Introduction to Operations Research

Cover
Title Page
Copyright Page
About the Authors
About the Case Writers
Dedication
Table of Contents
Preface
CHAPTER 1 Introduction
	1.1 The Origins of Operations Research
	1.2 The Nature of Operations Research
	1.3 The Relationship between Analytics and Operations Research
	1.4 The Impact of Operations Research
	1.5 Some Trends that Should Further Increase the Future Impact of Operations Research
	1.6 Algorithms and OR Courseware
	Selected References
	Problems
CHAPTER 2 Overview of How Operations Research and Analytics Professionals Analyze Problems
	2.1 Defining the Problem
	2.2 Gathering and Organizing Relevant Data
	2.3 Using Descriptive Analytics to Analyze Big Data
	2.4 Using Predictive Analytics to Analyze Big Data
	2.5 Formulating a Mathematical Model to Begin Applying Prescriptive Analytics
	2.6 Learning How to Derive Solutions from the Model
	2.7 Testing the Model
	2.8 Preparing to Apply the Model
	2.9 Implementation
	2.10 Conclusions
	Selected References
	Problems
CHAPTER 3 Introduction to Linear Programming
	3.1 Prototype Example
	3.2 The Linear Programming Model
	3.3 Assumptions of Linear Programming
	3.4 Additional Examples
	3.5 Formulating and Solving Linear Programming Models on a Spreadsheet
	3.6 Formulating Very Large Linear Programming Models
	3.7 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 3.1 Reclaiming Solid Wastes
	Previews of Added Cases on Our Website
		Case 3.2 Cutting Cafeteria Costs
		Case 3.3 Staffing a Call Center
		Case 3.4 Promoting a Breakfast Cereal
		Case 3.5 Auto Assembly
CHAPTER 4 Solving Linear Programming Problems: The Simplex Method
	4.1 The Essence of the Simplex Method
	4.2 Setting Up the Simplex Method
	4.3 The Algebra of the Simplex Method
	4.4 The Simplex Method in Tabular Form
	4.5 Tie Breaking in the Simplex Method
	4.6 Reformulating Nonstandard Models to Prepare for Applying the Simplex Method
	4.7 The Big M Method for Helping to Solve Reformulated Models
	4.8 The Two-Phase Method is an Alternative to the Big M Method
	4.9 Postoptimality Analysis
	4.10 Computer Implementation
	4.11 The Interior-Point Approach to Solving Linear Programming Problems
	4.12 Conclusions
	Appendix 4.1: An Introduction to Using LINDO and LINGO
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 4.1 Fabrics and Fall Fashions
	Previews of Added Cases on Our Website
		Case 4.2 New Frontiers
		Case 4.3 Assigning Students to Schools
CHAPTER 5 The Theory of the Simplex Method
	5.1 Foundations of the Simplex Method
	5.2 The Simplex Method in Matrix Form
	5.3 A Fundamental Insight
	5.4 The Revised Simplex Method
	5.5 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
CHAPTER 6 Duality Theory
	6.1 The Essence of Duality Theory
	6.2 Primal-Dual Relationships
	6.3 Adapting to Other Primal Forms
	6.4 The Role of Duality Theory in Sensitivity Analysis
	6.5 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
CHAPTER 7 Linear Programming under Uncertainty
	7.1 The Essence of Sensitivity Analysis
	7.2 Applying Sensitivity Analysis
	7.3 Performing Sensitivity Analysis on a Spreadsheet
	7.4 Robust Optimization
	7.5 Chance Constraints
	7.6 Stochastic Programming with Recourse
	7.7 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 7.1 Controlling Air Pollution
	Previews of Added Cases on Our Website
		Case 7.2 Farm Management
		Case 7.3 Assigning Students to Schools, Revisited
		Case 7.4 Writing a Nontechnical Memo
CHAPTER 8 Other Algorithms for Linear Programming
	8.1 The Dual Simplex Method
	8.2 Parametric Linear Programming
	8.3 The Upper Bound Technique
	8.4 An Interior-Point Algorithm
	8.5 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
CHAPTER 9 The Transportation and Assignment Problems
	9.1 The Transportation Problem
	9.2 A Streamlined Simplex Method for the Transportation Problem
	9.3 The Assignment Problem
	9.4 A Special Algorithm for the Assignment Problem
	9.5 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 9.1 Shipping Wood to Market
	Previews of Added Cases on Our Website
		Case 9.2 Continuation of the Texago Case Study
		Case 9.3 Project Pickings
CHAPTER 10 Network Optimization Models
	10.1 Prototype Example
	10.2 The Terminology of Networks
	10.3 The Shortest-Path Problem
	10.4 The Minimum Spanning Tree Problem
	10.5 The Maximum Flow Problem
	10.6 The Minimum Cost Flow Problem
	10.7 The Network Simplex Method
	10.8 A Network Model for Optimizing a Project’s Time-Cost Trade-Off
	10.9 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 10.1 Money in Motion
	Previews of Added Cases on Our Website
		Case 10.2 Aiding Allies
		Case 10.3 Steps to Success
CHAPTER 11 Dynamic Programming
	11.1 A Prototype Example for Dynamic Programming
	11.2 Characteristics of Dynamic Programming Problems
	11.3 Deterministic Dynamic Programming
	11.4 Probabilistic Dynamic Programming
