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PERT & CPM Application On A Project
Technical Report · April 2021
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PERT & CPM Application
On
TSC Expansion Project
1
PERT & CPM Application
On
TSC Expansion Project
Prepared for
Shabnaz Amin Auditi
Associate Professor
Department of Finance
Faculty of Business Studies
University of Dhaka.
Prepared by
Group: 5
Section: B
Batch: 23rd
Department of Finance
A combined effort by:
Serial No.
Name
ID No.
1.
2.
Zain Uz Zaman
Shadman Shahriar Sakib
23-015
23-070
3.
4.
5.
Partha Pratim Roy
Ananna Barua
Md. Saiful Islam
23-140
23-152
23-180
Remarks
Date of Submission: 17th April, 2021
2
Letter of Transmittal
17th April, 2021
Shabnaz Amin Auditi
Associate Professor
Department of Finance
Faculty of Business Studies
University of Dhaka.
Subject: Submission of a report on “PERT and CPM Application on TSC Expansion Project.”
Dear Madam,
With great pleasure we submit the report on “PERT and CPM Application on TSC Expansion
Project”. In this report our main purpose is to relate the topics of various analysis of various project
management issues with the real project data and plan. We have put our best effort to make this
report a success.
However, we hope that this report could have been a better one. And this has been obviously a
great source of learning for us to conduct similar research studies in future.
We would like to express our sincere appreciation and gratitude to you for your help in the
preparation of this report.
Sincerely yours,
Ananna Barua
Roll: 23-152
On behalf of group no: 05
Department of Finance
Faculty of Business Studies
University of Dhaka.
3
Table of Contents
Executive summary......................................................................................................................... 5
Introduction ..................................................................................................................................... 6
Part A: Theoretical Background ..................................................................................................... 7
Part B: The Case Analysis ............................................................................................................ 12
Case: Project: TSC Extension Building .................................................................................... 12
Solution ..................................................................................................................................... 13
Conclusion .................................................................................................................................... 20
4
Executive summary
A PERT chart helps a project manager analyze a project's tasks and estimate the amount of time
required to complete each task in the project. Using this information, the project manager can
estimate the minimum amount of time required to complete the entire project. This information
also helps the manager develop a project budget and determine the resources needed to accomplish
the project. PERT planning usually involves some sequential steps. On the other hand, CPM works
with controlling the completion cost with the reduction of the completion time. This method is
used with the action taken in critical path and activities.
In this case, we tried to incorporate the project of the plan of establishing a new building in the
TSC area of University of Dhaka. For this, we segmented our whole analysis into PERT and CPM
techniques.
Firstly, in PERT, we brought about almost sixteen related activities to complete the whole project.
And then with the activities, we got the network diagram. Then, we estimated three time points
which are optimistic, pessimistic and normal time; and from that we got the expected completion
time for each activity. Putting them in the network diagram, we got the expected completion time
of the project. After that, we tried to have a probability for another desired completion time, a
desired completion time for a given probability,
Secondly, in CPM, we tried to complete the project with a rise in cost as low as possible. And
same thing is done again to complete the project at in intermediate time; and concluded that
completion time and cost has an inverse relation.
5
Introduction
Overview
In today’s world managing a project from planning to controlling is huge task. A project manager
must be aware of what activities he is taking, what costs are associated, how to accomplish them
and how to complete this with a lower increased costs. This report creates a reflection of this.
Objective of the Study
Like every study, this report is also written in order to fulfill some objectives. The main reason
why this report is written are as follows:



To know about project planning and the subsequent tasks in detail
To analyze PERT and CPM in a real life project management
To understand how to reduce completion time with a lower cost rise
Limitations of the study
As always, the work of this report is not omnipotent. There were several limitations which are as
follows:


