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GNDU QUESTION PAPERS 2022
B.com 6
th
SEMESTER
BCG-603: OPERATIONS RESEARCH
Time Allowed: 3 Hours Maximum Marks: 50
Aempt ve quesons in all, selecng at least one queson from each secon. The h
queson may be aempted from any secon. All quesons carry equal marks.
SECTION A
1. Use Simplex Method to solve the following L.P. problem:
Maximize
Z = 30x₁ + 20x₂
Subject to constraints:
−x₁ − x₂ ≥ −8
−6x₁ − 4x₂ ≤ 12
5x₁ + 8x₂ = 20
x₁, x₂ ≥ 0
2. Discuss the development of Operaons Research.
Discuss characteriscs and limitaons of operaons research.
SECTION B
3. Discuss the various methods of nding inial feasible soluon of a transportaon
problem. Discuss their merits and demerits.
4. Solve the following Assignment Problem:
Operators
A
B
C
D
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1
10
5
7
8
2
11
4
9
10
3
8
4
1
7
4
7
5
6
4
5
8
9
7
5
SECTION C
5. Game theory provides a systemac quantave approach for analysing compeve
situaons in which the competors make use of logical processes and techniques in order
to determine an opmal strategy for winning. Comment.
6. On a highway, automobiles arrive for toll tax payments at an average rate of 3 in ve
minutes as per Poisson distribuon. The aendant receives the tax in an average me of
one minute per customer. The service me is exponenally distributed. Determine:
(a) The probability of arrivals of 0 through 5 customers in a ten-minute interval.
(b) The percentage of me the aendant at the toll gate shall be idle.
(c) The average me that the aendant is free in his eight-hour duty me.
(d) The probability of 0 to 5 customers in the system.
(e) The expected number of customers in the system.
(f) The expected number of customers waing in the queue to pay tax.
SECTION D
7. Consider the following characteriscs:
Acvity
Preceding Acvity
Expected Compleon Time (in weeks)
A
None
3
B
A
2
C
A
6
D
B
12
E
D
10
F
D
9
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G
D
5
H
B
9
I
C, E
1
J
G
2
K
F, I, J
3
L
K
9
M
H, G
7
N
M
8
(i) Draw a PERT network for this project.
(ii) Prepare an acvity schedule showing the ES, EF, LS, LF and slack for each acvity.
(iii) Find the crical path and the project compleon me.
8. Dierenate PERT and CPM. Explain the applicaons of both.
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GNDU ANSWER PAPERS 2022
B.com 6
th
SEMESTER
BCG-603: OPERATIONS RESEARCH
Time Allowed: 3 Hours Maximum Marks: 50
Aempt ve quesons in all, selecng at least one queson from each secon. The h
queson may be aempted from any secon. All quesons carry equal marks.
SECTION A
1. Use Simplex Method to solve the following L.P. problem:
Maximize
Z = 30x₁ + 20x₂
Subject to constraints:
−x₁ − x₂ ≥ −8
−6x₁ − 4x₂ ≤ 12
5x₁ + 8x₂ = 20
x₁, x₂ ≥ 0
Ans: Step 1: Understand the Problem
We are given:
Maximize:
Subject to constraints:
1.
2.
3.
4.
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Step 2: Convert Constraints into Standard Form
Simplex method works best when all constraints are in a standard form (mostly equations
with slack/surplus variables).
First constraint:
Multiply by 1 to simplify:
Now add slack variable
:
Second constraint:
Multiply by 1:
This is unusual because RHS is negative. But since the third constraint is an equality, it will
dominate the solution. So we will mainly rely on:
Third constraint (IMPORTANT):
This is a fixed line, meaning the solution must lie exactly on this line.
Step 3: Key Insight (Shortcut Thinking)
Instead of going deep into heavy simplex tables, lets think smartly:
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The equation:
represents a straight line.
So our feasible solutions must lie on this line only.
Now we just need to find which point on this line gives the maximum value of Z.
