Operations Research
ISBN: 9788126556380
604 pages
eBook also available for institutional users
For more information write to us at: acadmktg@wiley.com
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