# Operations Research

ISBN: 9788126556380

604 pages

eBook also available for institutional users

## Description

This is the first Indian book that shows applications of simple topics in Mathematics, ranging from linear functions, quadratic functions, concave and convex functions, sequences, combinatorial analysis to help Indian practicing manager in stating, defining, structuring, and resolving complex managerial problems. Extensive use of MS Excel is made to help the readers in carrying out complicated computations without any errors. The appendices at the end of chapters provide mathematical formulations for readers who wish to get into the details. Many real-life cases to sharpen the readers' skills in applying the ideas of Mathematics for analysis and resolution of unstructured problems are included.

Acknowledgements

Brief Contents

Part I

1. Management Functions, Decisions and Need for Analytical Aids

1.1 Illustrations

1.2 Anatomy of Decision Problem

1.3 The Role of Mathematics

1.4 A Preview of Chapters to Follow

1.5 Concluding Remarks

2. Mathematical Representation of Consequences: Functions

2.1 Introduction

2.2 Measuring Results of Alternatives

2.3 Sets and Related Concepts

2.4 Function

2.5 Some Simple Functions and Applications

2.6 Piecewise Linear Functions

2.7 Loss Functions

2.8 Graphs of Functions

2.9 Some More Results About Linear Functions

2.10 Intersection of Two Lines

3. Representation of Consequences: Some Special Functions

3.1 Introduction

3.2 Quadratic Functions

3.3 Graphs of Quadratic Functions

3.4 Behaviour of a Quadratic Function

3.5 Zeroes of Quadratic Function (Roots of a Quadratic Equation)

3.6 Exponential Functions

3.7 Logarithmic Functions

3.8 Sequences

3.9 Arithmetic Progression

3.10 Geometric Progression

3.11 Functions of Many Variables

4. Some Methods of Enumerating Alternatives, Permutations, Combinations

4.1 Introduction

4.2 Illustrative Examples of Enumeration

4.3 Ideas of Ordered Pairs and Multiplets

4.4 Formulae for Counting the Number of Available Choices

4.5 Applications to Occupancy Problems

4.6 Applications to Theory of Runs

4.7 Binomial Theorem

5. Linear Programming: A Class of Optimisation Problems

5.1 Introduction

5.2 Linear Programming: Formulation of Problems

5.3 General Formulation of Linear Programming Problems

5.4 Graphical Solutions to Linear Programming Problems

5.5 Primal and Dual Problems

5.6 Primal–Dual Relationship

5.7 Solutions to the Food Problem

5.8 Interpretations for Dual Variables

5.9 History of Linear Programming

5.10 Concluding Remarks

6. Transportation Problem

6.1 Introduction

6.2 Nature of Problem

6.3 Computational Procedure

6.4 Starting Solution and Test for Optimality of the Solution

6.5 Modifications in Solution Procedures to Deal with Special Situations

7. Transshipment Problem

7.1 Introduction

7.2 Transshipment Problem With Only Simple Pure Depots

7.3 Method 1

7.4 Method 2

8. Programme Evaluation Review Technique and Critical Path Method

8.1 Introduction

8.2 Project, Interrelated Activities, and Sequencing of Activities

8.3 Application of Linear Programming for the Sequencing of Activities

8.4 Determination of Critical Path Through Computation of Early Start, Early Finish, Late Start, and Late Finish

8.5 Total, Free, and Independent Float

8.6 Critical Path Determination Through Office Project

8.7 Critical Path Determination with Excel and VBA

8.8 Programme Evaluation and Review Technique (PERT)

8.9 Crashing of Activities

9. Integer Programming

9.1 Introduction

9.2 Background, Integer Programming Problems Where the Decision Variables Take Binary Values Either 0 or 1

9.3 Fixed Charge Problem

9.4 Earlier Method of Cutting Planes to Obtain an Integer Solution

