“Application of the Program Evaluation Review and Technique

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Table of Contents
Introduction..............................................................................................................................3
1.1 Origin of the Report.........................................................................................................3
1.2 Objective of the Report....................................................................................................4
1.3 Scope of the Report..........................................................................................................4
1.4 Limitation of the report....................................................................................................4
1.5 Sources and Methodology................................................................................................5
Chapter-2: Theoretical Background......................................................................................6
2.1 Program Evaluation and Review Technique (PERT):.....................................................6
2.2 Brief history of the PERT: ...............................................................................................6
2.3 Features of the PERT:......................................................................................................7
2.4 Advantages of the PERT:.................................................................................................8
2.5 Disadvantages of the PERT:............................................................................................9
2.6 Process of the PERT ......................................................................................................10
2.7 When to Use a PERT Chart ...........................................................................................13
2.8 Critical Path Method:.....................................................................................................13
2.9 Difference between PERT and CPM.............................................................................14
Chapter-3: Mathematical Problems and Solutions ............................................................15
Problem:1 (12.36) ................................................................................................................15
Problem: 2 (10.06) ...............................................................................................................16
Problem: 3(10.07) ................................................................................................................17
Problem: 4(10.10) ................................................................................................................19
Problem: 5(10.12) ................................................................................................................21
Chapter-4: Application of the PERT through a hypothetical Case ..................................23
1. Case Study: ......................................................................................................................23
2. Problem Solution: ............................................................................................................28
Recommendation....................................................................................................................33

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Conclusion ..............................................................................................................................33
References...............................................................................................................................34
Appendix.................................................................................................................................35
List of the Figures
Figure 1: Features of the PERT..............................................................................................7
Figure 2: Advantages of the PERT.........................................................................................8
Figure 3: Disadvantages of the PERT....................................................................................9

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Introduction
1.1 Origin of the Report
To have an overview of the Quantitative Technique in practical life we’ve a study on
“Application of the Program Evaluation Review and Technique”, a hypothetical company
in our country. Now a day’s education is not just limited to books and classrooms. In today’s
world, education is the tool to understand the real world and apply knowledge for the
betterment of the society as well as business. From education the theoretical knowledge is
obtained from courses of study, which is only the half way of the subject matter. Practical
knowledge has no alternative. The perfect coordination between theory and practice is of
paramount importance in the context of the modern business world in order to resolve the
dichotomy between these two areas. Therefore, for the B.B.A. program we are assigned to
prepare a report on “Application of the Program Evaluation Review and Technique”
Quantitative Technique (F-409) course by our honorable course teacher Shabnaz Amin
Auditi.
.

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1.2 Objective of the Report
Our objectives are…
 To increase our experience in data collection & analysis.
 To know about real application of the Program Evaluation Review and Technique.
 To have practical knowledge of Quantitative Techniques.
 To know the implications of Quantitative Techniques.
 To have better analytical abilities regarding Quantitative Techniques in real world.
1.3 Scope of the Report
While completing the report we’ve had a lot of scopes of gathering knowledge of real
business world and the wide horizon of business, although the report is only concerned
about the hypothetical Company. We have collected their information from the internet and
text books. We got almost all the information we needed because the website is very much
updated and resourceful. We are really grateful to our course teachers for assigning us such
an interesting and knowledgeable topic.
1.4 Limitation of the report
While preparing this report, we have faced some problems. The main problem was to co-
ordination all the group members. Moreover, during data collection we faced several
problems.
 Due to limited access of the data, this study may not be perfect to the scent percent.
 Lack of enough experience in analyzing of data.
Due to inadequate information, in-depth analysis could not be done in the report

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1.5 Sources and Methodology
The methodology of this report is collective. And the report was prepared through a lengthy
process.
The process of preparing the report is given bellow:
1. At first we held a discussion about the process we should follow to prepare the report.
2. Then we have divided the tasks among our group members.
3. At the first section of our report we have presented some theoretical background of PERT
and also present some PERT exercise problems and solutions.
4. Then we developed a hypothetical case using PERT approach and took idea from
regarding theoretical information from our recommended course curriculum conducted by
our course Teacher.
5. We learned how to write and evaluate a formal report from our “Business English
& Communication” course.
6. We checked formatting of the report and checked for mistakes for several times and at last,
we succeeded to prepare the report.

