3
11
H
E,F
4
5
18
I
G,H
1
2
9
Assignment Problems
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