##### OPERATION RESEARCH

Course Objective
After the completion of this course, students will be able to describe the basic components and fundamental principles of operation research and its application to industrial problems.

Course Outline

1. Introduction to operational research (6 hours)
1. Introduction to O.R.
1. System Orientation
2. Use of Interdisciplinary Teams in OR
3. Necessity Of OR In Business and Industry
4. Scope Of OR In Modern Management
5. OR and Decision Making
2. Overview of O.R.
1. Formulation of O.R. Models
2. Introduction to Different Techniques in OR
3. Simulation Modeling.

2. Linear programming (8 hours)
1. Formulation
1. Identification of Decision Variables
2. Constructing Objective Functions and Constraints
3. Assumptions
4. Practical Examples
2. Methods Of Solution
1. Graphical Method
2. Simplex Method (2-Phase and Big M Methods, Etc)
3. By Computer. (Using Public Domain Software)
3. Examples.

3. Duality theory and sensitivity analysis (8 hours)
1. Duality Theory
1. Existence of Dual of a LP Problem
2. Economic Interpretation of Duality.
3. Primal Dual Relationships in Formulation and Their Solutions.
2. Sensitivity Analyses or Post Optimality Analysis
1. Dual Simplex Method
2. Changes Affecting Feasibility
3. Changes Affecting Optimality
3. Examples.

4. Transportation models (TP) (6 hours)
1. The Transportation Algorithm
1. Formulation as a LP Problem
2. Determination of Initial Solutions
3. Stepwise Improvement to Obtain Optimal Solution
4. Special Cases Such As Multiple, Unbalanced, Degeneracy Etc
2. The Assignment Model
1. Formulation As TP
2. The Hungarian Method of Solution
3. Examples

5. Queuing models (7 hours)
1. Structure and Components of a Queuing Process
1. Examples of Real Queuing Systems
2. Queuing Theory Assumptions, Disciplines and Notations
3. Single and Multi Channel Queuing Models
4. Derivation of Necessary Formulae Under Steady-State Conditions Only
2. Example

6. Game theory (5 hours)
1. Formulation of Two-Person Zero-Sum Game
2. Solution of Simple Games
3. Mixed Strategy Games
1. Solving Using Graphical Method
2. Solving Using LP
4. Reduction Using Dominated Strategies
6. Examples.

7. Simulation (5 hours)
1. Simulation Process
2. Stochastic Simulation
1. Monte Carlo Sampling Process
2. Random Process Generation

3. Types of Simulation
4. Selected Simulation Application
1. Simulation of Queuing System
2. Simulation of Inventory System

Practicals:

1. Mathematical modeling of Blending Problems, transportation Problem, Trans-shipments problems.
2. Sensitivity Analysis of linear programming problems using spread sheet
3. Monte Carlo simulation using relevant software.
4. Simulation of queing system and inventory system.
5. Using spread sheet software for forecasting.
6. Preparing models using spread sheet.

Note: Students will be divided into groups and will be assigned a project task based on aforementioned topics.
References

1. Taha, Hamdy A., Seventh Edition ( with CD ROM ), “Operations Research, An Introduction”,
2. Bronson ,Richard, Naadimuthu ,Govindsami, Second Edition “Operations Research”,
3. Gupta, Prem Kumar, Hira, D.S., “Operations Research”
4. Sharma, J. K., ”Operation Research”
5. Rao, Adinath B., “Operations Research”
6. Panneerselvam, R., “Operations Research” PHP
7. Frederick Hillier Gerald, Lieberman, J., “Operations Research”, CBS
8. Goel, B. S. and Mittal, S.K, “Operations Research”, Pragati Prakashan Meerut, India

Evaluation Scheme:
The Questions will cover all the chapters in the syllabus. The evaluation scheme will be as indicated in the table below:

 Unit Chapters Hour Mark Distribution* 1 Introduction to operational research 6 8 2 Linear programming 8 20 3 Duality theory and sensitivity analysis 8 20 4 Transportation models (TP) 6 8 5 Queuing models 7 8 6 Game theory 5 8 7 Simulation 5 8 Total 45 80
*Note: There may be minor deviation in marks distribution.