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Chapter-2: Theoretical Background
2.1 Program Evaluation and Review Technique (PERT):
PERT (Program evaluation and Review Technique) is a project scheduling network technique
typically employed in research and development project in which a probabilistic time estimate
is made for each job or activity. This is actually a project management tool used to schedule,
organize, and coordinate tasks within a project. It is basically a method to analyze the tasks
involved in completing a given project, especially the time needed to complete each task, and
to identify the minimum time needed to complete the total project.
2.2 Brief history of the PERT:
CPM/PERT or Network Analysis as the technique is sometimes called, developed along two
parallel streams, one industrial and the other military. CPM was the discovery of M.R.Walker
of E.I.Du Pont de Nemours & Co. and J.E.Kelly of Remington Rand, circa 1957. The
computation was designed for the UNIVAC-I computer. The first test was made in 1958, when
CPM was applied to the construction of a new chemical plant. In March 1959, the method was
applied to a maintenance shut-down at the Du Pont works in Louisville, Kentucky.
Unproductive time was reduced from 125 to 93 hours. PERT was devised in 1958 for the
POLARIS missile program by the Program Evaluation Branch of the Special Projects office of
the U.S.Navy, helped by the Lockheed Missile Systems division and the Consultant firm of
Booz-Allen & Hamilton. The calculations were so arranged so that they could be carried out
on the IBM Naval Ordinance Research Computer (NORC) at Dahlgren, Virginia.

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2.3 Features of the PERT:
Some features of the PERT are mentioned below:
Figure 1: Features of the PERT
It is evaluated from planning aspect
It is a probabilistic approach
There are three different time dimensions:
-Most optimistic time (a)
-Most pessimistic time (b)
-Most likely time (m)
Where te= (a+4m+b)/6
It’s a model under uncertainty

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2.4 Advantages of the PERT:
Figure 2: Advantages of the PERT
1. The PERT Formula Can Give the Estimated Completion Date: By using the PERT Formula
combined with bottom-up estimating in project management, a savvy project manager can then
determine the estimated completion date for a project. The way this date is calculated is by
adding up the cumulative task durations that have been estimated utilizing the PERT Formula
or other estimation methods.
2. The Project Manager Can Determine Flexibility: Items with a large range between the
optimistic estimate and the pessimistic estimate for completion are flexible. Because of this, if
a project manager needs to crash the project schedule or fast track the project schedule, the
PERT formula can help them determine which action items contain this flexibility. In this case,
the PERT Formula has a distinct advantage for project managers.
3. The PERT Formula Helps the Project Manager Schedule Tasks: By estimating the time it
will take to complete tasks using the PERT Formula and the Standard Deviation formula,
project managers can schedule start and finish times for tasks in a more accurate manner. This
is a great benefit, especially in complex projects where start and finish dates might not be clear.
Using the task estimation method, the project manager would schedule all tasks due to their
Provide estimated completion date
Manager Can Determine Flexibility
Proper Use of
Resources
Efficient Monitoring
and Control
Helps the Project
Manager Schedule
Tasks
Tools for Decision
Making

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estimated completion time, and then use the start time of the first scheduled task and the end
time of the final scheduled task as the start and finish dates of the project.
4. Proper Use of Resources: PERT allows management to use resources more wisely
and resources can be transferred to troubled areas from other activities
5. Efficient Monitoring and Control: Identification of critical activities enables the use of an
efficient monitoring system.
6. Tools for Decision Making: PERT allows management to check the effectiveness
and efficiency of alternative ways of executing projects by examining possible trade-offs
between time and cost.
2.5 Disadvantages of the PERT:
There have some disadvantages of the PERT. These disadvantages are presented below:
Figure 3: Disadvantages of the PERT
Activity times in PERT may not follow Beta PD in reality
Overemphasis on
Critical path
Activity time
estimates are
subjective
Cost of crashing an
activity may not be
linear