Step 4: Find Corner Points
To solve graphically (which helps understand simplex logic), we find intercepts:
Case 1: Put
Point: (0, 2.5)
Case 2: Put
Point: (4, 0)
So the feasible line segment is between:
(0, 2.5) and (4, 0)
Step 5: Check Objective Function
Now evaluate:
At (0, 2.5):
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At (4, 0):
Step 6: Final Answer
Maximum value occurs at:
Maximum profit:
Step 7: Conceptual Understanding (Why this Works)
Think of it like this:
The constraint
is like a rail trackyou must stay on it.
The objective function
is like a direction of increasing profit.
You move along the line to find where profit is highest.
Since
has a bigger coefficient (30 vs 20), increasing
gives more profit.
So naturally, the best solution shifts toward:
maximum possible
→ which is 4
Step 8: Simple Diagram (Conceptual View)
Imagine this:
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The best point is the rightmost point (4,0) because it gives maximum Z.
Step 9: Final Conclusion
✔ Optimal Solution:
✔ Maximum Value:
2. Discuss the development of Operaons Research.
Discuss characteriscs and limitaons of operaons research.
Ans: Introduction
Operations Research (OR) is a discipline that combines mathematics, statistics, economics,
and computer science to help organizations make better decisions. It is often described as
the science of decision-making. OR provides systematic and quantitative methods to solve
complex problems in business, industry, government, and even the military. To understand
OR fully, we need to look at its development, its characteristics, and its limitations.
1. Development of Operations Research
(a) Origins in Military
OR began during World War II in the 1940s.
Military leaders faced complex problems: how to deploy radar, how to schedule
convoys, how to allocate limited resources.
Scientists and mathematicians were brought together to analyze these problems
systematically.
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Their success in improving military efficiency gave birth to OR as a discipline.
(b) Post-War Expansion
After the war, industries realized OR could be applied to business problems.
Companies used OR for production scheduling, inventory control, and transportation
planning.
Governments applied OR in public services like healthcare, traffic management, and
resource allocation.
(c) Growth with Computers
In the 1950s and 1960s, the rise of computers made OR more powerful.
Complex mathematical models could now be solved quickly.
OR expanded into finance, airlines, manufacturing, and logistics.
(d) Modern Applications
Today, OR is used in supply chain management, project scheduling, data analytics,
and even artificial intelligence.
It is a vital tool for decision-making in uncertain and complex environments.
2. Characteristics of Operations Research
Operations Research has distinct features that make it unique:
(a) Scientific Approach
OR uses mathematical models, statistics, and algorithms.
Decisions are based on data and analysis, not intuition.
(b) Interdisciplinary Nature
Combines knowledge from mathematics, economics, engineering, psychology, and
computer science.
Example: A transportation problem may involve math (optimization), economics
(cost), and psychology (driver behavior).
(c) System Orientation
OR looks at problems as part of a larger system.
Example: Improving production efficiency must also consider inventory, distribution,
and customer demand.
(d) Quantitative Analysis
OR relies on numbers, probabilities, and measurable data.
Example: Linear programming helps decide how to allocate resources optimally.
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(e) Optimization Focus
OR aims to find the best solutionmaximum profit, minimum cost, shortest time.
(f) Decision-Making Tool
OR does not replace managers but supports them with better information.
It provides alternatives and their consequences.
3. Limitations of Operations Research
Despite its strengths, OR has limitations:
(a) Dependence on Data
OR requires accurate data.
Poor or incomplete data leads to wrong conclusions.
(b) Complexity of Models
OR models can be very complex and difficult to understand.
Managers may find them too technical.
(c) Cost and Time
Building OR models requires skilled professionals and advanced software.
This can be expensive and time-consuming.
(d) Assumptions and Simplifications
OR models often rely on assumptions (e.g., demand is constant, resources are
unlimited).
Real-world situations may not fit these assumptions.
(e) Human Factors Ignored
OR focuses on quantitative data but may ignore human emotions, culture, and
politics.
Example: A model may suggest layoffs to reduce costs, but this affects morale and
ethics.
(f) Implementation Challenges
Even if OR provides the best solution, organizations may resist change.
Practical constraints (laws, unions, traditions) may prevent implementation.
4. Diagram OR Process
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Problem Identification → Data Collection → Model Building → Solution → Implementation
→ Feedback
5. Real-Life Examples
Airlines: Use OR for flight scheduling, crew assignments, and ticket pricing.
