Introduction to Operations Research

, by Hillier, Frederick S.

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ISBN: 9780072462395 | 0072462396
Cover: Hardcover
Copyright: 6/1/2000

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Supplemental Materials

Preface

xxiii

Introduction

(6)

The Origins of Operations Research

(1)

The Nature of Operations Research

(1)

The Impact of Operations Research

(2)

Algorithms and OR Courseware

(2)

Problems

(1)

Overview of the Operations Research Modeling Approach

(17)

Defining the Problem and Gathering Data

(3)

Formulating a Mathematical Model

(4)

Deriving Solutions from the Model

(2)

Testing the Model

(2)

Preparing to Apply the Model

(2)

Implementation

(1)

Conclusions

(3)

Selected References

(1)

Problems

(2)

Introduction to Linear Programming

(85)

Prototype Example

(6)

The Linear Programming Model

(5)

Assumptions of Linear Programming

(8)

Additional Examples

(17)

Some Case Studies

(6)

Displaying and Solving Linear Programming Models on a Spreadsheet

(6)

Formulating Very Large Linear Programming Models

(6)

Conclusions

(30)

The LINGO Modeling Language

(10)

Selected References

(1)

Learning Aids for This Chapter in Your Or Courseware

(1)

Problems

(13)

Auto Assembly

103

(1)

Cutting Cafeteria Costs

104

(2)

Staffing a Call Center

106

(3)

Solving Linear Programming Problems: The Simplex Method

109

(81)

The Essence of the Simplex Method

109

(5)

Setting Up the Simplex Method

114

(4)

The Algebra of the Simplex Method

118

(5)

The Simplex Method in Tabular Form

123

(5)

Tie Breaking in the Simplex Method

128

(4)

Adapting to Other Model Forms

132

(20)

Postoptimality Analysis

152

(8)

Computer Implementation

160

(3)

The Interior-Point Approach to Solving Linear Programming Problems

163

(5)

Conclusions

168

(22)

An Introduction to Using LINDO

169

(2)

Selected References

171

(1)

Learning Aids for This Chapter in Your OR Courseware

172

(1)

Problems

172

(10)

Fabrics and Fall Fashions

182

(3)

New Frontiers

185

(3)

Assigning Students to Schools

188

(2)

The Theory of the Simplex Method

190

(40)

Foundations of the Simplex Method

190

(12)

The Revised Simplex Method

202

(10)

A Fundamental Insight

212

(8)

Conclusions

220

(10)

Selected References

220

(1)

Learning Aids for This Chapter in Your OR Courseware

221

(1)

Problems

221

(9)

Duality Theory and Sensitivity Analysis

230

(79)

The Essence of Duality Theory

231

(8)

Economic Interpretation of Duality

239

(3)

Primal-Dual Relationships

242

(5)

Adapting to Other Primal Forms

247

(5)

The Role of Duality Theory in Sensitivity Analysis

252

(2)

The Essence of Sensitivity Analysis

254

(8)

Applying Sensitivity Analysis

262

(22)

Conclusions

284

(25)

Selected References

284

(1)

Learning Aids for This Chapter in Your OR Courseware

285

(1)

Problems

285

(17)

Controlling Air Pollution

302

(2)

Farm Management

304

(3)

Assigning Students to Schools (Revisited)

307

(2)

Other Algorithms for Linear Programming

309

(41)

The Dual Simplex Method

309

(3)

Parametric Linear Programming

312

(5)

The Upper Bound Technique

317

(3)

An Interior-Point Algorithm

320

(12)

Linear Goal Programming and Its Solution Procedures

332

(7)

Conclusions

339

(11)

Selected References

340

(1)

Learning Aids for This Chapter in Your OR Courseware

340

(1)

Problems

341

(6)

A Cure for Cuba

347

(3)

The Transportation and Assignment Problems

350

(55)

The Transportation Problem

351

(14)

A Streamlined Simplex Method for the Transportation Problem

365

(16)

The Assignment Problem

381

(10)

Conclusions

391

(14)

Selected References

391

(1)

Learning Aids for This Chapter in Your OR Courseware

392

(1)

Problems

392

(9)

Shipping Wood to Market

401

(1)

Project Pickings

402

(3)

Network Optimization Models

405

(63)

Prototype Example

406

(1)

The Terminology of Networks

407

(4)

The Shortest-Path Problem

411

(4)

The Minimum Spanning Tree Problem

415

(5)