Some specifications and assumptions are done based on subjective judgments
The entire realm of theories could not be brought in this report
6
Part A: Theoretical Background
Program Evaluation & Review Technique
Introduction
A PERT outline is project management equipment that gives a graphical portrayal of a venture's
timeline. The Program Evaluation Review Technique (PERT) separates the individual
undertakings of a task for evaluation. PERT was created in 1950 by the U.S. Naval force during
the Cold War and is proposed for huge projects, which are unpredictable, demand a progression
of successive assignments and acted in correspondence with different projects. A PERT graph is a
visual portrayal of a progression of occasions that that must occur within the scope of a project’s
lifetime. The direction of arrows indicates the flow and sequence of events required for project
completion. Dotted activity lines represent dummy activities—items that are located on another
PERT path. Numbers and time allotments are assigned and shown inside each vector.
Planning Mechanism & Functionality
A PERT chart helps a project manager analyze a project's tasks and estimate the amount of time
required to complete each task in the project. Using this information, the project manager can
estimate the minimum amount of time required to complete the entire project. This information
also helps the manager develop a project budget and determine the resources needed to accomplish
the project. PERT planning usually involves some sequential steps. Those are following:
1. Identifying Tasks and Milestones: Every project involves a series of required tasks. These tasks
are listed in a table allowing additional information on sequence and timing to be added later.
2. Placing the Tasks in a Proper Sequence: The tasks are analyzed and placed in a sequence to
get the desired results.
3. Network Diagramming: A network diagram is drawn using the activity sequence data showing
the sequence of serial and parallel activities.
4. Time Estimating: This is the time required to carry out each activity, in three parts:
Optimistic timing: The shortest time to complete an activity
Most likely timing: The completion time having the highest probability
Pessimistic timing: The longest time to complete an activity
7
5. Critical Path Estimating: This determines the total time required to complete a project.
Components of PERT
Activity: An activity represents an action and consumption of resources (time, money, energy)
required to complete a portion of a project. Activity is represented by an arrow.
Event: An event (or node) will always occur at the beginning and end of an activity. The event
has no resources and is represented by a circle. The ith event and jth event are the tail event and
head event respectively. The Event is the point of the diagram that refers to the starting or point of
completion of one or more tasks. This point of the diagram can be reached in practical use only
when all the steps leading to it are complete.
Preceding and Succeeding Activities: Activities performed before given events are known as
preceding activities. Sometimes it also noted as the Predecessor Activities. And the activities that
are performed after a given event are known as succeeding activities or just simply Successors.
Dummy Activity: An imaginary activity which does not consume any resource and time is called
a dummy activity. Dummy activities are simply used to represent a connection between events in
order to maintain a logic in the network. It is represented by a dotted line in a network.
Uses of PERT
PERT charts should be used when a project manager needs to:
a) Determine the project's critical path in order to guarantee all deadlines are met;
b) Display the various interdependencies of tasks;
c) Estimate the amount of time needed to complete the project; and
d) Prepare for more complex and larger projects.
Project managers find best results when they use a PERT chart at the beginning of the project.
Advantages of PERT

The PERT technique provides the ability to evaluate the time and resources necessary to a
project by tracking required assets at each stage of the process, as well as throughout the
course of the project.
8

PERT charts are useful in what-if analyses, helping companies understand all possible
workflows and choose the most efficient and beneficial path.

The analysis of the PERT chart includes data from various departments within an
organization. Combining all of the information helps identify each responsible team within
the company, while facilitating an environment where each department takes responsibility
for its work.

The process of creating a PERT chart also improves communication and enables an
organization to invest energy in projects that will enhance its strategic positioning.

PERT charts make unclear deadlines more predictable, clarify dependencies between tasks
and establish a clear order for completing the tasks.
Disadvantages of PERT

A strict focus on deadlines may not enable managers to see the full financial positioning of
the project.

PERT charts lack the flexibility to adapt to small changes that occur when confronted with a
roadblock.

If any calculations are inaccurate in the creation of the chart, delays could occur, causing
bottlenecks and negatively impacting the final delivery date.

PERT charts are subjective; their success depends on the experience of the project manager.
Consequently, some charts may include unreliable data or unrealistic expectations for the cost
and time frame of the project.