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2.6 Process of the PERT
There are two rules:
 Tasks (activities) are represented as arrows
 Milestone dates are nodes
PERT charts are also called activity-on-arrow diagrams (project manager’s slang). If drawings
need two weeks to complete before a report gets submitted, you would write:
If you have multiple simultaneous activities, for example an environmental permit application
while the drawings are being completed, you would write them side by side, joining back up
to the common milestone date (node). The longer pathway is easily visible.
That’s not too difficult is it? At any given time you can see whether a milestone date (node) is
complete and what type of timelines you are looking at relative to the final (project complete)
milestone.
Interpretation
What can you do with a PERT chart?
 Using the forward pass method, you can determine the earliest possible dates for each
milestone. To use the forward pass method, you start by writing a 0 (as in, “day 0”) on
the first node (in our example, node 1). Then proceed from left to right through each
path, adding up the duration of each activity and writing the milestone dates on each
node. Milestones can have multiple dates at this point, if they are part of multiple

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paths. Once you get to the right side, you go back through the chart and choose only
the highest date for each milestone (node) and discard the others. These is the earliest
possible dates for the milestones. Also, the overall project completion date is the
highest date on the last milestone.
 Using the backward pass method, you can determine the latest possible date for each
milestone. Just like the forward pass, but opposite, you start on the right, using the
highest date on the last milestone (the completion date). Proceed through each possible
path and write each date on the nodes by subtracting the activity durations. Then choose
only the lowest date for each milestone and discard the rest. These are the latest
possible dates of the milestones.
 For each milestone, you can subtract the earliest possible date from the latest possible
date to get the float. This is the amount of play that each activity has before it affects
the critical path.
The following table illustrates the results from the above example:
Milestone Earliest Latest Float
1 0 0 0 (critical path)
3 7 11 4
4 3 4 1
5 5 6 1
You can also generate the table in terms of activities rather than nodes.
 The Earliest Start (ES) date is the earliest possible date that the task can start given all
of tasks before it. It is the same as the earliest milestone date for the milestone
immediately to the left of the task (i.e. from the forward pass, the highest number on
the node immediately to the left).
 The Latest Finish (LF) date is the latest possible date that the task must be complete
without affecting the overall completion date. It is the same as the latest milestone date
for the node immediately to the right of the task (i.e. from the backward pass, the lowest
number on the node immediately to the right).

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 The Latest Start (LS) and Earliest Finish (EF) dates are calculated from the other two
by the somewhat obvious addition or subtraction of the task duration.
 LS = LF – Duration
 EF = ES + Duration
Activity Duration Earliest Start
(from forward
pass)
Latest Start
(LF –
Duration)
Earliest
Finish
(ES +
Duration)
Latest Finish
(from backward
pass)
1-2 2 days 0 0 2 2
1-4 3 days 0 1 3 4
2-3 5 days 2 6 7 11
2-6 6 days 2 2 8 8
4-6 3 days 3 5 6 8
4-5 2 days 3 4 5 6
5-6 2 days 5 6 7 8
6-7 4 days 8 8 12 12
5-7 3 days 5 9 8 12
3-8 3 days 7 11 10 14
7-8 2 days 12 12 14 14
I prefer using milestones instead of activities to generate the table, because it’s a bit more
intuitive and the calculations can be remembered easier.
Critical Path: Clearly, there is one path that results in the overall project completion date, and
all the others have some float. This is called the critical path, and a good project manager will
not only know what it is, but keep a good eye on those tasks throughout the project. It sounds
obvious, I know, but you’d be surprised how many project managers for million dollar projects
just “fly by the seat of their pants.”
Float: If a task is not on the critical path, it has float and can be sacrificed for resource
allocation, budget, or other purposes. The amount of float is very simple:
 Float = Latest Start – Earliest Start
 F = LS – ES
When Float = 0, the activity is on the critical path.