The Maximum Flow Problem

420

(9)

The Minimum Cost Flow Problem

429

(9)

The Network Simplex Method

438

(10)

Conclusions

448

(20)

Selected References

449

(1)

Learning Aids for This Chapter in Your OR Courseware

449

(1)

Problems

450

(8)

Aiding Allies

458

(6)

Money in Motion

464

(4)

Project Management with PERT/CPM

468

(65)

A Prototype Example--The Reliable Construction Co. Project

469

(1)

Using a Network to Visually Display a Project

470

(5)

Scheduling a Project with PERT/CPM

475

(10)

Dealing with Uncertain Activity Durations

485

(7)

Considering Time-Cost Trade-Offs

492

(10)

Scheduling and Controlling Project Costs

502

(6)

An Evaluation of PERT/CPM

508

(4)

Conclusions

512

(21)

Selected References

513

(1)

Learning Aids for This Chapter in Your OR Courseware

514

(1)

Problems

514

(10)

Steps to Success

524

(3)

School's out forever...''

527

(6)

Dynamic Programming

533

(43)

A Prototype Example for Dynamic Programming

533

(5)

Characteristics of Dynamic Programming Problems

538

(3)

Deterministic Dynamic Programming

541

(21)

Probabilistic Dynamic Programming

562

(6)

Conclusions

568

(8)

Selected References

568

(1)

Learning Aids for This Chapter in Your OR Courseware

568

(1)

Problems

569

(7)

Integer Programming

576

(78)

Prototype Example

577

(3)

Some BIP Applications

580

(5)

Innovative Uses of Binary Variables in Model Formulation

585

(6)

Some Formulation Examples

591

(9)

Some Perspectives on Solving Integer Programming Problems

600

(4)

The Branch-and-Bound Technique and Its Application to Binary Integer Programming

604

(12)

A Branch-and-Bound Algorithm for Mixed Integer Programming

616

(6)

Other Developments in Solving BIP Problems

622

(8)

Conclusions

630

(24)

Selected References

631

(1)

Learning Aids for This Chapter in Your OR Courseware

631

(1)

Problems

632

(10)

Capacity Concerns

642

(3)

Assigning Art

645

(4)

Stocking Sets

649

(4)

Assigning Students to Schools (Revisited Again)

653

(1)

Nonlinear Programming

654

(72)

Sample Applications

655

(4)

Graphical Illustration of Nonlinear Programming Problems

659

(5)

Types of Nonlinear Programming Problems

664

(6)

One-Variable Unconstrained Optimization

670

(3)

Multivariable Unconstrained Optimization

673

(6)

The Karush-Kuhn-Tucker (KKT) Conditions for Constrained Optimization

679

(4)

Quadratic Programming

683

(7)

Separable Programming

690

(7)

Convex Programming

697

(5)

Nonconvex Programming

702

(4)

Conclusions

706

(20)

Selected References

706

(1)

Learning Aids for This Chapter in Your OR Courseware

707

(1)

Problems

708

(12)

Savvy Stock Selection

720

(6)

Game Theory

726

(23)

The Formulation of Two-Person, Zero-Sum Games

726

(2)

Solving Simple Games--A Prototype Example

728

(5)

Games with Mixed Strategies

733

(2)

Graphical Solution Procedure

735

(3)

Solving by Linear Programming

738

(3)

Extensions

741

(1)

Conclusions

742

(7)

Selected References

743

(1)

Learning Aids for This Chapter in Your OR Courseware

743

(1)

Problems

743

(6)

Decision Analysis

749

(53)

A Prototype Example

750

(1)

Decision Making without Experimentation

751

(7)

Decision Making with Experimentation

758

(6)

Decision Trees

764

(6)

Utility Theory

770

(8)

The Practical Application of Decision Analysis

778

(3)

Conclusions

781

(21)

Selected References

781

(1)

Learning Aids for This Chapter in Your OR Courseware

782

(1)

Problems

782

(13)

Brainy Business

795

(3)

Smart Steering Support

798

(4)

Markov Chains

802

(32)

Stochastic Processes

802

(1)

Markov Chains

803

(5)

Chapman-Kolmogorov Equations

808

(2)

Classification of States of a Markov Chain

810

(2)

Long-Run Properties of Markov Chains

812

(6)

First Passage Times

818

(2)

Absorbing States

820

(2)

Continuous Time Markov Chains

822

(12)

