Operations Research

This comprehensive book provides the students with the basic knowledge of the processes involved in operations research and discusses the techniques of solutions to problems and their applications in daily life.

Beginning with an overview of the operations research models and decision-making, the book describes in detail the various optimization techniques such as linear and non-linear programming, integer linear programming, dynamic programming, genetic programming, and network techniques such as PERT (program evaluation review technique) and CPM (critical path method). It also explains the transportation and assignment problems, queuing theory, games theory, sequencing, replacement and capital investment decisions and inventory. Besides, the book discusses the Monte Carlo simulation techniques for solving queuing, demand forecasting, inventory and scheduling problems and elaborates on genetic algorithms.

Each mathematical technique is dealt with in two parts. The first part explains the theory underlying the methodology of solution to problems. The second part illustrates how the theory is applied to solve different kinds of problems.

This book is designed as a textbook for the undergraduate students of mechanical engineering, electrical engineering, production and industrial engineering, computer science and engineering and information technology. Besides, the book will also be useful to the postgraduate students of production and industrial engineering, computer applications, business administration, commerce, mathematics and statistics.

Preface

1. Introduction to Operations Research Models and Decision-Making

2. Linear Programming: Basic Concepts

3. Graphical Method

4. Simplex Method

5. Big M Method

6. Duality in Linear Programming

7. Sensitivity Analysis

8. Revised Simplex Method

9. Two-phase Simplex Method

10. Dual Simplex Method

11. Integer Linear Programming: Branch and Bound Algorithms

12. Integer Linear Programming: Gomory Cutting Plane Method

13. Transportation Problem

14. Assignment Model

15. Non-linear Programming:Classical Optimization Techniques

16. Non-linear Programming with Constraints Graphical Solution

17. Non-linear Programming: Multivariable Optimization with Equality Constraints: Lagrange Multipliers Method

18. Non-linear Programming: Multivariable Optimization with Inequality Constraints: Kuhn–Tucker Conditions

19. Non-linear Programming: Quadratic Programming and Separable Programming

20. Search Methods (Non-linear Programming)

21. Sequencing

22. Replacement and Capital Investment Decisions

23. Inventory

24. Theory of Games

25. Queueing Theory (Waiting Lines)

26. Network Problems

27. Network Techniques: Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT)

28. Dynamic Programming

29. Monte Carlo Simulation

30. Genetic Algorithms

31. Genetic Programming

Appendices

Index