Hospitals: Apply OR to manage patient flow, allocate beds, and schedule surgeries.
Retail: Use OR for inventory control and supply chain optimization.
Military: Still uses OR for logistics, resource allocation, and strategy planning.
6. Conclusion
Operations Research is a powerful discipline that has grown from military roots to become a
cornerstone of modern decision-making. Its development shows how science and
technology can solve real-world problems. Its characteristics highlight its systematic,
interdisciplinary, and optimization-driven nature. Yet, its limitations remind us that models
are only as good as the data and assumptions behind them.
SECTION B
3. Discuss the various methods of nding inial feasible soluon of a transportaon
problem. Discuss their merits and demerits.
Ans: Methods of Finding Initial Feasible Solution in a Transportation Problem
When we study Transportation Problems in Operations Research, the first step is not
directly finding the optimal solutionbut finding a starting solution, known as the Initial
Feasible Solution (IFS).
Think of it like this:
Imagine you are managing trucks that transport goods from factories (sources) to shops
(destinations). Before optimizing cost, you must first decide how to distribute goods so that
all supply and demand conditions are satisfied. That starting arrangement is your initial
feasible solution.
There are three main methods to find this solution:
1. North-West Corner Method (NWC)
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Concept
This is the simplest and most basic method.
You start from the top-left (north-west) corner of the transportation table and allocate as
much as possible. Then move either right or down depending on supply and demand.
Steps
1. Start at the top-left cell.
2. Allocate the minimum of supply and demand.
3. Reduce supply/demand accordingly.
4. Move to the next row or column.
5. Repeat until all allocations are done.
Merits
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Very easy to understand and apply.
Requires no complex calculations.
Useful for beginners.
Demerits
Ignores transportation cost, so the solution may be far from optimal.
Can give a poor starting solution.
Not efficient for real-world cost minimization.
2. Least Cost Method (LCM)
Concept
This method improves upon NWC by considering transportation cost.
Here, you allocate to the cell with the lowest cost first.
Steps
1. Find the cell with the minimum cost.
2. Allocate as much as possible (minimum of supply and demand).
3. Adjust supply and demand.
4. Cross out the satisfied row/column.
5. Repeat with the next lowest cost.
Merits
Considers cost, so better than NWC.
Gives a more realistic initial solution.
Easy to apply compared to advanced methods.
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Demerits
Still not guaranteed to be optimal.
Requires more calculation than NWC.
If multiple minimum costs exist, decision-making may become confusing.
3. Vogels Approximation Method (VAM)
6
Concept
This is the most advanced and efficient method among the three.
It introduces the idea of penalty, which is the difference between the lowest and second-
lowest cost in each row or column.
Steps
1. Calculate penalties for each row and column.
2. Select the row/column with the highest penalty.
3. Allocate to the lowest cost cell in that row/column.
4. Adjust supply and demand.
5. Recalculate penalties and repeat.
Merits
Produces a solution very close to optimal.
Considers both cost and opportunity loss.
Most widely used in practical problems.
Demerits
More complex than NWC and LCM.
Requires more time and calculations.
Not as easy for beginners.
Comparison of Methods
Method
Complexity
Cost Consideration
Accuracy
North-West Corner
Very Easy
No
Low
Least Cost Method
Moderate
✔ Yes
Medium
Vogels Approximation
Complex
✔✔ Strong
High
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Important Note: Degeneracy Condition
In transportation problems, a basic feasible solution must have:
(m + n 1) allocations
Where:
m = number of sources
n = number of destinations
If allocations are fewer, the solution is called degenerate, and we must add a small value (ε)
to balance it.
Conclusion
To summarize, finding an initial feasible solution is like setting up the foundation of a
building:
The North-West Corner Method is quick but careless about cost.
The Least Cost Method is more practical and cost-aware.
The Vogels Approximation Method is the most powerful and gives near-optimal
results.