Selected References

827

(1)

Learning Aids for This Chapter in Your OR Courseware

828

(1)

Problems

828

(6)

Queueing Theory

834

(73)

Prototype Example

835

(1)

Basic Structure of Queueing Models

835

(5)

Examples of Real Queueing Systems

840

(1)

The Role of the Exponential Distribution

841

(7)

The Birth-and-Death Process

848

(4)

Queueing Models Based on the Birth-and-Death Process

852

(19)

Queueing Models Involving Nonexponential Distributions

871

(8)

Priority-Discipline Queueing Models

879

(6)

Queueing Networks

885

(4)

Conclusions

889

(18)

Selected References

890

(1)

Learning Aids for This Chapter in Your OR Courseware

890

(1)

Problems

891

(14)

Reducing In-Process Inventory

905

(2)

The Application of Queueing Theory

907

(28)

Examples

907

(2)

Decision Making

909

(3)

Formulation of Waiting-Cost Functions

912

(5)

Decision Models

917

(6)

Some Award-Winning Applications of Queueing Theory

923

(3)

Conclusions

926

(9)

Selected References

926

(1)

Learning Aids for This Chapter in Your OR Courseware

926

(1)

Problems

927

(5)

Queueing Quandary

932

(3)

Inventory Theory

935

(74)

Examples

936

(2)

Components of Inventory Models

938

(3)

Deterministic Continuous-Review Models

941

(10)

A Deterministic Periodic-Review Model

951

(5)

A Stochastic Continuous-Review Model

956

(5)

A Stochastic Single-Period Model for Perishable Products

961

(14)

Stochastic Periodic-Review Models

975

(8)

Larger Inventory Systems in Practice

983

(4)

Conclusions

987

(22)

Selected References

987

(1)

Learning Aids for This Chapter in Your OR Courseware

987

(1)

Problems

988

(12)

Brushing Up on Inventory Control

1000

(2)

TNT: Tackling Newsboy's Teachings

1002

(2)

Jettisoning Surplus Stock

1004

(5)

Forecasting

1009

(44)

Some Applications of Forecasting

1010

(3)

Judgmental Forecasting Methods

1013

(1)

Time Series

1014

(2)

Forecasting Methods for a Constant-Level Model

1016

(2)

Incorporating Seasonal Effects into Forecasting Methods

1018

(3)

An Exponential Smoothing Method for a Linear Trend Model

1021

(4)

Forecasting Errors

1025

(1)

Box-Jenkins Method

1026

(2)

Causal Forecasting with Linear Regression

1028

(8)

Forecasting in Practice

1036

(2)

Conclusions

1038

(15)

Selected References

1038

(1)

Learning Aids for This Chapter in Your OR Courseware

1038

(1)

Problems

1039

(9)

Finagling the Forecasts

1048

(5)

Markov Decision Processes

1053

(31)

A Prototype Example

1053

(3)

A Model for Markov Decision Processes

1056

(3)

Linear Programming and Optimal Policies

1059

(5)

Policy Improvement Algorithm for Finding Optimal Policies

1064

(5)

Discounted Cost Criterion

1069

(15)

Selected References

1077

(1)

Learning Aids for This Chapter in Your OR Courseware

1078

(1)

Problems

1078

(6)

Simulation

1084

(92)

The Essence of Simulation

1084

(13)

Some Common Types of Applications of Simulation

1097

(4)

Generation of Random Numbers

1101

(4)

Generation of Random Observations from a Probability Distribution

1105

(5)

Outline of a Major Simulation Study

1110

(5)

Performing Simulations on Spreadsheets

1115

(11)

Variance-Reducing Techniques

1126

(5)

Regenerative Method of Statistical Analysis

1131

(7)

Conclusions

1138

(18)

Selected References

1140

(1)

Learning Aids for This Chapter in Your OR Courseware

1140

(1)

Problems

1141

(10)

Planning Planers

1151

(2)

Pricing under Pressure

1153

(3)

APPENDIXES

1. Documentation for the OR Courseware

1156

(3)

2. Convexity

1159

(6)

3. Classical Optimization Methods

1165

(4)

4. Matrices and Matrix Operations

1169

(5)

5. Tables

1174

(2)

PARTIAL ANSWERS TO SELECTED PROBLEMS

1176

(19)

INDEXES

Author Index

1195

(4)

Subject Index

1199

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Introduction to Operations Research

Table of Contents

Supplemental Materials