Creating a PERT chart is labor-intensive, requiring additional time and resources. Also, in
order for the chart to remain valuable, it must be consistently reviewed and maintained.
Critical Path Method (CPM)
Synopsys of the CPM
The critical path method (CPM) is a scheduling procedure that uses a network diagram to depict a
project and the sequences of tasks required to complete it, which are known as paths. It is a
powerful but simple technique for analyzing, planning, and scheduling complex projects. Complex
projects that lend themselves to an analysis by CPM are as follows:
9

Launching a new product.

Construction of highways and large buildings.

Installing a computer system.

Missile countdown procedures.
Project management uses CPM for creating project schedules and helping project managers for
creating the project's timeline. CPM includes:
1. Identification of necessary tasks that are required to complete the project.
2. Estimation of project task’s duration.
3. Calculation of the critical path based on the dependency and duration of the project task in
order to identify the critical activities.
4. Focusing on analyzing, planning, and scheduling critical activities.
5. Set project milestones and then expectations of stakeholders related to deadlines.
These considerations allow us to gain insight into which activities must be prioritized and help us
to allocate the necessary resources required to complete the project tasks.
Calculation of the Critical Path
There are some steps that have to be followed strictly to calculate the critical path in project
management. These are as follows:
1. Collecting all the activities leading to the final deliverable.
2. Identifying necessary tasks that are dependent on other tasks before they can begin.
3. Creating a network diagram or a critical path analysis chart that depicts the order of the project
activities.
4. Estimating the duration of each activity.
5. Using the critical path algorithm with two parts, a forward pass, and a backward pass.
6. In the case of the forward pass, use the duration and network diagram to determine their earliest
start (ES) and earliest finish (EF).
7. ES equal to the EF of the activity’s predecessor, and EF= ES+t, where t is the duration of the
activity.
8. Backward pass begins by assigning the last activity’s earliest finish as its latest finish (LF).
9. LF is the smallest of the start times for the activity that follows immediately and LS= LF-t.
10
10. Identifying the float of each activity. Float= LS-ES.
11. Identifying the critical path. The critical path has no float. That means zero float activities
make up the critical path.
These are the steps to calculate the critical path in project management.
Distinction between PERT & CPM
Point of
Difference
PERT
CPM
Meaning
PERT is a project management
technique, used to manage uncertain
activities of a project.
CPM is a statistical technique of
project management that manages well
defined activities of a project.
What is it?
A technique of planning and control
of time.
A method to control cost and time.
Orientation
Event-oriented
Activity-oriented
Evolution
Evolved as Research &
Development project
Evolved as Construction project
Model
Probabilistic Model
Deterministic Model
Focuses on
Time
Time-cost trade-off
Estimates
Three time estimates
One time estimate
Appropriate for
High precision time estimate
Reasonable time estimate
Management of
Unpredictable Activities
Predictable activities
Nature of jobs
Non-repetitive nature
Repetitive nature
Critical and Noncritical activities
No differentiation
Differentiated
Suitable for
Research and Development Project
Non-research projects like civil
construction, ship building etc.
Crashing concept
Not Applicable
Applicable
11
Part B: The Case Analysis
Case: Project: TSC Extension Building
A building will be built in TSC of University of Dhaka. The building will be built in the location
of TSC swimming pool while the swimming pool will be removed. To build that building several
activities are needed to be done. List of activities along with their predecessors are provided below:
Activity Name
Digging/Excavation
