Operations Research: An Introduction

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