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Operations Research

Book Description

This book elucidates the basic concepts and applications of operations research. Written in a lucid, well-structured and easy-to-understand language, the key topics are explained with adequate depth and self-explanatory flow charts. A wide range of solved examples and end-of-chapter exercises makes this book an ideal companion for active learners.

Table of Contents

  1. Cover
  2. Title Page
  3. Contents
  4. About the Author
  5. Dedication
  6. Foreword
  7. Preface
  8. Chapter 1: Introduction
    1. 1.1 The History of Operations Research
    2. 1.2 The Meaning of Operations Research
    3. 1.3 Models of Operations Research
    4. 1.4 Scope of Operations Research
    5. 1.5 Phases of OR
    6. 1.6 Limitations of Operations Research
    7. Exercise Problems
    8. Review Questions
  9. Chapter 2: Linear Programming Problem (LPP)
    1. 2.1 Introduction
    2. 2.2 General Model of the Linear Programming Problem
    3. 2.3 Characteristics of an LPP
    4. 2.4 Assumptions of Linear Programming
    5. 2.5 Formulation of an LPP
    6. 2.6 Standard Form of an LPP
    7. 2.7 Solution to an LPP
    8. 2.8 Types of Possible Solutions to an LPP
    9. 2.9 Convex Set and Extreme Point
    10. 2.10 Graphical Solution to an LPP
    11. 2.11 Simplex Methods
    12. 2.12 Penalty Method/Big-M Method/Charnes Method
    13. 2.13 Two-phase Method
    14. 2.14 The Duality Concept in a Linear Programming
    15. 2.15 Dual Simplex Method (DSM)
    16. 2.16 The Revised Simplex Method (RSM)
    17. Exercise Problems
    18. Answers to the Exercise Problems
    19. Review Questions
  10. Chapter 3: Sensitivity Analysis (or) Post-Optimal Analysis
    1. 3.1 Introduction
    2. 3.2 Change in the Objective Function Co-efficient of a Non-basic Variable
    3. 3.3 Change in the Objective Function Co-efficient of a Basic Variable
    4. 3.4 Change in the Right-hand Side of a Constraint
    5. 3.5 Change in the Column of a Non-basic Variable
    6. 3.6 Adding a New Constraint
    7. 3.7 Adding a New Variable
    8. Exercise Problems
    9. Answers to the Exercise Problems
    10. Review Questions
  11. Chapter 4: Transportation Problem
    1. 4.1 Introduction
    2. 4.2 Conversion of a TP into an Equivalent LPP Form
    3. 4.3 Formulation of a Transportation Problem
    4. 4.4 Concepts of Feasibility Basicness, and Degeneracy in the Solution
    5. 4.5 Methods Used to Find the Solution to a Transportation Problem
    6. 4.6 Description of Various Methods to Find the Initial Basic Feasible Solution
    7. 4.7 Stepping Stone Method/Modified Distributive Method
    8. 4.8 Transshipment Problems
    9. 4.9 Sensitivity Analysis for Transportation Problem
    10. Exercise Problems
    11. Answers to the Exercise Problems
    12. Review Questions
  12. Chapter 5: Assignment Problem
    1. 5.1 Introduction
    2. 5.2 General Model of the Assignment Problem
    3. 5.3 Conversion into an Equivalent LPP
    4. 5.4 Solution to the Assignment Problem
    5. 5.5 Travelling Salesman Problem
    6. Exercise Problems
    7. Answers to the Exercise Problems
    8. Review Questions
  13. Chapter 6: PERT - CPM
    1. 6.1 Introduction
    2. 6.2 Method for Construction of a Network
    3. 6.3 Numbering the Nodes
    4. 6.4 Critical Path Method (CPM)
    5. 6.5 Project Evaluation Review Technique (PERT)
    6. 6.6 PERT-Cost
    7. 6.7 Resource Levelling
    8. Exercise Problems
    9. Answers to the Exercise Problems
    10. Review Questions
  14. Chapter 7: Sequencing
    1. 7.1 Introduction
    2. 7.2 Johnson’s Method (Rule)
    3. 7.3 Graphical Method
    4. Exercise Problems
    5. Answers to the Exercise Problems
    6. Review Questions
  15. Chapter 8: Queuing Theory
    1. 8.1 Introduction
    2. 8.2 Some Queuing Terminologies
    3. 8.3 Model : 1 Single Server Model with Infinite Queue (M/M/1): (∞/FCFS)
    4. 8.4 Model : 2 Single Server Model with Finite Queue (M/M/1): (N/FCFS)
    5. 8.5 Model : 3 Multi-server Model with Infinite Queue (M/M/C): (∞/FCFS)
    6. 8.6 Model : 4 Multi-server Model with Finite Queue (M/M/C): (N/FCFS)
    7. Exercise Problems
    8. Answers to the Exercise Problems
    9. Review Questions
  16. Chapter 9: Dynamic Programming
    1. 9.1 Introduction
    2. 9.2 Calculus Method to Solve a DPP
    3. 9.3 Tabular Method to Solve a DPP
    4. 9.4 DPP Application to Solve an LPP
    5. Exercise Problems
    6. Answers to the Exercise Problems
    7. Review Questions
  17. Chapter 10: Non-Linear Programming
    1. 10.1 Introduction
    2. 10.2 General Structure of an NLPP
    3. 10.3 Formulation of an NLPP
    4. 10.4 Methods to Solve an NLPP
    5. 10.5 Constrained Optimization with Inequality Constraints
    6. 10.6 Quadratic Programming Problem (QPP)
    7. 10.7 Wolfe’s Method to Solve a QPP
    8. 10.8 Beals Method to Solve a QPP
    9. Exercise Problems
    10. Answers to the Exercise Problems
    11. Review Questions
  18. Appendix A
  19. Appendix B
  20. Notes
  21. Acknowledgments
  22. Copyright
  23. Back Cover