	11.5 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
CHAPTER 12 Integer Programming
	12.1 Prototype Example
	12.2 Some BIP Applications
	12.3 Using Binary Variables to Deal with Fixed Charges
	12.4 A Binary Representation of General Integer Variables
	12.5 Some Perspectives on Solving Integer Programming Problems
	12.6 The Branch-and-Bound Technique and its Application to Binary Integer Programming
	12.7 A Branch-and-Bound Algorithm for Mixed Integer Programming
	12.8 The Branch-and-Cut Approach to Solving BIP Problems
	12.9 The Incorporation of Constraint Programming
	12.10 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 12.1 Capacity Concerns
	Previews of Added Cases on Our Website
		Case 12.2 Assigning Art
		Case 12.3 Stocking Sets
		Case 12.4 Assigning Students to Schools, Revisited Again
CHAPTER 13 Nonlinear Programming
	13.1 Sample Applications
	13.2 Graphical Illustration of Nonlinear Programming Problems
	13.3 Types of Nonlinear Programming Problems
	13.4 One-Variable Unconstrained Optimization
	13.5 Multivariable Unconstrained Optimization
	13.6 The Karush-Kuhn-Tucker (KKT) Conditions for Constrained Optimization
	13.7 Quadratic Programming
	13.8 Separable Programming
	13.9 Convex Programming
	13.10 Nonconvex Programming (with Spreadsheets)
	13.11 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 13.1 Savvy Stock Selection
	Previews of Added Cases on Our Website
		Case 13.2 International Investments
		Case 13.3 Promoting a Breakfast Cereal, Revisited
CHAPTER 14 Metaheuristics
	14.1 The Nature of Metaheuristics
	14.2 Tabu Search
	14.3 Simulated Annealing
	14.4 Genetic Algorithms
	14.5 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
CHAPTER 15 Game Theory
	15.1 The Formulation of Two-Person, Zero-Sum Games
	15.2 Solving Simple Games—A Prototype Example
	15.3 Games with Mixed Strategies
	15.4 Graphical Solution Procedure
	15.5 Solving by Linear Programming
	15.6 Extensions
	15.7 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
CHAPTER 16 Decision Analysis
	16.1 A Prototype Example
	16.2 Decision Making without Experimentation
	16.3 Decision Making with Experimentation
	16.4 Decision Trees
	16.5 Utility Theory
	16.6 The Practical Application of Decision Analysis
	16.7 Multiple Criteria Decision Analysis, Including Goal Programming
	16.8 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 16.1 Brainy Business
	Preview of Added Cases on Our Website
		Case 16.2 Smart Steering Support
		Case 16.3 Who Wants to Be a Millionaire?
		Case 16.4 University Toys and the Engineering Professor Action Figures
CHAPTER 17 Queueing Theory
	17.1 Prototype Example
	17.2 Basic Structure of Queueing Models
	17.3 Some Common Types of Real Queueing Systems
	17.4 The Role of the Exponential Distribution
	17.5 The Birth-and-Death Process
	17.6 Queueing Models Based on the Birth-and-Death Process
	17.7 Queueing Models Involving Nonexponential Distributions
	17.8 Priority-Discipline Queueing Models
	17.9 Queueing Networks
	17.10 The Application of Queueing Theory
	17.11 Behavioral Queueing Theory
	17.12 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 17.1 Reducing In-Process Inventory
	Preview of an Added Case on Our Website
		Case 17.2 Queueing Quandary
CHAPTER 18 Inventory Theory
	18.1 Examples
	18.2 Components of Inventory Models
	18.3 Deterministic Continuous-Review Models
	18.4 A Deterministic Periodic-Review Model
	18.5 Deterministic Multiechelon Inventory Models for Supply Chain Management
	18.6 A Stochastic Continuous-Review Model
	18.7 A Stochastic Single-Period Model for Perishable Products
	18.8 Revenue Management
	18.9 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 18.1 Brushing Up on Inventory Control
	Previews of Added Cases on Our Website
		Case 18.2 TNT: Tackling Newsboy’s Teaching
		Case 18.3 Jettisoning Surplus Stock
CHAPTER 19 Markov Decision Processes
	19.1 A Prototype Example
	19.2 A Model for Markov Decision Processes
	19.3 Linear Programming and Optimal Policies
	19.4 Markov Decision Processes in Practice
	19.5 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
CHAPTER 20 Simulation
	20.1 The Essence of Simulation
	20.2 Some Common Types of Applications of Simulation
	20.3 Generation of Random Numbers
	20.4 Generation of Random Observations from a Probability Distribution
	20.5 Simulation Optimization
	20.6 Outline of a Major Simulation Study
	20.7 Conclusions
	Selected References
	Learning Aids for this Chapter on Our Website
	Problems
	Case 20.1 Reducing In-Process Inventory, Revisted
	Previews of Added Cases on Our Website
		Case 20.2 Planning Planers
		Case 20.3 Pricing under Pressure
APPENDIXES
	1. Documentation for the OR Courseware
	2. Convexity
	3. Classical Optimization Methods
	4. Matrices and Matrix Operations
	5. Table for a Normal Distribution
PARTIAL ANSWERS TO SELECTED PROBLEMS
INDEXES
	Author Index
	Subject Index