Operations Research

Title
Contents
1. Linear Programming–I
	1.1 Linear Models
	1.2 Graphical Solution and Fundamentals
	1.3 Mathematical Facts
	1.4 Fundamentals of Simplex and Examples
	1.5 Special Cases and Methods
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
2. Linear Programming–II
	2.1 Primal and Dual
	2.2 Sensitivity Analysis
	2.3 Goal Programming
	2.4 Master Problems—Primal and Dual
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
3. Transportation Problem
	3.1 Mathematical Model and Characteristics of Transportation Problem
	3.2 Methods of Finding Basic Feasible Solution (BFS)
	3.3 Unbalanced Transportation Problem
	3.4 Degeneracy in Transportation Problem
	3.5 How to Solve Degeneracy?
	3.6 Modified Distribution Method (MODI Method)
	3.7 Loops and Optimization
	3.8 Trans-shipment Problem
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
4. Assignment Problem
	4.1 Illustration 1
	4.2 Mathematical Model
	4.3 Some Additional Features of A.P.
	4.4 Solution Method
	4.5 Solution of Illustration 1
	4.6 Assignment Techniques and Maximization Problem
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
5. Integer Programming Problem
	5.1 Graphical Solution and Discussion
	5.2 Gomory’s Cutting Plane Method and Geometric Meaning
	5.3 Illustrations
	5.4 Branch and Bound Method
	5.5 Zero–One Programming
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
6. Special Types of Problems and Applications
	6.1 Graph Theory
	6.2 Travelling Salesman’s Problem
	6.3 Chinese Postman’s Problem
	6.4 Minimal Spanning Tree (MST)
	6.5 Shortest Path Problems
	6.6 Maximal Flow and Minimum Cut
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
7. Sequencing Problems
	7.1 Important Features of Sequencing Problem
	7.3 Different Types of Problems
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
8. Simulation
	8.1 What is Simulation?
	8.2 Different Types of Models
	8.3 Nature of Simulation
	8.4 Application of Simulation
	8.5 Random Numbers
	8.6 Monte-Carlo Simulation
	8.7 Illustrations
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
9. Game Theory
	9.1 Some Definitions Related to Game Theory
	9.2 Saddle Point—A Classical Approach
	9.3 Mixed Strategy and Pure Strategy
	9.4 Dominance Principles
	9.5 Solution Procedures
	9.6 Application of Game Theory in Finance and Business
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
10. Replacement Theory
	10.1 Replacement of Items with Increasing Maintenance Cost and Falling Scrap Value
	10.2 Replacement in the Case when Net Present Worth of Money Value is Considered
	10.3 Replacement of Items that Suddenly Fail
	10.4 Staff Replacement and Mortality Problems
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
11. Queuing Theory
	11.1 Components of ‘Q’ System
	11.2 Three Point Program
	11.3 Additional Points
	11.4 Why do we Study the ‘Q’ System?
	11.5 Empirical ‘Q’ Models
	11.6 Operating Characteristic of a ‘Q’ System
	11.7 Single Channel; Poisson Arrival; Exponential Service Rate
	11.8 List of Formulas/Derived Results
	11.9 Single Channel System and Minimum Cost Plan
	11.10 Multi-channel System: (M/M/K) Type
	11.11 Illustrations
	11.12 Other Waiting Line Models
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
12. Inventory Management
	12.1 Types of Inventory
	12.2 What Inventory can Cause?
	12.3 Classes of Inventory System
	12.4 Demand Pattern—An Overview
	12.5 Different Types of Additional Costs
	12.6 Classification of Inventory System
	12.7 Different Models
	12.8 Illustrations
	12.9 Essentials of ‘Q’ System: Fixed Order Quantity System— Reorder level, Lead time demand, Reserve stock, and Safety stock
	12.10 Periodic Review System
	12.11 Inventory Model with Price Breaks
	12.12 Inventory Models with Probabilistic Demand
	12.13 Multiple Items with Storage Limitations
	12.14 Inventory Classification System
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
13. Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT)
	13.1 Main Features of Project
	13.2 Basic Differences—CPM & PERT
	13.3 Activity
	13.4 Network
	13.5 Forward Pass and Backward Pass
	13.6 Floats and Critical Path
	13.7 PERT
	13.8 Crashing
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
14. Dynamic Programming
	14.1 Dynamic Programming and its Characteristics
	14.2 Formulation of Dynamic Programming Problem
	14.3 Application Area of Dynamic Programming
	14.4 Useful Graph of Alternatives
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
15. Non-Linear Programming Problems
	15.1 Different Classes
	15.2 Constrained Optimization Problem
	15.3 Separable Programming
	15.4 Solution Methods (Unconstrained optimization) Illustrations
	15.5 Constrained Optimization
	Additional Questions for Practice (with Hints and Answers)
	Points to Remember
	Exercises
	Numerical Problems
16. Decision Theory and Markov Chains
	16A DECISION THEORIES
	16A.1 Three Steps Program
	16A.2 Decision–making
	16A.3 Decision-making under Uncertainty
	16A.4 Decision-making Through Use of Incremental Analysis
	16A.5 Bayesian Approach to Decision Theory
	16A.6 Decision Tree Approach in Decision-making
	16B MARKOV CHAINS AND ANALYSIS
	16B.1 Introduction
	16B.2 Markov Process and Markov Chain
	16B.3 Application Area
	16B.4 Markov Chains
	16B.5 Markov Process
	Additional Questions for Practice (with Hints and Answers)
	Exercises
	Numerical Problems
Appendix Statistical and other Tables
Index