9.5 Introduction to “Solver”: A Computer Package for Solving Integer Programming Problems

10. Sequences: Ideas and Applications

10.1 Introduction

10.2 Definition of a Sequence and Arithmetic Progression of a Sequence with a Special Structure

10.3 Arithmetic Progression

10.4 Geometric Progression – A Sequence with Special Structure

10.5 Capital Budgeting Decisions

Part II

11. Probability Theory: Ideas and Applications

11.1 Introduction

11.2 Some Illustrative Examples where Chance Factors Play a Major Role in Getting the Tangible Results

11.3 Sample Space: An Introduction

11.4 Relations among Events

11.5 Probabilities in Discrete Sample Spaces, Definitions, and Rules

12. Conditional Probability: Ideas and Applications

12.1 Introduction

13. Random Variables, Summary Measures, and Measures of Dispersion

13.1 Random Variables

13.1.1 Idea of Unknown Quantities

13.2 Summary Measures, Expectation, Fractiles, and Measures of Dispersion

13.3 Joint Distribution of Random Variables, Covariance, Independence of Two Random Variables, and Conditional Probabilities

13.4 Conditional Probabilities and Conditional Expectations

14. Binomial, Poisson, and Normal Distributions

14.1 Introduction

14.2 Binomial Distribution

14.3 Poisson Distribution

14.4 Normal Distribution

14.5 Exponential Distribution

15. The Birth and Death Process

15.1 Introduction

15.2 Illustrative Examples

15.3 Introduction to the Poisson Process

15.4 The Birth and Death Process

15.5 Exponential Holding Times

15.6 Formulae for Determining the Operating Characteristics of the System

15.7 Servicing of Machines

16. Decision Theory

16.1 Introduction

16.2 Definition of Sensitivity and Break-Even Point

16.3 Methods Commonly Used for Resolving a Decision Problem Under Uncertainty

16.4 Ideas of Decision Tree for Resolving Decision Problems Under Uncertainty

16.5 Practical Applications of EMV

16.6 Comparison of Lotteries, Preference Functions, and Certainty Equivalent

16.7 EMV not an Acceptable Criteria for Choice and Search for Other Criterion

16.8 Cash Equivalent, Risk Preferences

16.9 Concluding Remarks

17. Loss Functions with Special Structures

17.1 Introduction

17.2 Newsboy Problem

17.3 A Two-Action Problem with Linear Losses

17.4 Quadratic Loss Function

17.5 A Reservation Problem

17.6 A Scrap Allowance Problem

18. Test of Hypothesis, Point and Interval Estimation

18.1 Introduction

18.2 An Illustrative Example

18.3 Formal Approach

18.4 Point and Interval Estimation

18.5 Determination of Sample Size Considering the Decision Maker’s Prior Judgments and Economics of Sampling

19. Inventory

19.1 Introduction

19.2 Modifications in the EOQ Formula

19.3 EOQ Formula for Backorders

19.4 Organisation’s Minimum Cost of Maintaining Inventory when the Customer Allows Backordering

19.5 Lead-Time between Ordering and Getting Supplies, Backordering of Orders not Allowed

19.6 Precautionary Motive for Holding Inventory, Static Inventory Management when Demand is Uncertain

19.7 Deciding Reorder Level When the Lead-Time is Uncertain

19.8 The Speculative Motive

19.9 In-Process Inventory in Textile Mill

19.10 Note on Material Requirement Planning (MRP)

20. Game Theory

20.1 Introduction

20.2 Zero-Sum Games

21. Pricing of Water – A Subset of Scarce Natural Resource

21.1 Introduction

21.2 Arvind’s Decision to Recycle Treated Water, Avoiding Pollution and Saving Scarce Resource

21.3 Concluding Remarks

22. Duality Theory

22.1 Introduction

22.2 Primal and Dual Problem

Summary

Problems

Index

I must commend Wiley on bringing out a very good book on Operations Research authored by Prof. Mote and Prof. Mahadevan. It is indeed a valuable resource for post graduate students and practitioners!”

-------- Prof. Debabrata Ghosh