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2.7 When to Use a PERT Chart
PERT charts serve multiple purposes for the project manager.
At the beginning of the project they are a good tool for calculation of the project duration and
for knowing what the important tasks are. You probably already do this. When something
comes up, you think about the tasks involved, which order they go in, and which ones you need
to do on time to ensure the overall completion date (critical path). The PERT chart is
effectively nothing more than the hard copy of your thought process.
During the project, PERT charts are a good tool for calculation of the critical path and float,
especially when the project changes, but they are not the best at showing you what your project
team needs to be working on right now. Thus, I find they are more of a project control
technique, answering questions such as:
 Is your project deadline in jeopardy?
 Do you need to allocate more resources to a certain task?
Have you every drawn a PERT chart? Tell us how you did it and how it impacted the project?
2.8 Critical Path Method:
The critical path method, or CPM, was developed by DuPont, to analyse the process of shutting
down plants for maintenance, then restarting them at the end of the maintenance cycle. The
process involved in this was so complicated, that the critical path method had to be developed
to identify and prioritise the vital activities. Similar to a Gantt chart, the CPM provides a
graphical representation of the project, and the times expected to complete each activity.
However, the CPM does not fix the start and end times of each activity; rather it is used to
determine the activities which fall on the critical path. The critical path is the path where all
activities directly follow each other, and hence there is no idle time. As such, the length of the
critical path determines the total time taken for the project.
The main difference between CPM and the Gantt chart is that CPM displays the activities as
single nodes, with the dependencies as lines connecting the nodes. As such, the CPM shows
all the paths and dependencies which will be followed throughout the project. This allows
project managers to determine which paths will have some idle time, and which will be critical
to the final project completion time, thus enabling project managers to prioritise resources to
the critical path.

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2.9 Difference between PERT and CPM
Though PERT and CPM are used for project management, there are differences between CPM
and PERT. The relative table for PERT vs CPM is shown below:
CPM PERT
CPM uses activity oriented network. PERT uses event oriented Network.
Durations of activity may be estimated with
a fair degree of accuracy.
Estimate of time for activities are not so
accurate and definite.
It is used extensively in construction
projects.
It is used mostly in research and development
projects, particularly projects of non-
repetitive nature.
Deterministic concept is used. Probabilistic model concept is used.
CPM can control both time and cost when
planning.
PERT is basically a tool for planning.
In CPM, cost optimization is given prime
importance. The time for the completion of
the project depends upon cost optimization.
The cost is not directly proportioned to time.
Thus, cost is the controlling factor.
In PERT, it is assumed that cost varies
directly with time. Attention is therefore
given to minimize the time so that minimum
cost results. Thus in PERT, time is the
controlling factor.

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Chapter-3: Mathematical Problems and Solutions
Problem:1 (12.36)
A) Construct a PERT Network.

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B) Compute the probability that the project will be completed within 32 weeks
Standard deviation of critical path (A-C-F-H-J-L)
= √(
1.5
6
)
2
+ (
4
6
)
2
+ (
4
6
)
2
+ (
2
6
)
2
+ (
3
6
)
2
+ (
4
6
)
2
=1.33
Z value =
32−27.25
1.33
=2.07
The corresponding Z value of 2.07 is 98.08%.
Decision: The probability that the project will be completed within 32 weeks is 98.08%
Problem: 2 (10.06)
As a project manager you are faced with the activity network and estimated activity times
shown in the following figure. For each activity determine,
1. Earliest starting time
2. Earliest finish time
3. Latest start time
4. Latest finish time
5. Slack
In addition identify the critical path.

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Solution: 2
Activity ES LS EF LF
Slack =(LS-
ES)or(LF-
EF)
A 0 0 3 3 0
B 3 4 5 6 1
C 3 5 6 8 2
D 3 3 7 7 0
E 7 7 8 8 0
F 7 8 9 10 1
G 5 6 7 8 1
H 5 8 10 13 3
I 8 8 13 13 0
J 9 10 12 13 1
k 13 13 16 16 0
L 9 14 11 16 5
M 16 16 20 20 0
Critical Path: A-D-E-I-K-M
Problem: 3(10.07)
Based on our evaluation, however the immediate predecessors of each activity are as follows:

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Activity
Immediate
Predecessor
Activity
Immediate
Predecessor
A - H E
B - I G
C A J E
D B K H
E B L F
F C M L, I, K, J
G D
1. Draw the revised activity network.
2. Compute the earliest start and finish times for the revised network based on the
assumption that each activity takes 1 hour longer than its alphabetic predecessor (i.e.
A= 1 hour, B= 2 hour, etc.). Find the slack of each activity. Identify the critical path.
How much less time does the production run take under this revised activity network
than it did with the original network?
Solution 3:

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Activity ES LS EF LF
Slack =(LS-
ES)or(LF-EF)
A 0 0 1 1 0
B 0 0 1 1 0
C 1 1 3 3 0
D 1 1 3 3 0
E 1 1 3 3 0
F 3 3 6 6 0
G 3 3 6 6 0
H 3 3 6 6 0
I 6 6 10 10 0
J 3 7 6 10 4
k 6 6 10 10 0
L 6 6 10 10 0
M 10 10 15 15 0
Critical Path: A-C-F-L-M or B-D-G-I-M or B-E-H-K-M
Problem: 4(10.10)
Compute the expected activity time and the standard deviation for each activity based on the
activity network shown below and the associated activity times given below, Compute the
expected value and SD for each activity time. Find the earliest start times, earliest finish times,
latest start times, latest finish times and slack for each activity. Specify the critical path.
Activity a m b
A 1 2 3
B 1 3 5
C 2 3 10
D 2 5 8
E 1 2 3
F 1 1 1
G 1 1 1
H 1 3 5
I 2 4 6
J 1 5 9

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Solution 4:
Activity Optimistic(a)
Most
probable(m) Pessimistic(b)
Expected Value
=(a+4m+b)/6
Standard
Deviation
=(b-a)/6
A 1 2 3 2 0.33
B 1 3 5 3 0.67
C 2 3 10 4 1.33
D 2 5 8 5 1.00
E 1 2 3 2 0.33
F 1 1 1 1 0.00
G 1 1 1 1 0.00
H 1 3 5 3 0.67
I 2 4 6 4 0.67
J 1 5 9 5 1.33
Activity ES LS EF LF Slack =(LS-ES)or(LF-EF)
A 0 0 2 2 0
B 2 6 5 9 4
C 2 2 6 6 0
D 5 9 10 14 4
E 10 14 12 16 4
F 6 6 7 7 0
G 6 6 7 7 0
H 7 8 10 11 1
I 7 7 11 11 0
J 11 11 16 16 0

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Critical Path: AC-F-I-J or A-C-G-I-J
Problem: 5(10.12)
As a project manager, you are faced with the activity network of figures given below and the
associated estimates of optimistic, most probable and pessimistic activity times are shown
below.
a) Compute the expected activity time and standard deviation for each activity time assuming
a uni-model beta probability distribution for each activity time. Identify the critical path and
expected time for the completion of the project.
b) Under the usual assumptions find the probability that the activities on the critical path will
be completed within 27 weeks.
C) How many weeks should be allowed to give a 90% probability of completing the critical
path on time?
Solution 5:
A.
Activ
ity
Optimist
ic(a)
Most
probable(m
)
Pessimist
ic(b)
Expected
Value=(a+4m+b)/6
Standard
Deviation:(b-a)/6
A 1 3 5 3 0.67
B 1 3 5 3 0.67
C 4 5 6 5 0.33
D 1 4 7 4 1.00
E 7 8 9 8 0.33
F 4 6 8 6 0.67
G 4 5 6 5 0.33
H 7 9 11 9 0.67
I 1 3 5 3 0.67

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Critical Path: A-E-F-G-I
Variance of the project length= (.67) ^2+ (.33) ^2+ (.67) ^2+ (.33) ^2+ (.67) ^2
=1.56
Standard Deviation of the project length= (1.56) ^.5 = 1.25
b) Z= (T-exp)/ Standard Deviation = (27-25)/1.25=1.6
Which means that there is 91% chance to be completed within 27 weeks?
c) We know that when probability is 90% the value of Z is 1.28
Then, Z= (T-exp)/Standard Deviation
By putting the value in the above equation we get T=26.6 weeks
Which indicates that 26.6 weeks should be allowed to give a 90% probability of completing
the critical path on time?

