Operations research

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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