OPERATION
RESEARCH
,BBA - OPERATIONS RESEARCH
INDEX
UNIT – I : Introduction to Operations Research
1. 1. Nature and Meaning of Operations Research
2. 2. Characteristics of Operations Research
3. 3. Applications and Scope of Operations Research
4. 4. Models and Methodology of Operations Research
5. 5. Limitations of Operations Research
6. 6. Linear Programming Problem (LPP)
- Concept and Formulation
- Graphical Method
- Simplex Method
- Maximization and Minimization Problems
- Big-M Method and Algorithm
UNIT – II : Transportation and Assignment Problems
7. 1. Transportation Problem – Introduction and Concept
8. 2. Mathematical Formulation of Transportation Problem
9. 3. Methods for Finding Initial Feasible Solution
- North-West Corner Rule (NWC)
- Least Cost Method (LCM)
- Vogel’s Approximation Method (VAM)
10.4. Methods for Finding Optimal Solution
- Stepping Stone Method
- MODI (u–v) Method
11.5. Degeneracy in Transportation Problem
12.6. Assignment Problem – Concept and Importance
13.7. Mathematical Formulation of Assignment Problem
14.8. Hungarian Method for Solving Assignment Problem
UNIT – III : Game Theory and Queuing Theory
15.1. Game Theory – Introduction and Concept
16.2. Two-Person Zero-Sum Game
17.3. Pure Strategies and Saddle Point
18.4. Mixed Strategies and Probability Approach
19.5. Applications of Game Theory in Management
20.6. Queuing Theory – Introduction
,21.7. Basic Structure of a Queuing Model
22.8. Kendall’s Notation (A/B/C : D/E System)
23.9. Queuing Models
- M/M/1 Infinite Queue Model
- M/M/1 Finite Queue Model
UNIT – IV : Network Analysis
24.1. Introduction to Network Analysis
25.2. Components of a Network
26.3. Constructing a Project Network Diagram (Activity on Node – AoN Notation)
27.4. Critical Path Method (CPM)
- Concepts, Steps, and Applications
- Calculation of EST, LST, EET, LET, Float and Slack
28.5. PERT (Program Evaluation and Review Technique)
- Concepts and Assumptions
- Expected Time Formula
- Variance and Standard Deviation
- Formula for Probability of Completion: P(Z ≤ (TS – TE) / √ΣV)
29.6. Applications of CPM and PERT in Management
UNIT 1: INTRODUCTION TO OPERATION RESEARCH
, A. Origin and Historical Development of
Operations Research
Operations Research (O.R.) is a branch of applied mathematics and
analytical science that deals with problem-solving and decision-making
in complex situations. Its origin lies in the practical necessity of solving real-
life, large-scale problems during World War II, which demanded scientific
management of limited resources such as manpower, equipment, aircraft,
and materials.
Before the war, decision-making in organizations was often based on
intuition or experience, rather than systematic analysis. However, the
increasing complexity of military operations during World War II — such as
planning aircraft deployment, detecting enemy submarines, optimizing radar
usage, and managing supply chains — made it essential to bring together
scientists and military experts to find logical, data-driven solutions. These
teams, formed primarily in Britain and the United States, were the first to
engage in what later became known as Operations Research.
In 1937, the term “Operations Research” was first used by the British Air
Ministry when they appointed a team of scientists to study how radar
equipment could be best utilized for air defense. These scientists analyzed
real battlefield problems, developed mathematical models, and provided
practical recommendations to the military. Their success was remarkable:
the improved use of radar helped Britain win the Battle of Britain by
enhancing early detection and interception of enemy aircraft.
During the same period, the U.S. Navy and Army also established research
teams to study convoy routing, anti-submarine tactics, and resource
distribution. The outcomes of these studies directly contributed to increased
military efficiency, reduced losses, and faster strategic responses. Thus, the
wartime success of O.R. established it as a vital scientific discipline.
