Operations Research: An Introduction

Description

For junior/senior undergraduate and first-year graduate courses in Operations Research in departments of Industrial Engineering, Business Administration, Statistics, Computer Science, and Mathematics. Operations Research provides a broad focus on algorithmic and practical implementation of Operations Research (OR) techniques, using theory, applications, and computations to teach students OR basics. The book can be used conveniently in a survey course that encompasses all the major tools of operations research, or in two separate courses on deterministic and probabilistic decision-making. With.  Read more... Cover Title Page Copyright Page Contents What's New in the Tenth Edition Acknowledgments About the Author Trademarks Chapter 1 What is Operations Research? 1.1 Introduction 1.2 Operations Research Models 1.3 Solving the OR Model 1.4 Queuing and Simulation Models 1.5 Art of Modeling 1.6 More than Just Mathematics 1.7 Phases of an OR Study 1.8 About this Book Bibliography Problems Chapter 2 Modeling with Linear Programming 2.1 Two-Variable LP Model 2.2 Graphical LP Solution 2.2.1 Solution of a Maximization Model 2.2.2 Solution of a Minimization Model 2.3 Computer Solution with Solver and AMPL2.3.1 LP Solution with Excel Solver 2.3.2 LP Solution with AMPL 2.4 Linear Programming Applications 2.4.1 Investment 2.4.2 Production Planning and Inventory Control 2.4.3 Workforce Planning 2.4.4 Urban Development Planning 2.4.5 Blending and Refining 2.4.6 Additional LP Applications Bibliography Problems Chapter 3 The Simplex Method and Sensitivity Analysis 3.1 LP Model in Equation Form 3.2 Transition from Graphical to Algebraic Solution 3.3 The Simplex Method 3.3.1 Iterative Nature of the Simplex Method 3.3.2 Computational Details of the Simplex Algorithm3.3.3 Summary of the Simplex Method 3.4 Artificial Starting Solution 3.4.1 M-Method 3.4.2 Two-Phase Method 3.5 Special Cases in the Simplex Method 3.5.1 Degeneracy 3.5.2 Alternative Optima 3.5.3 Unbounded Solution 3.5.4 Infeasible Solution 3.6 Sensitivity Analysis 3.6.1 Graphical Sensitivity Analysis 3.6.2 Algebraic Sensitivity Analysis-Changes in the Right-Hand Side 3.6.3 Algebraic Sensitivity Analysis-Objective Function 3.6.4 Sensitivity Analysis With Tora, Solver, and AMPL 3.7 Computational Issues In Linear Programming 3.7 Computational Issues In Linear Programming133.7 Computational Issues In Linear Programming13 Bibliography Problems Chapter 4 Duality and Post-Optimal Analysis 4.1 Definition of the Dual Problem 4.2 Primal-Dual Relationships 4.2.1 Review of Simple Matrix Operations 4.2.2 Simplex Tableau Layout 4.2.3 Optimal Dual Solution 4.2.4 Simplex Tableau Computations 4.3 Economic Interpretation of Duality 4.3.1 Economic Interpretation of Dual Variables 4.3.2 Economic Interpretation of Dual Constraints 4.4 Additional Simplex Algorithms 4.4.1 Dual Simplex Algorithm 4.4.2 Generalized Simplex Algorithm4.5 Post-Optimal Analysis 4.5.1 Changes Affecting Feasibility 4.5.2 Changes Affecting Optimality Bibliography Problems Chapter 5 Transportation Model and Its Variants 5.1 Definition of the Transportation Model 5.2 Nontraditional Transportation Models 5.3 The Transportation Algorithm 5.3.1 Determination of the Starting Solution 5.3.2 Iterative Computations of the Transportation Algorithm 5.3.3 Simplex Method Explanation of the Method of Multipliers 5.4 The Assignment Model 5.4.1 The Hungarian Method