Operations Research Applications and Algorithms (with CD-ROM and InfoTrac)

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ISBN: 9780534380588 | 0534380581
Cover: Hardcover
Copyright: 7/25/2003

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The market-leading textbook for the course, Winston's OPERATIONS RESEARCH owes much of its success to its practical orientation and consistent emphasis on model formulation and model building. It moves beyond a mere study of algorithms without sacrificing the rigor that faculty desire. As in every edition, Winston reinforces the book's successful features and coverage with the most recent developments in the field. The Student Suite CD-ROM, which now accompanies every new copy of the text, contains the latest versions of commercial software for optimization, simulation, and decision analysis.

Preface

xii

About the Author

xvi

An Introduction to Model-Building

(10)

An Introduction to Modeling

(4)

The Seven-Step Model-Building Process

(1)

CITGO Petroleum

(1)

San Francisco Police Department Scheduling

(2)

GE Capital

(2)

Basic Linear Algebra

(38)

Matrices and Vectors

(9)

Matrices and Systems of Linear Equations

(2)

The Gauss-Jordan Method for Solving Systems of Linear Equations

(10)

Linear Independence and Linear Dependence

(4)

The Inverse of a Matrix

(6)

Determinants

(7)

Introduction to Linear Programming

(78)

What Is a Linear Programming Problem?

(7)

The Graphical Solution of Two-Variable Linear Programming Problems

(7)

Special Cases

(5)

A Diet Problem

(4)

A Work-Scheduling Problem

(4)

A Capital Budgeting Problem

(6)

Short-Term Financial Planning

(3)

Blending Problems

(10)

Production Process Models

(5)

Using Linear Programming to Solve Multiperiod Decision Problems: An Inventory Model

100

(5)

Multiperiod Financial Models

105

(4)

Multiperiod Work Scheduling

109

(18)

The Simplex Algorithm and Goal Programming

127

(100)

How to Convert an LP to Standard Form

127

(3)

Preview of the Simplex Algorithm

130

(4)

Direction of Unboundedness

134

(2)

Why Does an LP Have an Optimal bfs?

136

(4)

The Simplex Algorithm

140

(9)

Using the Simplex Algorithm to Solve Minimization Problems

149

(3)

Alternative Optimal Solutions

152

(2)

Unbounded LPs

154

(4)

The LINDO Computer Package

158

(5)

Matrix Generators, LINGO, and Scaling of LPs

163

(5)

Degeneracy and the Convergence of the Simplex Algorithm

168

(4)

The Big M Method

172

(6)

The Two-Phase Simplex Method

178

(6)

Unrestricted-in-Sign Variables

184

(6)

Karmarkar's Method for Solving LPs

190

(1)

Multiattribute Decision Making in the Absence of Uncertainty: Goal Programming

191

(11)

Using the Excel Solver to Solve LPs

202

(25)

Sensitivity Analysis: An Applied Approach

227

(35)

A Graphical Introduction to Sensitivity Analysis

227

(5)

The Computer and Sensitivity Analysis

232

(14)

Managerial Use of Shadow Prices

246

(2)

What Happens to the Optimal z-Value If the Current Basis Is No Longer Optimal?

248

(14)

Sensitivity Analysis and Duality

262

(98)

A Graphical Introduction to Sensitivity Analysis

262

(5)

Some Important Formulas

267

(8)

Sensitivity Analysis

275

(14)

Sensitivity Analysis When More Than One Parameter Is Changed: The 100% Rule

289

(6)

Finding the Dual of an LP

295

(7)

Economic Interpretation of the Dual Problem

302

(2)

The Dual Theorem and Its Consequences

304

(9)

Shadow Prices

313

(10)

Duality and Sensitivity Analysis

323

(2)

Complementary Slackness

325

(4)

The Dual Simplex Method

329

(6)

Data Envelopment Analysis

335

(25)

Transportation, Assignment, and Transshipment Problems

360

(53)

Formulating Transportation Problems

360

(13)

Finding Basic Feasible Solutions for Transportation Problems

373

(9)

The Transportation Simplex Method

382

(8)

Sensitivity Analysis for Transportation Problems

390

(3)

Assignment Problems

393

(7)

Transshipment Problems

400

(13)

Network Models

413

(62)

Basic Definitions

413

(1)

Shortest-Path Problems

414

(5)

Maximum-Flow Problems

419

(12)

CPM and PERT

431

(19)

Minimum-Cost Network Flow Problems

450

(6)

Minimum Spanning Tree Problems

456

(3)

The Network Simplex Method

459

(16)

Integer Programming

475

(87)

Introduction to Integer Programming

475

(2)

Formulating Integer Programming Problems

477

(35)