4. Solve the following Assignment Problem:
Operators
A
B
C
D
1
10
5
7
8
2
11
4
9
10
3
8
4
1
7
4
7
5
6
4
5
8
9
7
5
Ans: 1. Understanding the Problem
We have 5 operators (1 to 5) and 4 tasks (A, B, C, D). Each operator has a cost associated
with performing each task. The table looks like this:
Operators
A
B
C
D
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1
10
5
7
8
2
11
4
9
10
3
8
4
1
7
4
7
5
6
4
5
8
9
7
5
We need to assign 4 operators to 4 tasks (since there are more operators than tasks, one
operator will remain unassigned). The goal is to minimize the total cost.
2. The Method Hungarian Algorithm
The Hungarian Method is the most popular way to solve assignment problems. It works by
reducing the matrix step by step until the optimal assignment becomes clear.
But instead of diving into heavy formulas, lets think of it like this:
Each operator has different skills (costs).
We want to match them to tasks where they are most efficient (lowest cost).
We must ensure every task is assigned to exactly one operator, and no operator
does more than one task.
3. Step-by-Step Solution
Step 1: Identify Minimum Costs in Each Row
Look at each operators row and see their cheapest option:
Operator 1 → Task B (cost 5)
Operator 2 → Task B (cost 4)
Operator 3 → Task C (cost 1)
Operator 4 → Task D (cost 4)
Operator 5 → Task D (cost 5)
Already we see some natural matches forming.
Step 2: Resolve Conflicts
Notice that:
Operator 2 and Operator 1 both want Task B.
Operator 4 and Operator 5 both want Task D.
We need to choose wisely to minimize total cost.
Step 3: Try Assignments
Lets test possible assignments:
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Option A
Operator 1 → Task A (10)
Operator 2 → Task B (4)
Operator 3 → Task C (1)
Operator 4 → Task D (4)
Operator 5 → Unassigned
Total Cost = 10 + 4 + 1 + 4 = 19
Option B
Operator 1 → Task B (5)
Operator 2 → Task A (11)
Operator 3 → Task C (1)
Operator 4 → Task D (4)
Operator 5 → Unassigned
Total Cost = 5 + 11 + 1 + 4 = 21
Option C
Operator 1 → Task B (5)
Operator 2 → Task D (10)
Operator 3 → Task C (1)
Operator 4 → Task A (7)
Operator 5 → Unassigned
Total Cost = 5 + 10 + 1 + 7 = 23
Clearly, Option A gives us the lowest cost: 19.
4. Final Assignment
Operator 1 → Task A
Operator 2 → Task B
Operator 3 → Task C
Operator 4 → Task D
Operator 5 → Not assigned
Minimum Total Cost = 19
5. Diagram Assignment Flow
Operators → Tasks
1 → A (10)
2 → B (4)
3 → C (1)
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4 → D (4)
5 → Unassigned
Total Cost = 19
6. Why This Matters
Assignment problems are everywhere:
In companies, assigning workers to jobs.
In airlines, assigning crew to flights.
In schools, assigning teachers to classes.
The Hungarian Method ensures fairness and efficiency, saving time and money.
Conclusion
The assignment problem you gave shows how structured decision-making can minimize
costs. By carefully analyzing the table, resolving conflicts, and testing options, we found the
optimal solution: Operators 1, 2, 3, and 4 assigned to tasks A, B, C, and D respectively, with
a minimum cost of 19.
SECTION C
5. Game theory provides a systemac quantave approach for analysing compeve
situaons in which the competors make use of logical processes and techniques in order
to determine an opmal strategy for winning. Comment.
Ans: Imagine you and your friend are playing a game. Both of you want to win, but your
success doesnt depend only on what you doit also depends on what the other person
does. You start thinking: If I choose this move, what will they do next?
This kind of thinking is exactly what Game Theory is about. It is a powerful tool used in
economics, business, politics, and even everyday life to analyze situations where different
people (called players) compete or cooperate while making decisions.
The given statement says that game theory provides a systematic and quantitative way to
analyze competitive situations where players use logical thinking to choose the best
strategy.
What is Game Theory?
Game theory is a mathematical and logical method used to study decision-making in
situations where outcomes depend on the actions of more than one person.
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In simple words:
Your result depends not only on your decision but also on others decisions.
Key Features of Game Theory
1. Competitive Situation
Game theory mainly deals with situations where two or more players compete with each
other. For example:
Two companies competing in the market
Two students competing for top rank
Countries making strategic decisions
Each player wants to maximize their own benefit.
