Introduction to Operations Research

, by Hillier, Frederick S.; Lieberman, Gerald J.

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ISBN: 9780078414473 | 0078414474
Cover: Hardcover
Copyright: 3/1/1995

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Summary

Supplemental Materials

Textbook providing a rigorous treatment in a stimulating manner. Includes realistic examples, illustrations, and exercises. 3 1/2 inch disk included. DLC: Operations research.

Preface

1 INTRODUCTION

(7)

1.1 The Origins of Operations Research

(2)

1.2 The Nature of Operations Research

(1)

1.3 The Impact of Operations Research

(1)

1.4 Algorithms and OR Courseware

(4)

2 OVERVIEW OF THE OPERATIONS RESEARCH MODELING APPROACH

(17)

2.1 Defining the Problem and Gathering Data

(2)

2.2 Formulating a Mathematical Model

(4)

2.3 Deriving Solutions from the Model

(2)

2.4 Testing the Model

(2)

2.5 Preparing to Apply the Model

(2)

2.6 Implementation

(1)

2.7 Conclusions

(3)

3 INTRODUCTION TO LINEAR PROGRAMMING

(56)

3.1 Prototype Example

(6)

3.2 The Linear Programming Model

(6)

3.3 Assumptions of Linear Programming

(7)

3.4 Additional Examples

(17)

3.5 Some Case Studies

(5)

3.6 Conclusions

(14)

4 SOLVING LINEAR PROGRAMMING PROBLEMS: THE SIMPLEX METHOD

(72)

4.1 The Essence of the Simplex Method

(5)

4.2 Setting Up the Simplex Method

(3)

4.3 The Algebra of the Simplex Method

(5)

4.4 The Simplex Method in Tabular Form

(5)

4.5 The Breaking in the Simplex Method

100

(3)

4.6 Adapting to Other Model Forms

103

(19)

4.7 Post-Optimality Analysis

122

(7)

4.8 Computer Implementation

129

(2)

4.9 The Interior-Point Approach to Solving Linear Programming Problems

131

(5)

4.10 Conclusions

136

(17)

5 THE THEORY OF THE SIMPLEX METHOD

153

(43)

5.1 Foundations of the Simplex Method

153

(12)

5.2 The Revised Simplex Method

165

(9)

5.3 A Fundamental Insight

174

(8)

5.4 Conclusions

182

(14)

6 DUALITY THEORY AND SENSITIVITY ANALYSIS

196

(67)

6.1 The Essence of Duality Theory

197

(7)

6.2 Economic Interpretation of Duality

204

(2)

6.3 Primal-Dual Relationships

206

(4)

6.4 Adapting to Other Primal Forms

210

(5)

6.5 The Role of Duality Theory in Sensitivity Analysis

215

(2)

6.6 The Essence of Sensitivity Analysis

217

(6)

6.7 Applying Sensitivity Analysis

223

(15)

6.8 Conclusions

238

(25)

7 OTHER ALGORITHMS FOR LINEAR PROGRAMMING

263

(40)

7.1 The Dual Simplex Method

264

(2)

7.2 Parametric Linear Programming

266

(5)

7.3 The Upper Bound Technique

271

(3)

7.4 An Interior-Point Algorithm

274

(11)

7.5 Linear Goal Programming and Its Solution Procedures

285

(7)

7.6 Conclusions

292

(11)

8 THE TRANSPORTATION AND ASSIGNMENT PROBLEMS

303

(50)

8.1 The Transportation Problem

304

(11)

8.2 A Streamlined Simplex Method for the Transportation Problem

315

(14)

8.3 The Assignment Problem

329

(9)

8.4 Conclusions

338

(15)

9 NETWORK ANALYSIS, INCLUDING PERT-CPM

353

(71)

9.1 Prototype Example

355

(1)

9.2 The Terminology of Networks

356

(3)

9.3 The Shortest-Path Problem

359

(3)

9.4 The Minimum Spanning Tree Problem

362

(4)

9.5 The Maximum Flow Problem

366

(6)

9.6 The Minimum Cost Flow Problem

372

(6)

9.7 The Network Simplex Method

378

(11)

9.8 Project Planning and Control with PERT-CPM

389

(15)

9.9 Conclusions

404

(20)

10 DYNAMIC PROGRAMMING

424

(46)

10.1 A Prototype Example for Dynamic Programming

425

(5)

10.2 Characteristics of Dynamic Programming Problems

430

(3)

10.3 Deterministic Dynamic Programming

433

(20)

10.4 Probabilistic Dynamic Programming

453

(5)

10.5 Conclusions

458

(12)

11 GAME THEORY

470

(24)

11.1 The Formulation of Two-Person, Zero-Sum Games

471

(1)

11.2 Solving Simple Games-A Prototype Example

472

(5)

11.3 Games With Mixed Strategies

477

(2)

11.4 Graphical Solution Procedure

479

(3)

11.5 Solving by Linear Programming

482

(3)