Piling
Tank Set up
Base Welding
Base Pillars
Base Beam
Column Pillars
Up Beam
Roof Welding
Ceiling Lining
Wall Brick Stringing
Wall Lining, Door Window
Electric Wiring`
Tiles set up
Painting, Finishing up
Water Pipe set up
Activity Name
Digging/Excavation
Piling
Tank Set up
Base Welding
Base Pillars
Base Beam
Column Pillars
Up Beam
Roof Welding
Ceiling Lining
Wall Brick Stringing
Wall Lining, Door
Window
Electric Wiring,
Optimistic
Pessimistic
Most Likely
Activity Predecessor Time(Weeks) Time(Weeks) Time(Weeks)
A
---2
4
3
B
A
6
12
9
C
A
5
13
6
D
B,C
1
5
3
E
D
6
14
7
F
D
5
11
8
G
E,F
2
10
6
H
G
8
8
8
I
F
2
10
9
J
I
3
15
6
K
J,F
9
15
12
L
K
11
25
15
M
K
10
30
14
N
L
5
15
7
O
N
9
15
12
P
M
10
20
18
Activity
A
B
C
D
E
F
G
H
I
J
K
Crash
Time(Weeks)
1
7
6
3
6
6
6
7
6
5
9
Normal
Cost(BDT)
12,000
18,000
25,000
15,000
30,000
24,000
40,000
50,000
60,000
42,000
48,000
Crash
Cost(BDT)
16,000
24,000
30,000
15,000
34,000
30,000
40,000
52,000
66,000
44,000
60,000
L
M
13
14
62,000
30,000
77,000
36,000
12
Tiles set up
Painting, Finishing up
Water Pipe set up
N
O
P
7
8
13
54,000
42,000
40,000
59,000
54,000
50,000
Requirements:
1) Draw the network diagram with the all related activities.
2) What is the expected completion time of the project and what are the critical activities
3) a) What is the probability to complete the project at 88 weeks?
b) What is the completion time if it has 90% probability?
4) a) What will the crash time to complete the project? What will be the additional cost and
total revised cost to complete the project at crash time? Draw the revised network.
b) What will be the additional cost and total revised cost to complete the project at
intermediate time of 80 weeks? Draw the revised network.
Solution to the Case
Problem A
In this case, we tried to retrieve the related activities to build the new building in TSC area of
University of Dhaka.
For this, firstly, we tried to draw the network diagram according to the activities and their
predecessor activities. The network diagram we found to build the new building in TSC is:
13
Here is the network, where along with sixteen different activities there are two dummy activities
which were used to connect two different activities which don’t have direct relationship.
Problem B
At this time, we estimated three different points of times which are optimistic (the shortest possible
to complete one activity), pessimistic (the highest possible time to complete one activity) and most
likely time (the possible time to complete when all the factors are in normal mode). From these
three time we got the expected completion time and the variance of each activity.
Expected completion time = [(optimistic time + pessimistic time +4*most likely time) / 6]
Variance of each activity = [(pessimistic time – optimistic time)/6]^2
For our case, the three time points, expected completion time and variance are given below:
Activity
Optimistic
Time(Weeks)
Pessimistic
Time(Weeks)
Most Likely
Time(Weeks)
Normal
Time(Weeks)
Variance
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
2
6
5
1
6
5
2
8
2
3
9
11
10
5
9
10
4
12
13
5
14
11
10
8
10
15
15
25
30
15
15
20
3
9
6
3
7
8
6
8
9
6
12
15
14
7
12
18
3
9
7
3
8
8
6
8
8
7
12
16
16
8
12
17
0.1111
1.0000
1.7778
0.4444
1.7778
1.0000
1.7778
0.0000
1.7778
4.0000
1.0000
5.4444
11.1111
2.7778
1.0000
2.7778
With these expected completion time points, we got the expected completion time of the project.
14
So, the completion date of the project is 92 weeks which we got from the network where the critical
activities are A,B,D,E,F,G,H,J,K,L,N,O.
Problem C
Here, firstly, we tried to find out the probability of completing the project at 88 weeks and after
that we found out the required weeks to complete the project where the probability to complete the
project is 90%.
Probability to complete the project at 88 weeks:
To get this probability, we use the Z-score of normal probability distribution, where
Mean = expected completion time (X bar) = 92 weeks
Target completion time (X) = 88 weeks
Standard deviation of critical activities (sigma) = 4.509
So, the Z-score = {(Target time – expected time) / standard deviation of critical activities}