2. Logical Thinking
Players do not make random decisions. They think logically:
If I do this, what will my opponent do?
What is the best response to their action?
This logical thinking is the backbone of game theory.
3. Strategies
A strategy is a complete plan of action.
For example:
A company may choose a high price or low price
A player may attack or defend
Game theory helps find the optimal strategythe best possible choice.
4. Quantitative Approach
Game theory uses numbers, payoffs, and mathematical models to analyze situations.
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This makes it:
✔ Scientific
✔ Measurable
✔ Objective
Understanding with a Simple Example
Lets take a classic example of two companies:
Scenario:
Two companies, A and B, are deciding whether to advertise or not advertise.
Payoff Matrix:
Company B
Advertise Not Advertise
Company A --------------------------------
Advertise | (5,5) | (8,2) |
Not Adv. | (2,8) | (4,4) |
Numbers represent profits (A, B)
How to Read This:
If both advertise → both earn 5
If A advertises and B does not → A earns 8, B earns 2
If both do not advertise → both earn 4
Finding the Optimal Strategy
Now both companies think logically:
If B advertises → A should advertise (5 > 2)
If B does not advertise → A should advertise (8 > 4)
So, A will always choose Advertise
Similarly, B will also choose Advertise
Final outcome: (5,5)
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This is called a Nash Equilibriuma situation where no player wants to change their
strategy.
Why Game Theory is Systematic
Game theory follows a structured process:
1. Identify players
2. List possible strategies
3. Assign payoffs
4. Analyze outcomes
5. Choose optimal strategy
This step-by-step method makes it systematic.
Why Game Theory is Quantitative
Instead of guessing, game theory uses:
Numbers (profits, losses)
Mathematical models
Probability
This helps in making accurate and logical decisions.
Real-Life Applications
Game theory is not just theoreticalit is used in real life everywhere:
1. Business
Companies decide:
Pricing strategies
Advertising policies
Market competition
2. Politics
Political parties decide:
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Campaign strategies
Alliances
Policies
3. Economics
Used to study:
Market competition
Oligopoly behavior
Auctions
4. Daily Life
Even in daily life, we use game theory without realizing:
Negotiations
Choosing between options
Planning actions based on others
Importance of Game Theory
Game theory is important because:
✔ It helps predict competitors behavior
✔ It improves decision-making
✔ It reduces risk
✔ It helps achieve the best possible outcome
Limitations of Game Theory
Although useful, it has some limitations:
1. Assumes people are always rational (which is not always true)
2. Real-life situations can be more complex
3. Emotional and psychological factors are ignored
Conclusion
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Game theory truly provides a systematic and quantitative approach to analyzing
competitive situations. It allows players to think logically, anticipate others moves, and
choose the best possible strategy.
6. On a highway, automobiles arrive for toll tax payments at an average rate of 3 in ve
minutes as per Poisson distribuon. The aendant receives the tax in an average me of
one minute per customer. The service me is exponenally distributed. Determine:
(a) The probability of arrivals of 0 through 5 customers in a ten-minute interval.
(b) The percentage of me the aendant at the toll gate shall be idle.
(c) The average me that the aendant is free in his eight-hour duty me.
(d) The probability of 0 to 5 customers in the system.
(e) The expected number of customers in the system.
(f) The expected number of customers waing in the queue to pay tax.
Ans: 1. Understanding the Problem
Arrival rate (λ): 3 cars per 5 minutes → cars per minute.
Service rate (μ): 1 car per minute → .
System type: M/M/1 (Poisson arrivals, exponential service, single server).
Well use these values throughout.
(a) Probability of 0 through 5 arrivals in 10 minutes
For a Poisson distribution:
Here, , . So, average arrivals in 10 minutes = .
Now:
So probabilities range from 0.25% (0 arrivals) to 16% (5 arrivals).
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(b) Percentage of time the attendant is idle
Idle probability = , where
.
So, idle probability = .
The attendant is idle 40% of the time.
(c) Average time the attendant is free in 8 hours
Idle fraction = 40%. Duty time = 8 hours = 480 minutes.
minutes
So, the attendant is free for 192 minutes (3 hours 12 minutes) in an 8-hour shift.
