Operations research [electronic resource] : an introduction

Cover Contents Foreword Preface About the Author Chapter 1: Introduction 1.1 The History of Operations Research 1.2 The Meaning of Operations Research 1.3 Models of Operations Research 1.4 Scope of Operations Research 1.4.1 Agriculture 1.4.2 In Organisation/Industry 1.4.3 In Military Operations 1.4.4 Planning 1.4.5 In Transport 1.4.6 In Hospitals 1.4.7 In Production Management 1.4.8 In Marketing 1.4.9 In Finance 1.4.10 L.I.C. 1.5 Phases of OR 1.6 Limitations of Operations Research Exercise Problems Review Questions Chapter 2: Linear Programming Problem (LPP) 2.1 Introduction 2.2 General Model of the Linear Programming Problem 2.3 Characteristics of an LPP 2.4 Assumptions of Linear Programming 2.4.1 Limitations of Linear Programming 2.5 Formulation of an LPP 2.6 Standard Form of an LPP 2.6.1 Conversion of an LPP into Standard Form with Maximization Objective 2.7 Solution to an LPP 2.8 Types of Possible Solutions to an LPP 2.8.1 Basic Solution 2.8.2 Basic Feasible Solution 2.8.3 Basic Infeasible Solution 2.8.5 Unique Optimum Solution 2.8.6 Multiple Optimum Solution 2.8.7 Basic and Non-Basic Variables 2.8.8 Degenerate Solution 2.8.4 Optimal Solution 2.9 Convex Set and Extreme Point 2.9.1 Important Points to be Remembered 2.10 Graphical Solution to an LPP 2.11 Simplex Methods 2.11.1 Simplex Method-I/Ordinary Simplex Method 2.12 Penalty Method/Big-M Method/Charnes Method 2.13 Two-phase Method 2.14 The Duality Concept in a Linear Programming 2.14.1 Definition of the Dual problem 2.14.2 Standard Form of the Primal 2.14.3 Standard Form of the Dual 2.14.4 Structural and Computational Relationship Between Primal and Dual Problems 2.14.5 In Matrix Notation (Primal & Dual) 2.14.6 Shadow Price (Dual Price/Accounting Price) 2.14.7 Economic Importance of Shadow Price 2.15 Dual Simplex Method (DSM) 2.15.1 Canonical Form of an LPP 2.16 The Revised Simplex Method (RSM) 2.16.1 Type 1 2.16.2 Type-II 2.16.3 Type-III Exercise Problems Answers to the Exercise Problems Review Questions Chapter 3: Sensitivity Analysis (or) Post-Optimal Analysis 3.1 Introduction 3.2 Change in the Objective Function Co-efficient of a Non-basic Variable 3.3 Change in the Objective Function Co-efficient of a Basic Variable 3.4 Change in the Right-hand Side of a Constraint 3.5 Change in the Column of a Non-basic Variable 3.6 Adding a New Constraint 3.7 Adding a New Variable Exercise Problems Answers to the Exercise Problems Review Questions Chapter 4: Transportation Problem 4.1 Introduction 4.1.1 The Transportation Problem can be Described as Follows 4.2 Conversion of a TP into an Equivalent LPP Form 4.3 Formulation of a Transportation Problem 4.4 Concepts of Feasibility Basicness, and Degeneracy in the Solution 4.4.1 Basic and Non-basic Cells 4.5 Methods Used to Find the Solution to a Transportation Problem 4.6 Description of Various Methods to Find the Initial Basic Feasible Solution 4.6.1 North West Corner Rule 4.6.2 Row Minima Method 4.6.3 Column Minima Method 4.6.4 Least Cost Method/Matrix Minima Method 4.6.5 Vogel’s Approximation Method 4.6.6 Effectiveness of Various Methods 4.7 Stepping Stone Method/Modified Distributive Method 4.8 Transshipment Problems 4.9 Sensitivity Analysis for Transportation Problem 4.9.1 Change in the Objective Function Coefficient by a Non-basic Variable 4.9.2 Change in the Objective Function Coefficient of a Basic Variable 4.9.3 Increasing Both Supply Si and Demand dj by Δ Exercise Problems Answers to the Exercise Problems Review Questions Chapter 5: Assignment Problem 5.1 Introduction 5.2 General Model of the Assignment Problem 5.3 Conversion into an Equivalent LPP 5.4 Solution to the Assignment Problem 5.5 Travelling Salesman Problem Exercise Problems Answers to the Exercise Problems Review Questions Chapter 6: PERT - CPM 6.1 Introduction 6.1.1 Activity 6.1.2 Activity Duration/Activity Time 6.1.3 Event 6.1.4 Network/Arrow Diagram of a Project 6.2 Method for Construction of a Network 6.3 Numbering the Nodes 6.3.1 Dummy Activity 6.3.2 Precedence Relationships 6.4 Critical Path Method (CPM) 6.4.1 ES and EC Time of an Activity 6.4.2 Latest Start (LS) and Latest Completion (LC) Time of an Activity 6.4.3 Total Slack (TS) 6.4.4 Free Slack (FS) 6.4.5 Independent Float (IF) 6.4.6 Critical Activity and Critical Path 6.5 Project Evaluation Review Technique (PERT) 6.6 PERT-Cost 6.6.1 Crashing 6.6.2 Project Cost 6.7 Resource Levelling Exercise Problems Answers to the Exercise Problems Review Questions Chapter 7: Sequencing 7.1 Introduction 7.1.1 Assumptions 7.2 Johnson's Method (Rule) 7.3 Graphical Method Exercise Problems Answers to the Exercise Problems Review Questions Chapter 8: Queuing Theory 8.1 Introduction 8.2 Some Queuing Terminologies 8.2.1 The Input/Arrival Process 8.2.2 Queue Discipline 8.2.3 Service Mechanism 8.2.4 Service Channel 8.2.5 Maximum Capacity of the Queue 8.2.6 Classification of Queues 8.2.7 Methods Used to Solve a Queuing Situation 8.3 Model : 1 Single Server Model with Infinite Queue (M/M/1): (∞/FCFS) 8.4 Model : 2 Single Server Model with Finite Queue (M/M/1): (N/FCFS) 8.5 Model : 3 Multi-server Model with Infi nite Queue (M/M/C): (∞/FCFS) 8.6 Model : 4 Multi-server Model with Finite Queue (M/M/C): (N/FCFS) Exercise Problems Answers to the Exercise Problems Review Questions Chapter 9: Dynamic Programming 9.1 Introduction 9.1.1 Methods Used to Solve a DP 9.1.2 Characteristics of a DPP 9.1.3 Merits and Demerits of a DPP 9.1.4 Construction of a Recursive Equation 9.2 Calculus Method to Solve a DPP 9.3 Tabular Method to Solve a DPP 9.4 DPP Application to Solve an LPP Exercise Problems Answers to the Exercise Problems Review Questions Chapter 10: Non-Linear Programming 10.1 Introduction 10.2 General Structure of an NLPP 10.3 Formulation of an NLPP 10.4 Methods to Solve an NLPP 10.4.1 Lagrangian Method for Equality Constraints 10.4.2 Sufficient Conditions 10.4.3 Constrained Optimization with Two or More Equality Constraints 10.5 Constrained Optimization with Inequality Constraints 10.5.1 Kuhn-Tucker Conditions 10.6 Quadratic Programming Problem (QPP) 10.7 Wolfe's Method to Solve a QPP 10.8 Beals Method to Solve a QPP Exercise Problems Answers to the Exercise Problems Review Questions Appendix A Appendix B Index