11.6 Extensions

485

(1)

11.7 Conclusions

486

(8)

12 INTERGER PROGRAMMING

494

(64)

12.1 Prototype Example

495

(2)

12.2 Some Other Formulation Possibilities with Binary Variables

497

(6)

12.3 Some Formulation Examples

503

(8)

12.4 Some Perspectives on Solving Integer Programming Problems

511

(4)

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

515

(12)

12.6 A Branch-and-Bound Algorithm for Mixed Integer Programming

527

(6)

12.7 Recent Developments in Solving BIP Problems

533

(8)

12.8 Conclusions

541

(17)

13 NONLINEAR PROGRAMMING

558

(70)

13.1 Sample Applications

559

(4)

13.2 Graphical Illustration of Nonlinear Programming Problems

563

(5)

13.3 Types of Nonlinear Programming Problems

568

(6)

13.4 One-Variable Unconstrained Optimization

574

(3)

13.5 Multivariable Unconstrained Optimization

577

(5)

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

582

(4)

13.7 Quadratic Programming

586

(5)

13.8 Separable Programming

591

(7)

13.9 Convex Programming

598

(5)

13.10 Nonconvex Programming

603

(3)

13.11 Conclusions

606

(22)

14 MARKOV CHAINS

628

(33)

14.1 Stochastic Processes

629

(1)

14.2 Markov Chains

630

(3)

14.3 Chapman-Kolmogorov Equations

633

(2)

14.4 Classification of States of a Markov Chain

635

(3)

14.5 First Passage Times

638

(2)

14.6 Long-Run Properties of Markov Chains

640

(6)

14.7 Absorption States

646

(2)

14.8 Continuous-Time Markov Chains

648

(13)

15 QUEUEING THEORY

661

(72)

15.1 Prototype Example

662

(1)

15.2 Basic Structure of Queueing Models

662

(5)

15.3 Examples of Real Queueing Systems

667

(1)

15.4 The Role of the Exponential Distribution

668

(6)

15.5 The Birth-and-Death Process

674

(5)

15.6 Queueing Models Based on the Birth-and-Death Process

679

(17)

15.7 Queueing Models Involving Nonexponential Distributions

696

(8)

15.8 Priority-Discipline Queueing Models

704

(5)

15.9 Queueing Networks

709

(4)

15.10 Conclusions

713

(20)

16 THE APPLICATION OF QUEUEING THEORY

733

(23)

16.1 Examples

734

(1)

16.2 Decision Making

735

(3)

16.3 Formulation of Waiting-Cost Functions

738

(4)

16.4 Decision Models

742

(6)

16.5 Conclusions

748

(8)

17 INVENTORY THEORY

756

(50)

17.1 Examples

757

(2)

17.2 Components of Inventory Models

759

(2)

17.3 Deterministic Models

761

(11)

17.4 Stochastic Models

772

(25)

17.5 Conclusions

797

(9)

18 FORECASTING

806

(27)

18.1 Judgemental Techniques

807

(1)

18.2 Time Series

808

(1)

18.3 Forecasting Procedures for a Constant-Level Model

809

(3)

18.4 A Forecasting Procedure for a Linear Trend Model

812

(2)

18.5 A Forecasting Procedure for a Constant Level with Seasonal Effects Model

814

(3)

18.6 Forecasting Errors

817

(1)

18.7 Box-Jenkins Method

818

(1)

18.8 Linear Regression

819

(7)

18.9 Conclusions

826

(7)

19 MARKOV DECISION PROCESSES

833

(31)

19.1 A Prototype Example

834

(2)

19.2 A Model for Markov Decision Processes

836

(3)

19.3 Linear Programming and Optimal Policies

839

(4)

19.4 A Policy Improvement Algorithm for Finding Optimal Policies

843

(5)

19.5 Discounted Cost Criterion

848

(7)

19.6 Conclusions

855

(9)

20 DECISION ANALYSIS

864

(36)

20.1 A Prototype Example

865

(1)

20.2 Decision Making without Experimentation

865

(4)

20.3 Decision Making with Experimentation

869

(5)

20.4 Decision Trees

874

(3)

20.5 Utility Theory

877

(6)

20.6 Conclusions

883

(17)

21 SIMULATION

900

(45)

21.1 Illustrative Examples

902

(7)

21.2 Formulating and Implementing a Simulation Model

909

(10)

21.3 Experimental Design for Simulation

919

(7)

21.4 Regenerative Method of Statistical Analysis

926

(6)

21.5 Conclusions

932

(13)

APPENDIXES

945

(27)

1 Documentation for the OR Courseware

947

(4)

2 Convexity

951

(8)

3 Classical Optimization Methods

959

(4)

4 Matrices and Matrix Operations

963

(7)

5 Tables

970

(2)

Answers to Selected Problems

972

(10)

Indexes

982

Author Index

982

(4)

Subject Index

986

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Introduction to Operations Research

Summary

Table of Contents

Supplemental Materials