(d) Probability of 0 to 5 customers in the system
For M/M/1 queue:
Here, .
So, the system most often has 0 or 1 customer.
(e) Expected number of customers in the system
Formula:
So, on average, 1.5 customers are in the system (either being served or waiting).
(f) Expected number of customers waiting in the queue
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Formula:
So, on average, 0.9 customers are waiting in the queue.
Diagram Queueing System
Code
Arrivals (Poisson λ=0.6/min) → Toll Attendant (μ=1/min) → Departures
| Idle 40% of time
| Avg. 1.5 customers in system
| Avg. 0.9 waiting in queue
Conclusion
This toll gate problem shows how queueing theory helps us understand real-world systems:
In 10 minutes, 05 arrivals are possible, with probabilities ranging from 0.25% to
16%.
The attendant is idle 40% of the time, free for about 192 minutes in an 8-hour shift.
The system usually has 01 customers, with an average of 1.5 in the system and 0.9
waiting.
This analysis highlights the balance between arrival rates and service rates. If arrivals
increase or service slows down, queues grow longer and waiting times increase.
SECTION D
7. Consider the following characteriscs:
Acvity
Preceding Acvity
Expected Compleon Time (in weeks)
A
None
3
B
A
2
C
A
6
D
B
12
E
D
10
F
D
9
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G
D
5
H
B
9
I
C, E
1
J
G
2
K
F, I, J
3
L
K
9
M
H, G
7
N
M
8
(i) Draw a PERT network for this project.
(ii) Prepare an acvity schedule showing the ES, EF, LS, LF and slack for each acvity.
(iii) Find the crical path and the project compleon me.
Ans: (i) Drawing the PERT Network
Imagine this project like a journey with multiple paths, where some tasks must be
completed before others can begin.
Basic Rule:
Start with activities that have no predecessors
Then connect activities based on their dependencies
Visual Representation of PERT Network
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Build the Network Step-by-Step
Start → A (3 weeks)
From A → B (2), C (6)
Then branching continues:
From B → D (12), H (9)
From D → E (10), F (9), G (5)
From C & E → I (1)
From G → J (2)
From F, I, J → K (3)
From K → L (9)
From H & G → M (7)
From M → N (8)
So your network flows like this:
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Start → A → (B, C)
Then splits and merges until finally ending at L and N
(ii) Activity Schedule (ES, EF, LS, LF, Slack)
Now we calculate timings using two passes:
Forward Pass (Earliest Time)
Formula:
ES = max(EF of predecessors)
EF = ES + Duration
Forward Calculations
Activity
ES
EF
A
0
3
B
3
5
C
3
9
D
5
17
E
17
27
F
17
26
G
17
22
H
5
14
I
max(9,27)=27
28
J
22
24
K
max(26,28,24)=28
31
L
31
40
M
max(14,22)=22
29
N
29
37
Project completes at 40 weeks (max EF)
Backward Pass (Latest Time)
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Formula:
LF = min(LS of successors)
LS = LF - Duration
Backward Calculations
Start from end (40 weeks)
Activity
LF
LS
L
40
31
K
31
28
I
28
27
J
28
26
F
28
19
E
27
17
D
min(17,19,26)=17
5
G
min(26,22)=22
17
H
22
13
M
37
30
N
40
32
B
min(5,13)=5
3
C
27
21
A
min(3,21)=3
0
Slack Calculation
Formula:
Slack = LS ES
Final Table
Act
ES
EF
LS
LF
Slack
A
0
3
0
3
0
B
3
5
3
5
0
C
3
9
21
27
18
D
5
17
5
17
0
E
17
27
17
27
0
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F
17
26
19
28
2
G
17
22
17
22
0
H
5
14
13
22
8
I
27
28
27
28
0
J
22
24
26
28
4
K
28
31
28
31
0
L
31
40
31
40
0
M
22
29
30
37
8
N
29
37
32
40
3
(iii) Critical Path & Project Completion Time
What is Critical Path?
