## Description

Operations Research is an analytical tool used to supplement managers in decision-making which is an important function of the management of any organization. This book deals with the application of quantitative techniques in Operations Research through a large number of examples which would aid students in understanding the optimization techniques in depth and managers in tackling different problems associated with decision-making such as determination of optimum quantity of products to be manufactured, quantity of products to be transported, assignment of work, selection of strategy and determination of optimum time.

## Table of Content

**Chapter 1 INTRODUCTION**

1.1 Origin and Development of Operations Research

1.2 Definition of OR

1.3 Areas of Application of OR

1.4 OR Methodology

1.5 Features and Limitations of OR

**Chapter 2 LINEAR PROGRAMMING**

2.1 Introduction

2.2 Formulation of Linear Programming Models

2.3 Graphical Solution of Linear Programming Problem (LPP)

Exercises

**Chapter 3 SIMPLEX METHOD**

3.1 Introduction

3.2 Slack and Surplus Variables

3.3 Basic Solution

3.4 Basic Feasible Solution

3.5 Optimum Basic Feasible Solution

3.6 Simplex Problem in Table Form

3.7 Minimisation Problem

3.8 Artificial Variable

3.9 Two-phase Method

3.10 Degeneracy in LPP

Exercises

**Chapter 4 DUAL SIMPLEX METHOD**

4.1 The Dual Problem

4.2 General Primal–Dual Pair

4.3 Formulation of a Dual Problem

4.4 Economic Interpretation of Dual Problem

4.5 Dual Simplex Method

Exercises

**Chapter 5 TRANSPORTATION PROBLEMS**

5.1 Introduction

5.2 Formulation of LPP

5.3 Methods of Obtaining Initial Basic Feasible Solution

5.4 Optimality Check

5.5 Balanced Transportation Problem

5.6 Degeneracy in Transportation Problem

5.7 Maximisation Problems

Exercises

**Chapter 6 ASSIGNMENT PROBLEMS**

6.1 Introduction

6.2 Hungarian Method

6.3 Ticking Method

6.4 Maximisation Problem

6.5 Travelling Salesman Problems

Exercises

**Chapter 7 GAME THEORY**

7.1 Introduction

7.2 Two-person Zero-sum Game

7.3 Pay-off Matrix

7.4 The Maximin and Minimax Principle

7.5 Saddle Point

7.6 Theory of Dominance

7.6.1 General Rule for Dominance

7.7 Mixed Strategy Game with 2×2 Pay-off Matrix and without Saddle Point

7.8 Graphical Solution

Exercises

**Chapter 8 NETWORK ANALYSIS**

8.1 Introduction

8.2 Basic Rules for Drawing Networks

8.3 Types of Activities

8.4 Fulkerson’s Rule

8.5 Critical Path in Network Analysis

8.6 Scheduling of Activities

8.7 Performance Evaluation and Review Technique (PERT)

8.8 Critical Path Method (CPM)

Exercises

**Chapter 9 QUEUING THEORY**

9.1 Introduction

9.2 Characteristics of Queuing System

9.3 Pure Birth Model

9.4 Pure Death Model

9.5 Steady-state Performance Analysis

9.6 Single-server Queuing Models

9.7 Multiple Server Models

Exercises

**Chapter 10 REPLACEMENT PROBLEM**

10.1 Introduction

10.2 Replacement of Items Whose Maintenance Cost Increases with Time and

Value of Money Remains Same During the Period

10.3 Replacement of Items Whose Maintenance Cost Increases with Time and

Value of Money also Changes with Time

10.4 Present Value Concept

10.5 Replacement of Items that Fail Completely

10.5.1 Individual Replacement Policy

10.5.2 Group Replacement Policy

10.6 Rate of Replacement and Total Cost in Group Replacement

10.7 Staff Problem

Exercises

**Chapter 11 DYNAMIC PROGRAMMING**

11.1 Introduction

11.2 Dynamic Programming System

11.3 Dynamic Programming for Profit Optimisation

**Chapter 12 SEQUENCING**

12.1 Introduction

12.2 Assumptions

12.3 n Jobs and 2 Machines

12.3.1 Algorithm

12.4 n Jobs and 3 Machines in the Order ABC

12.5 Two Jobs and n Machines

Exercises

**Chapter 13 INTEGER PROGRAMMING PROBLEMS**

13.1 Introduction

13.2 Gomory’s Constraint

13.3 Pure and Mixed Integer Programming Problems

13.4 Zero–one Programming Problem

13.5 Gomory’s All-integer Cutting Plane Method

13.6 Geometrical Interpretation of the Cutting Plane Method

13.7 Branch and Bound Method

Exercises

**Chapter 14 DECISION ANALYSIS **

14.1 Introduction

14.2 History of Decision Analysis

14.3 A Prototype Example

14.4 Decision-making without Experimentation

14.4.1 Maximin Principle

14.4.2 Most Likely Principle

14.4.3 Bayes’ Decision Rule

14.4.4 Sensitivity Analysis

14.5 Decision-making with Experimentation

14.5.1 A Prototype Example 1

14.5.2 A Prototype Example 2

14.6 The General Decision Tree Model

Exercises

**Chapter 15 METAHEURISTICS**

15.1 Introduction

15.2 Nature of Metaheuristics

15.3 A Travelling Salesman Problem

15.4 Tabu Search

15.4.1 Steps in Tabu Search Method

15.5 Spanning Tree

15.6 Simulated Annealing

**Chapter 16 SIMULATION**

16.1 Introduction

16.2 Simulation Process

16.3 Types of Simulation

16.3.1 Total Enterprise Simulation

16.3.2 Interactive Simulation

16.3.3 Non-interactive Simulation

16.3.4 Functional Simulation

16.3.5 Concepts Simulation

16.3.6 Planning Simulation

16.3.7 Process simulation

16.4 The Basic Steps in Simulation

16.5 When to use Simulation?

16.5.1 Type of Problem

16.5.2 Availability of Resources

16.5.3 Costs

16.5.4 Availability of Data

16.6 Monte Carlo Simulation

16.6.1 Steps in Monte Carlo Simulation

16.8 Advantages and Disadvantages of Simulation

16.8.1 Advantages

16.8.2 Disadvantages

Exercises

**Chapter 17 PROJECT MANAGEMENT**

17.1 Introduction

17.2 Phases of Project Management

17.2.1 Planning

17.2.2 Scheduling

17.2.3 Controlling

17.3 Work Breakdown Structure

17.4 Control Charts

17.5 Control Charts for Variables

17.5.1 Objectives of Control Charts for Variables

17.5.2 X-Chart and R-Chart

17.5 Limitations of Variable Charts

17.6 Control Charts for Attributes

17.7 P-Chart

17.7.1 Comparison of X- and R-Chart with P-Chart

17.7.2 Limitations of P-Chart

17.8 nP-Charts

17.9 Difference between Defect and Defective

17.9.1 Types of Defects

17.10 Control Charts for Defects

17.11 Control Charts for Defects Per Unit

• Exercises

• Appendix

• Bibliography

• Index

## About The Author

**B.J. Ranganath** is a distinguished professor with 45 years of teaching and research experience. He has authored books on Tool Engineering and Manufacturing Engineering, and has guided 12 Ph.D. students. He has published 250 technical papers in journals and conferences.

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