The Branch-and-Bound Method for Solving Pure Integer Programming Problems

512

(11)

The Branch-and-Bound Method for Solving Mixed Integer Programming Problems

523

(1)

Solving Knapsack Problems by the Branch-and-Bound Method

524

(3)

Solving Combinatorial Optimization Problems by the Branch-and-Bound Method

527

(13)

Implicit Enumeration

540

(5)

The Cutting Plane Algorithm

545

(17)

Advanced Topics in Linear Programming

562

(48)

The Revised Simplex Algorithm

562

(5)

The Product Form of the Inverse

567

(3)

Using Column Generation to Solve Large-Scale LPs

570

(6)

The Dantzig-Wolfe Decomposition Algorithm

576

(17)

The Simplex Method for Upper-Bounded Variables

593

(4)

Karmarkar's Method for Solving LPs

597

(13)

Nonlinear Programming

610

(97)

Review of Differential Calculus

610

(6)

Introductory Concepts

616

(14)

Convex and Concave Functions

630

(7)

Solving NLPs with One Variable

637

(12)

Golden Section Search

649

(6)

Unconstrained Maximization and Minimization with Several Variables

655

(5)

The Method of Steepest Ascent

660

(3)

Lagrange Multipliers

663

(7)

The Kuhn--Tucker Conditions

670

(10)

Quadratic Programming

680

(8)

Separable Programming

688

(5)

The Method of Feasible Directions

693

(2)

Pareto Optimality and Tradeoff Curves

695

(12)

Review of Calculus and Probability

707

(30)

Review of Integral Calculus

707

(3)

Differentiation of Integrals

710

(1)

Basic Rules of Probability

710

(3)

Bayes' Rule

713

(2)

Random Variables, Mean, Variance, and Covariance

715

(7)

The Normal Distribution

722

(8)

z-Transforms

730

(7)

Decision Making under Uncertainty

737

(66)

Decision Criteria

737

(4)

Utility Theory

741

(14)

Flaws in Expected Maximization of Utility: Prospect Theory and Framing Effects

755

(3)

Decision Trees

758

(9)

Bayes' Rule and Decision Trees

767

(6)

Decision Making with Multiple Objectives

773

(12)

The Analytic Hierarchy Process

785

(18)

Game Theory

803

(43)

Two-Person Zero-Sum and Constant-Sum Games: Saddle Points

803

(4)

Two-Person Zero-Sum Games: Randomized Strategies, Domination, and Graphical Solution

807

(9)

Linear Programming and Zero-Sum Games

816

(11)

Two-Person Nonconstant-Sum Games

827

(5)

Introduction to n-Person Game Theory

832

(2)

The Core of an n-Person Game

834

(3)

The Shapley Value

837

(9)

Deterministic EOQ Inventory Models

846

(34)

Introduction to Basic Inventory Models

846

(2)

The Basic Economic Order Quantity Model

848

(11)

Computing the Optimal Order Quantity When Quantity Discounts Are Allowed

859

(6)

The Continuous Rate EOQ Model

865

(3)

The EOQ Model with Back Orders Allowed

868

(4)

When to Use EOQ Models

872

(1)

Multiple-Product EOQ Models

873

(7)

Probabilistic Inventory Models

880

(43)

Single-Period Decision Models

880

(1)

The Concept of Marginal Analysis

880

(1)

The News Vendor Problem: Discrete Demand

881

(5)

The News Vendor Problem: Continuous Demand

886

(2)

Other One-Period Models

888

(2)

The EOQ with Uncertain Demand: The (r, q) and (s, S) Models

890

(8)

The EOQ with Uncertain Demand: The Service Level Approach to Determining Safety Stock Level

898

(9)

(R, S) Periodic Review Policy

907

(4)

The ABC Inventory Classification System

911

(2)

Exchange Curves

913

(10)

Markov Chains

923

(38)

What Is a Stochastic Process?

923

(1)

What Is a Markov Chain?

924

(4)

n-Step Transition Probabilities

928

(3)

Classification of States in a Markov Chain

931

(3)

Steady-State Probabilities and Mean First Passage Times

934

(8)

Absorbing Chains

942

(8)

Work-Force Planning Models

950

(11)

Deterministic Dynamic Programming

961

(55)

Two Puzzles

961

(1)

A Network Problem

962

(7)

An Inventory Problem

969

(5)

Resource-Allocation Problems

974

(11)

Equipment-Replacement Problems

985

(4)

Formulating Dynamic Programming Recursions

989

(12)

The Wagner--Whitin Algorithm and the Silver--Meal Heuristic

1001

(5)

Using Excel to Solve Dynamic Programming Problems

1006

(10)

Probabilistic Dynamic Programming

1016

(35)

