## Course Description

Operational Research is the study of scientific approaches to decision-making. Through mathematical modeling, it seeks to design, improve, and operate complex systems in the best possible way. The mathematical tools used for the solution of such models are either deterministic or stochastic, depending on the nature of the system modeled. In addition, the course will cover powerful modeling and solution techniques for decision-making problems used by many successful companies to help them save or earn millions of dollars. The module includes topics such as linear programming, transportation, assignment, inventory control, replacement theory, and game theory. Analytic techniques and computer packages will be used to solve problems faced by business managers in decision environments.

## Course Objective

The general objectives of this course are to provide a broad orientation of the field of optimization, with emphasis on basic theory and methods for continuous and discrete optimization problems in finite dimensions. It also provides insight into its use for analyzing practical optimization problems.

## Units

**Unit 1: Introduction to Operations Research (5 Hrs)**

- Introduction
- History of Operations Research
- Stages of Development of Operations Research
- Relationship between Manager and OR Specialist
- OR Tools and Techniques
- Applications of Operations Research
- Limitations of Operations Research

**Unit 2: Linear Programming Problem (10 Hrs)**

- Introduction to Linear Programming
- Linear Programming Problem Formulation
- Formulation with Different Types of Constraints
- Graphical Analysis of Linear Programming
- Graphical Linear Programming Solution
- Multiple Optimal Solutions
- Unbounded Solution
- Infeasible Solution
- Basics of Simplex Method
- Simplex Method Computation
- Simplex Method with More Than Two Variables
- Primal and Dual Problems
- Economic Interpretation

**Unit 3: Transportation and Assignment Problem (8 Hrs)**

- Transportation Problems Definition
- Linear Form
- Solution Methods:
- North West Corner Method
- Least Cost Method
- Vogel’s Approximation Method

- Degeneracy in Transportation
- Modified Distribution Method
- Unbalanced Problems and Profit Maximization Problems
- Transshipment Problems
- Assignment Problem Structure and Solution:
- Short-Cut Method (Hungarian Method)
- Unbalanced Assignment Problem
- Infeasible Assignment Problem
- Maximization in an Assignment Problem
- Crew Assignment Problem

**Unit 4: Queuing Theory (6 Hrs)**

- Basis of Queuing Theory
- Elements of Queuing Theory
- Kendall’s Notation
- Operating Characteristics of a Queuing System
- Classification of Queuing Models

**Unit 5: Inventory Control (6 Hrs)**

- Inventory Classification
- Different Costs Associated with Inventory
- Economic Order Quantity
- Inventory Models with Deterministic Demands
- ABC Analysis

**Unit 6: Replacement Theory (6 Hrs)**

- Introduction
- Replacement of Capital Equipment Depreciated Over Time
- Replacement by Alternative Equipment
- Group and Individual Replacement Policy

**Unit 7: Game Theory (7 Hrs)**

- Introduction
- Characteristics of Game Theory
- Two Person, Zero Sum Games
- Pure Strategy
- Dominance Theory
- Mixed Strategies (2×2, mx2)
- Algebraic and Graphical Methods

**Teaching Methods**

The general teaching pedagogy includes:

- Class Lectures
- Presentations
- Group Works
- Case Studies
- Guest Lecturers
- Research Works
- Project Works
- Assignments (Theoretical and Practical)

The teaching faculty will determine the choice of teaching pedagogy and is encouraged to select software tools as per the requirements of topics for practical activities.

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## References / Suggested Readings
- Hillier, F.S., & Lieberman, G.J. (1995). _Introduction to Operations Research_, 7th edition. The McGraw-Hill Companies, Inc.
- Natarajan, A. M., Balasubramani, P., & Tamilarasi, A. (2007). _Operations Research_. Pearson Education Inc.
- Sharma, J.K. (2009). _Operational Research: Theory and Application_. Macmillan Publishers India Ltd.
- Taha, H.A. (2017). _Operations Research: A Introduction_, 10th edition, Global edition. Pearson Education, Inc. Pearson Prentice Hall.
- Wagner, H. N. (2003). _Operations Research_, Prentice Hall.
- Vohra, N. D. (2003). _Operations Research_, Tata McGraw-Hill.
- Winston, L.W. (2004). _Operations Research: Applications and Algorithms_, 4th edition. Indian University.
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