= {(88-92)/ 4.509} or -0.89
The probability at -0.89, Z-score is 0.1875
15
So, to complete the project at 88 weeks, it has a probability of 0.1875.
Weeks where chance of completion is 90%:
Here for 90% probability of completing the project the corresponding Z-score is 1.33
Now, Z-score = {(Target time – expected time) / standard deviation of critical activities}
 1.33 = {(X – 92)/ 4.509
 X = 98 weeks (almost)
So, it has 90% probability that the project can be completed in 98 weeks.
Problem D
Here we tried to find out the increased amount of cost if we complete the project at crash time and
an intermediate time.
16
Firstly we look at the normal time-cost and crash time-cost of the project. And with the
information, we found increased cost per activity.
Activity
Normal
Time(Weeks)
Crash
Time(Weeks)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
3
9
7
3
8
8
6
8
8
7
12
16
16
8
12
17
1
7
6
3
6
6
6
7
6
5
9
13
14
7
8
13
Normal
Cost
(BDT)
12,000
18,000
25,000
15,000
30,000
24,000
40,000
50,000
60,000
42,000
48,000
62,000
30,000
54,000
42,000
40,000
Crash
Cost
(BDT)
16,000
24,000
30,000
15,000
34,000
30,000
40,000
52,000
66,000
44,000
60,000
77,000
36,000
59,000
54,000
50,000
Increased cost per
activity (BDT)
2,000
3,000
5,000
2,000
3,000
2,000
3,000
1,000
4,000
5,000
3,000
5,000
3,000
2,500
From our previous analysis, we found that the normal completion time, critical path and activities
and normal cost. Which are:
Critical Path: A-B-D-E-G-H-J-K-L-N-O and A-B-D-F-G-H-J-K-L-N-O
Normal Time: 92 weeks
Total Cost with normal time: BDT 592, 000
Now we see the network diagram with crash time and find out the completion time of the project
at crash.
17
From this network diagram at crash time, we found:
Critical Path: A-B-D-E-G-H-J-K-L-N-O
Crash Time: 72 weeks
Total Cost with crash time: BDT 687,000
Now, we will see whether we can complete the project at 72 weeks where the total cost will be
less than BDT 687,000 or incremental cost will be less than (687,000 - 592, 000) or BDT 95,000.
For this the actions we took are:
Least cost schedule (to complete project in 72 weeks)
Activity
Weeks Reduced
Cost Increased (BDT)
J
2
2000
A
2
4000
E
2
4000
H
1
2000
O
4
12000
B
2
6000
K
3
12000
P
4
10000
L
3
15000
18
M
1
3000
N
1
5000
F
2
Total
6000
81000
It is possible to reduce the project completion time to crash time i.e 72 weeks without increasing
cost by BDT 95,000 or (687,00 – 592,000), if the decision is taken in the mentioned way then
project can be completed within crash time but increasing cost by only BDT 81,000.
Now, New total cost = BDT (592,000 + 81,000)
= BDT 673,000
Revised Network- (reducing the project length to crash time i.e. 72 weeks)
Now, again we will see what will be the increased amount of cost, if we want to complete the
project at 80 weeks instead of 92 weeks.
For this, the actions we have taken are:
Least cost schedule (to complete project in 80 weeks)
Activity
J
A
E
F
H
O
B
Weeks Reduced
2
2
2
2
1
3
2
Total
Cost Increased (BDT)
2000
4000
4000
6000
2000
9000
6000
33000
Now, the new total cost to complete the project at 80 weeks
19
= BDT (592,000 + 33,000)
= BDT 625,000
Revised Network- (to reduce project completion time to 80 weeks)
Time-Cost Trade-off
So, we saw that; if we want to reduce the project completion time, the cost of the project goes up.
And for higher completion time, it has lower cost to complete the project. So there is trade-off with
the completion time and project cost.
Fact
Normal
Intermediate
Crash
Time
(weeks)
92
80
72
Cost (BDT)
592000
620000
673000
Conclusion
In this case, we tried to incorporate the project of the plan of establishing a new building in the
TSC area of University of Dhaka. For this, we segmented our whole analysis into PERT and CPM
techniques. We estimated related activities and their completion time with various time estimates.
And then fond the completion time. Then found out the probabilities with some other completion
time. And lastly, we tried to reduce the project completion time with a lower cost structure through
Critical Path Method.
20
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