When Current Stage Costs Are Uncertain, but the Next Period's State Is Certain

1016

(3)

A Probabilistic Inventory Model

1019

(4)

How to Maximize the Probability of a Favorable Event Occurring

1023

(6)

Further Examples of Probabilistic Dynamic Programming Formulations

1029

(7)

Markov Decision Processes

1036

(15)

Queuing Theory

1051

(94)

Some Queuing Terminology

1051

(2)

Modeling Arrival and Service Processes

1053

(1)

Birth--Death Processes

1053

(19)

The M/M/1/GD/∞/∞ Queuing System and the Queuing Formula L = λW

1072

(11)

The M/M/1/GD/c/∞ Queuing System

1083

(4)

The M/M/s/GD/∞/∞ Queuing System

1087

(8)

The M/G/∞/GD/∞/∞ and GI/G/∞/GD/∞/∞ Models

1095

(2)

The M/G/∞/GD/∞/∞ Queuing System

1097

(2)

Finite Source Models: The Machine Repair Model

1099

(5)

Exponential Queues in Series and Open Queuing Networks

1104

(8)

The M/G/s/GD/s/∞ System (Blocked Customers Cleared)

1112

(3)

How to Tell Whether Interarrival Times and Service Times Are Exponential

1115

(4)

Closed Queuing Networks

1119

(5)

An Approximation for the G/G/m Queuing System

1124

(2)

Priority Queuing Models

1126

(5)

Transient Behavior of Queuing Systems

1131

(14)

Simulation

1145

(46)

Basic Terminology

1145

(1)

An Example of a Discrete-Event Simulation

1146

(7)

Random Numbers and Monte Carlo Simulation

1153

(5)

An Example of Monte Carlo Simulation

1158

(4)

Simulations with Continuous Random Variables

1162

(11)

An Example of a Stochastic Simulation

1173

(7)

Statistical Analysis in Simulations

1180

(3)

Simulation Languages

1183

(1)

The Simulation Process

1184

(7)

Simulation with Process Model

1191

(21)

Simulating an M/M/1 Queuing System

1191

(4)

Simulating an M/M/2 System

1195

(4)

Simulating a Series System

1199

(4)

Simulating Open Queuing Networks

1203

(4)

Simulating Erlang Service Times

1207

(3)

What Else Can Process Model Do?

1210

(2)

Simulation with the Excel Add-in @Risk

1212

(63)

Introduction to @Risk: The News Vendor Problem

1212

(10)

Modeling Cash Flows from a New Product

1222

(10)

Product Scheduling Models

1232

(6)

Reliability and Warranty Modeling

1238

(6)

The RISKGENERAL Function

1244

(4)

The RISKCUMULATIVE Random Variable

1248

(1)

The RISKTRIGEN Random Variable

1249

(1)

Creating a Distribution Based on a Point Forecast

1250

(2)

Forecasting the Income of a Major Corporation

1252

(4)

Using Data to Obtain Inputs for New Product Simulations

1256

(11)

Simulation and Bidding

1267

(2)

Playing Craps with @Risk

1269

(2)

Simulating the NBA Finals

1271

(4)

Forecasting Models

1275

(61)

Moving-Average Forecast Methods

1275

(6)

Simple Exponential Smoothing

1281

(2)

Holt's Method: Exponential Smoothing with Trend

1283

(3)

Winter's Method: Exponential Smoothing with Seasonality

1286

(6)

Ad Hoc Forecasting

1292

(10)

Simple Linear Regression

1302

(10)

Fitting Nonlinear Relationships

1312

(5)

Multiple Regression

1317

(19)

Appendix 1: @Risk Crib Sheet

1336

(14)

Appendix 2: Cases

1350

(20)

Case 1 Help, I'm Not Getting Any Younger

1351

(1)

Case 2 Solar Energy for Your Home

1351

(1)

Case 3 Golf-Sport: Managing Operations

1352

(3)

Case 4 Vision Corporation: Production Planning and Shipping

1355

(1)

Case 5 Material Handling in a General Mail-Handling Facility

1356

(3)

Case 6 Selecting Corporate Training Programs

1359

(3)

Case 7 Best Chip: Expansion Strategy

1362

(2)

Case 8 Emergency Vehicle Location in Springfield

1364

(1)

Case 9 System Design: Project Management

1365

(1)

Case 10 Modular Design for the Help-You Company

1366

(2)

Case 11 Brite Power: Capacity Expansion

1368

(2)

Appendix 3: Answers to Selected Problems

1370

(32)

Index

1402

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Operations Research Applications and Algorithms (with CD-ROM and InfoTrac)

Summary

Table of Contents

Supplemental Materials