Operations research

Title
Foreword
Preface
Contents
1 Operations Research
	1.1 What is Operations Research?
	1.2 Characteristics of OR
	1.3 Phases of OR
	1.4 Scope of OR
	1.5 Drawbacks and Difficulties of OR
2 Linear Programming
	2.1 Introduction
	2.2 Formulation
	2.3 Graphical Method of Solution
	Exercises
	Answers
3 Simplex Method
	3.1 Introduction
	3.2 Simplex Method
	Short Answer Questions
	Exercises
	Answers
4 Artificial Variables
	4.1 Artificial Variables
	4.2 Big M Method (Charne’s Penalty Method)
	4.3 Two-Phase Method
	Short Answer Questions
	Exercises
	Answers
5 Dual Simplex Method
	5.1 Dual Simplex Method
	Short Answer Questions
	Exercises
	Answers
6 Duality
	6.1 Rules for Writing the Dual of a Primal
	6.2 Duality Theorems
	6.3 Principle of Duality
	6.4 Economic Interpretation of the Dual
	6.5 Complementary Slackness Theorem
	Short Answer Questions
	Exercises
	Answers
7 Revised Simplex Method
	7.1 Step-by-Step Procedure
	7.2 Advantages of Revised Simplex Method Over the Ordinary Simplex Method
	Exercises
	Answers
8 Bounded Variable Technique
	8.1 Step-by-Step Procedure of Bounded Variable Technique
	Exercises
	Answers
9 Integer Programming
	9.1 Gomary’s Cutting Plane Method
	9.2 Gomary’s Algorithm (Step-by-Step Procedure)
	9.3 Mixed Integer Programming
	9.4 Branch and Bound Method
	Exercises
	Answers
10 Sensitivity Analysis
	10.1 Discrete Changes in cj
	10.2 Discrete Changes in bi
	10.3 Changes in the Matrix Elements aij
	10.4 Addition of a Variable
	10.5 Addition of a Constraint
	Exercises
	Answers
11 Transportation Problem
	11.1 Mathematical Formulation
	11.2 Initial Basic Feasible Solution
	11.3 Testing for Optimality
	11.4 Optimization—MODI Method (Modified Distribution Method)
	11.5 Degeneracy
	11.6 Unbalanced Transportation Problem
	11.7 Maximization Type
	Exercises
	Answers
12 Assignment Problems
	12.1 What is an Assignment Problem?
	12.2 Mathematical Formulation
	12.3 Method of Solving an AP
	12.4 Step-by-Step Procedure of Hungarian Method (Minimization Problem)
	12.5 Maximization Assignment Problem
	12.6 Unbalanced Assignment Problem
	12.7 Travelling Salesman Problem
	Exercises
	Answers
13 Decision Theory
	13.1 What is Decision Theory?
	13.2 Steps in Decision Making
	13.3 Maximin and Maximax Criteria
	13.4 Hurwicz Criterion and Laplace Criterion
	13.5 Minimax Regret Criterion (Savage Criterion)
	13.6 Decision-Making Under Risk
	13.7 Expected Opportunity Loss Criterion (EOL)
	Exercises
	Answers
14 theory of Games
	14.1 Introduction
	14.2 Two-Person Zero Sum Games
	14.3 Games with Saddle Point (Pure Strategy)
	14.4 Games without Saddle Points (Mixed Strategy)
	14.5 Formula for Finding the Value of the Game in Case of 2 × 2 Games without Saddle Point
	14.6 Dominance Property
	14.7 Graphical Method
	14.8 Algebraic Method
	14.9 Linear Programming Method
	Exercises
	Answers
15 Dynamic Programming
	15.1 Introduction
	15.2 Dynamic Programming Method
	15.3 Applications to Mathematical Problems
	15.4 Solution of Linear Programming Problems
	Exercises
	Answers
16 Sequencing Problems
	16.1 Introduction
	16.2 Processing n Jobs through Two Machines
	16.3 Processing n Jobs on Three Machines
	16.4 Processing n Jobs through m Machines
	Exercises
	Answers
17 Queueing Theory
	17.1 Introduction
	17.2 Characteristics of a Queueing System
	17.3 Symbols and Assumptions
	17.4 Transient and Steady States
	17.5 Model I (M/M/1/• Queueing Model)
	17.6 Model 2—M/M/1/N (Queue with Finite Capacity N)
	17.7 Model 3—(Multichannel System) M/M/C/•
	17.8 Model 4—(Multichannel System with Limited Capacity) M/M/C/N
	Exercises
	Answers
18 Inventory Models
	18.1 Introduction
	18.2 Costs Involved in Inventory Control
	18.3 Characteristics of Inventory System
	18.4 Deterministic Inventory Models with no Shortage
	18.5 Probabilistic Model
	Exercises
	Answers
19 Replacement Models
	19.1 Introduction
	19.2 Replacement of Items which Deteriorate in Efficiency with Time
	19.3 Replacement of Items that Fail Completely
	Exercises
	Answers
20 Project Scheduling (PERT and CPM)
	20.1 Introduction
	20.2 Network Diagrams
	20.3 Critical Path Method
	20.4 PERT Calculations
	Exercises
	Answers
	Short Answer Questions
21 Simulation
	21.1 Introduction
	21.2 Event Type Simulation
	21.3 Monte–Carlo Technique
	Exercises
	Answers
Index