After the war ended in 1945, industries realized that the same analytical
methods used for military efficiency could be applied to business and
management problems. Companies started using O.R. techniques for
production scheduling, inventory control, transportation optimization, and
RESEARCH
,BBA - OPERATIONS RESEARCH
INDEX
UNIT – I : Introduction to Operations Research
1. 1. Nature and Meaning of Operations Research
2. 2. Characteristics of Operations Research
3. 3. Applications and Scope of Operations Research
4. 4. Models and Methodology of Operations Research
5. 5. Limitations of Operations Research
6. 6. Linear Programming Problem (LPP)
- Concept and Formulation
- Graphical Method
- Simplex Method
- Maximization and Minimization Problems
- Big-M Method and Algorithm
UNIT – II : Transportation and Assignment Problems
7. 1. Transportation Problem – Introduction and Concept
8. 2. Mathematical Formulation of Transportation Problem
9. 3. Methods for Finding Initial Feasible Solution
- North-West Corner Rule (NWC)
- Least Cost Method (LCM)
- Vogel’s Approximation Method (VAM)
10.4. Methods for Finding Optimal Solution
- Stepping Stone Method
- MODI (u–v) Method
11.5. Degeneracy in Transportation Problem
12.6. Assignment Problem – Concept and Importance
13.7. Mathematical Formulation of Assignment Problem
14.8. Hungarian Method for Solving Assignment Problem
UNIT – III : Game Theory and Queuing Theory
15.1. Game Theory – Introduction and Concept
16.2. Two-Person Zero-Sum Game
17.3. Pure Strategies and Saddle Point
18.4. Mixed Strategies and Probability Approach
19.5. Applications of Game Theory in Management
20.6. Queuing Theory – Introduction
,21.7. Basic Structure of a Queuing Model
22.8. Kendall’s Notation (A/B/C : D/E System)
23.9. Queuing Models
- M/M/1 Infinite Queue Model
- M/M/1 Finite Queue Model
UNIT – IV : Network Analysis
24.1. Introduction to Network Analysis
25.2. Components of a Network
26.3. Constructing a Project Network Diagram (Activity on Node – AoN Notation)
27.4. Critical Path Method (CPM)
- Concepts, Steps, and Applications
- Calculation of EST, LST, EET, LET, Float and Slack
28.5. PERT (Program Evaluation and Review Technique)
- Concepts and Assumptions
- Expected Time Formula
- Variance and Standard Deviation
- Formula for Probability of Completion: P(Z ≤ (TS – TE) / √ΣV)
29.6. Applications of CPM and PERT in Management
UNIT 1: INTRODUCTION TO OPERATION RESEARCH
, A. Origin and Historical Development of
Operations Research
Operations Research (O.R.) is a branch of applied mathematics and
analytical science that deals with problem-solving and decision-making
in complex situations. Its origin lies in the practical necessity of solving real-
life, large-scale problems during World War II, which demanded scientific
management of limited resources such as manpower, equipment, aircraft,
and materials.
Before the war, decision-making in organizations was often based on
intuition or experience, rather than systematic analysis. However, the
increasing complexity of military operations during World War II — such as
planning aircraft deployment, detecting enemy submarines, optimizing radar
usage, and managing supply chains — made it essential to bring together
scientists and military experts to find logical, data-driven solutions. These
teams, formed primarily in Britain and the United States, were the first to
engage in what later became known as Operations Research.
In 1937, the term “Operations Research” was first used by the British Air
Ministry when they appointed a team of scientists to study how radar
equipment could be best utilized for air defense. These scientists analyzed
real battlefield problems, developed mathematical models, and provided
practical recommendations to the military. Their success was remarkable:
the improved use of radar helped Britain win the Battle of Britain by
enhancing early detection and interception of enemy aircraft.
During the same period, the U.S. Navy and Army also established research
teams to study convoy routing, anti-submarine tactics, and resource
distribution. The outcomes of these studies directly contributed to increased
military efficiency, reduced losses, and faster strategic responses. Thus, the
wartime success of O.R. established it as a vital scientific discipline.
After the war ended in 1945, industries realized that the same analytical
methods used for military efficiency could be applied to business and
management problems. Companies started using O.R. techniques for
production scheduling, inventory control, transportation optimization, and