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Chapter-4: Application of the PERT through a
hypothetical Case
U-KAPS: The Ultimate Hoody Builder
1. Case Study:
U-KAPS is one of the leading suppliers of various qualities of to the Different faculties of
University of Dhaka. Receiving large orders seems to be a smaller challenge in comparison to
the challenge of delivering on time. The small sector players of this business in University of
Dhaka usually face this problem and are levied with heavy fine owing to not able to meet the
promised delivery time while receiving orders. This paper is an attempt to provide the solution
of this problem to these small sector players by implying Critical Path Method in the planning
department of Hoody manufacturing. In later stages the same method may also be applied in
various departments like manufacturing and sampling of the hoody making company to cater
the problem of on time delivery. The Critical Path on the network is identified and is monitored
continuously to observe any shift in the critical path. Thus solution to the problem lies in:
Identifying the critical path, monitoring the critical path, Resource levelling using crashing.
Planning in Hoody production and supply using PERT Technique:
Problem Formulation:
To make, solve and monitor a PERT network for a project of making 15000 Hoody for
University of Dhaka is given in specification sheet. The critical path during the project based
on the stipulated time is to be calculated and all the activities lying on the path are to be closely
monitored so as to avoid delay in the completion of the project. The consignment should reach
the buyer within 120 days of the receipt of the order. The order has been booked on 01/08/17
and should reach the buyer by 30/11/17.

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Planning manager has spoken with various departments and obtained optimistic (to), most
likely (tl) and pessimistic (tp) time element for every activity involved in this process.
Activit
y
Immediate
Predecesso
r
to
(days
)
tm
(days)
tp
(days)
t=(to+4tm+tp)/6
(days)
A 8 10 18 11
B A 5 7 9 7
C B 14 18 22 18
D B 2 3 4 3
E C 7 9 11 9
F D 7 9 11 9
G E 7 9 11 9
H E 4 6 8 6
I E 4 5 6 5
J I 12 15 18 15
K F,G 2 3 4 3
L K,H 8 10 12 10
M J,L 20 28 36 28
N J,L 8 10 18 11
O N 6 8 10 8
P M,O 15 19 23 19
Q P 16 20 36 22

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The details of every event and activity involved are as follows:
Events Activity
i. Order Received 01/08/17 A. Confirmation sample
making
ii. Confirmation sample sent B. Confirmation sample
approval
iii. Confirmation sample
approved
C. Gather tools and notions
iv. Gathered tools and notions D. Select pattern and fabric
v. Selected pattern and fabric E. cut pattern pieces
vi. cut pattern pieces F. Prepare and sew the pockets
vii. Prepare and sew the
pockets
G. Sew the shoulder seams
viii. Sewed the shoulder
seams
H. Sew the sleeves

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ix. Sewed the sleeves I. Sew the side seams
x Sewed the side seams J. Sew and attach the cuffs
xi. Sewed and attach the cuffs K. Attach the hem band
xii. Attached the hem band L. Attach the front bands
xiii. Attached the front bands M. Add the zipper

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xiv. Added the zipper N. Sew the hood & hood
bands
xv. Sew the hood & hood
bands
O. Insert the cording
xvi. Insert the cording P. Lasting and packaging
xvii. Lasting and packaging
done
Q. Material shipping
xviii. Material received by the
buyer

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2. Problem Solution:
First of all, we are calculating the expected time through the following formula
Expected time, 𝑡={𝑎+4𝑚+𝑏}/6
Activity Optimistic (a)
Most Likely
(m)
Pessimistic
(b)
Expected Time
(Te) SD
A 8 10 18 11 1.666667
B 5 7 9 7 0.666667
C 14 18 22 18 1.333333
D 2 3 4 3 0.333333
E 7 9 11 9 0.666667
F 7 9 11 9 0.666667
G 7 9 11 9 0.666667
H 4 6 8 6 0.666667
I 4 5 6 5 0.333333
J 12 15 18 15 1
K 2 3 4 3 0.333333
L 8 10 12 10 0.666667
M 20 28 36 28 2.666667
N 8 10 18 11 1.666667
O 6 8 10 8 0.666667
P 15 19 23 19 1.333333
Q 16 20 36 22 3.333333
Total 145 189 257 193
Step 1: PERT network is made based on the precedence rule

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Calculating the forward pass:

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Calculating the backward pass:
Calculating the difference between forward and backward pass. The Longest Critical path with the activities
having minimum difference is calculated.
Here the critical path is determined based on the slack=0 in the period of making the hoody.
This critical path will make the delivery within 140 days period.
Critical Path: A-B-C-E-G-K-L-M-P-Q

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Probability of the completion of the project in 140 days:
In this case study, we have found that there is 78.17% chance that U-KAPS will be able to
complete the project.
Probability that the project will be completed in 140 days
Standard Deviation of Critical Path 5.142416
Z Value 0.777844468
From z value table we get the value of 0.78167
**There is 78.167% chance that the project will be completed in 140 days
Probability of the completion of the project in 140 days:
By using the Z value calculation, we can say that there is 12.17% to complete the project.
Probability that the project will be completed in 130 days
Standard Deviation of Critical Path 5.142416
Z Value -1.166766702
From z value table we get the value of 0.12165
**There is 12.165% chance that the project will be completed in 130 days
Slack time: the slack time is calculated based on the Earliest start (ES) date and Latest
Finish (LF) date.
The Earliest Start (ES) date is the earliest possible date that the task can start given all of tasks
before it. It is the same as the earliest milestone date for the milestone immediately to the left
of the task (i.e. from the forward pass, the highest number on the node immediately to the left).
The Latest Finish (LF) date is the latest possible date that the task must be complete without
affecting the overall completion date. It is the same as the latest milestone date for the node
immediately to the right of the task (i.e. from the backward pass, the lowest number on the
node immediately to the right).
The Latest Start (LS) and Earliest Finish (EF) dates are calculated from the other two by the
somewhat obvious addition or subtraction of the task duration.
 LS = LF – Duration
 EF = ES + Duration

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Activity
Earliest
Start
Time
(ES)
Latest
Start Time
(LS)
Earliest
Finish Time
(LF)
Latest
Finish
Time
(LF)
Slack (LS-
ES)
Slack (LF-
EF)
Activity
on Critical
Path
A 0 0 11 11 0 0 YES
B 11 11 18 18 0 0 YES
C 18 18 36 36 0 0 YES
D 18 42 21 45 24 24
E 36 36 45 45 0 0 YES
F 21 45 30 54 24 24
G 45 45 54 54 0 0 YES
H 45 51 51 57 6 6
I 45 47 50 52 2 2
J 50 52 55 67 2 12
K 54 54 57 57 0 0 YES
L 57 57 67 67 0 0 YES
M 67 67 95 95 0 0 YES
N 67 76 78 87 9 9
O 78 87 86 95 9 9
P 95 95 114 114 0 0 YES
Q 114 114 136 136 0 0 YES
Here the critical path is drawn based on the slack variable where the slack is zero, the critical
path is gone away.
Critical Path: A-B-C-E-G-K-L-M-P-Q
In this case study, U-KAPS will be able to make supply all the hoody within the deadline if
they follow the critical path which is developed by using the Performance Evaluation and
Review Technique (PERT).

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Recommendation
From the detailed analysis we recommend U-KAPS to use the PERT technique to schedule its
projects as in case of the recent order for U-KAPS it has been able to deliver it within the 120
days requirement.
Conclusion
PERT helps a manager to schedule time and tasks and make the optimum use of resources to
get optimum results. It helps answering question like the projects finish time, start and finish
time of individual activities of a project and the critical path.
We have prepared Theoretical background and discussion of PERT, exercise problems and
solutions from books prescribed in the course outline and from the materials provided in the
class.
We have also developed a hypothetical case study to give a favor of real life problem solving
scenario to our learnings in the course.
U-KAPS the hoody manufacturer is able to meet the deadline of 120 days and identify the
critical path and estimated slack times and probability of completion of the project in time.

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References
Aczel, A. (2012). Complete Business Statistics. Tata McGraw-Hill.
Bhadur, R. (2008). Production and operation management. Jaipur, India: Book Enclave.
Constable, C. (1976). Operation Management. USA: John Wiley Sons.
David M. Levine. (2017). Business Statistics. Pearson India.
Kazmier, L. (2009). Schaum's Outline of Business Statistics (4th Edition). Ney York, USA:
McGraw-Hill Professional Publishing.

“Application of the Program Evaluation Review and Technique

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