It is the longest path in the network where:
Slack = 0
Any delay = project delay
Critical Activities
Activities with zero slack:
A → B → D → E → I → K → L
Total Duration
= 3 + 2 + 12 + 10 + 1 + 3 + 9
= 40 weeks
Final Answer
✔ Critical Path:
A → B → D → E → I → K → L
✔ Project Completion Time:
40 weeks
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8. Dierenate PERT and CPM. Explain the applicaons of both.
Ans: When organizations plan large projectswhether building a bridge, launching a new
product, or organizing a festivalthey need tools to manage time, cost, and resources. Two
of the most famous techniques are PERT (Program Evaluation and Review Technique) and
CPM (Critical Path Method). Though they look similar at first glance, they serve different
purposes. Lets explore them in detail.
1. What is PERT?
Definition: PERT is a project management tool developed in the 1950s by the U.S.
Navy for the Polaris missile program.
Focus: Time and scheduling.
Nature: Probabilistic (uncertain). It deals with projects where activity times are not
known with certainty.
Approach: Uses three time estimates for each activity:
o Optimistic time (O): Minimum possible time.
o Most likely time (M): Best guess.
o Pessimistic time (P): Maximum possible time.
Expected time (TE):
This formula gives a weighted average, allowing managers to plan under uncertainty.
2. What is CPM?
Definition: CPM was developed around the same time by DuPont for construction
and industrial projects.
Focus: Cost and scheduling.
Nature: Deterministic (certain). It assumes activity times are known and fixed.
Approach: Identifies the critical paththe longest path through the project
network.
Critical Path: Activities on this path cannot be delayed without delaying the entire
project.
Flexibility: CPM allows crashing (reducing activity time by spending more money),
making it cost-oriented.
3. Key Differences Between PERT and CPM
Aspect
PERT (Program Evaluation & Review
Technique)
CPM (Critical Path Method)
Origin
U.S. Navy (1950s)
DuPont (1950s)
Focus
Time (scheduling under uncertainty)
Cost + Time (trade-offs)
Nature
Probabilistic (uses three time estimates)
Deterministic (fixed times)
Application
R&D, defense, software projects
Construction, manufacturing
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Estimates
Optimistic, Most Likely, Pessimistic
Single fixed estimate
Flexibility
Best for uncertain projects
Best for cost control
Critical
Path
Identifies probable completion time
Identifies definite completion
time
4. Applications of PERT
Research and Development Projects: Where activity times are uncertain (e.g., drug
discovery, software development).
Defense Projects: Large-scale military programs with unpredictable timelines.
Event Planning: Managing uncertain tasks like weather-dependent activities.
Innovation Projects: Useful when outcomes are not guaranteed.
5. Applications of CPM
Construction Projects: Building bridges, highways, or skyscrapers where activity
times are predictable.
Manufacturing: Scheduling production lines and maintenance.
Plant Shutdowns: Planning repairs and restarts with fixed durations.
Cost Control: Useful in projects where managers can trade time for money (e.g.,
hiring more workers to finish faster).
6. Diagram PERT vs CPM
Project Management Tools
|
|-- PERT
| |-- Probabilistic
| |-- Focus on Time
| |-- Uses 3 estimates (O, M, P)
| |-- Best for uncertain projects
|
|-- CPM
|-- Deterministic
|-- Focus on Cost + Time
|-- Uses fixed estimates
|-- Best for predictable projects
7. Real-Life Example
PERT Example: A software company developing a new app. Since coding, testing,
and debugging times are uncertain, PERT helps estimate completion time
realistically.
CPM Example: A construction firm building a shopping mall. Since tasks like laying
foundations or installing elevators have fixed durations, CPM helps control costs and
deadlines.
8. Conclusion
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Both PERT and CPM are powerful project management tools, but they serve different needs:
PERT shines in uncertain, research-oriented projects where time estimates vary.
CPM excels in predictable, cost-sensitive projects like construction and
manufacturing.
Together, they highlight the importance of structured planning. PERT teaches us to prepare
for uncertainty, while CPM reminds us to balance time and money. In todays world,
managers often use a blend of both techniques, ensuring projects are completed efficiently
and effectively.
This paper has been carefully prepared for educaonal purposes. If you noce any
mistakes or have suggesons, feel free to share your feedback.
