Table Of Content

th edition y Introduction to Management Science Thomas M. Cook American Airlines, Inc. Robert A. Russell The University of Tulsa PRENTICE HALL, Englewood Cliffs, New Jersey 07632 n Library of Congress Cata1oging-ln-Pub1ication Data Cook, Thomas M. Intrcauction to management science / Thomas M. Cook, Robert A. Russe 1 1 . — 5th eb. p. cm. Includes bib'iiograohical references and index. ISBN 0-13-485707-0 1. Management--Mathematica1 models. 2. Operations research. 3. Management science. I. Russell. Robert A., II. Title. HD30.25.C67 1993 658.4'034—dc20 92-11562 CIP The corporate logos reproduced on the cover and with the chapter opening scenarios are done so with permission, courtesy of the following: Homart Development Co.; U.S. Air Force; North American Van Lines, Inc.; American Airlines, Inc.; Citgo Petroleum Corporation; General Motors Corporation; E. I. duPont Nemours & Company; The LTV Corporation; Mobil Oil Corporation; Phillips Petroleum Company; Ohio Edison Co.; Manitoba Telephone System; The Xerox Corporation (Xerox is a registered trademark of the Xerox Corporation); United Airlines; IBM Corporation; ICI Pharmaceuticals; Digital Equipment Corporation; and Arizona Department of Transportation Acquisition Editor: Valerie Ashton Editor-in-Chief: Joseph Heider Production Editors: Lisa Kinne/Keith Faivre Marketing Manager: Sandra Steiner Copy Editor: Keith Faivre Designers: Lorraine Mullaney/Maureen Eide Cover Designer: Rosemarie Paccione Prepress Buyer: Trudy Pisciotti Manufacturing Buyers: Patrice Fraccio/Robert Anderson Supplements Editor: Lisamarie Brassini Editorial Assistant: AnnMarie Dunn Production Assistant: Renee Pelletier 1993, 1989, 1985, 1981, 1977 by Prentice-Hall, Inc. sj-JIs A Simon & Schuster Company r^F Englewood Cliffs, New Jersey 07632 All rights reserved. No part of this book may be MjS reproduced, in any form or by any means, without permission in writing from the publisher. Printed in the United States of America 10 987654321 ISBN □-13-4aS7D7-D Prentice-Hall International (UK) Limited, London Prentice-Hall of Australia Pty. Limited, Sydney Prentice-Hall Canada Inc., Toronto Prentice-Hall Hispanoamericana, S.A., Mexico Prentice-Hall of India Private Limited, New Delhi Prentice-Hall of Japan, Inc., Tokyo Simon & Schuster Asia Pte. Ltd., Singapore Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro Contents Preface xiv Introduction 1 Homart Development Co., 1 Introduction 2 Historical Overview 3 The Nature of Management Science 7 The Scientific Method 7 A Systems Approach 9 Models in Management Science 11 Basic Steps in the OR/MS Approach 15 Management Science and the Functional Areas of Business 18 Management Science in Action 20 Summary 24 Looking Ahead 25 Review Questions 27 Problems 28 Bibliography 31 l m University Libraries Carnegie Mellon University Pittsburgh, Pennsylvania 15213 IV CONTENTS 2 r H a i * Linear Programming: Formulation and Applications 32 U.S. Air Force, 32 What is Linear Programming? 33 General Areas of Application 34 Problems LP Can Be Used On 35 The LP Model 36 Formulating LP Models 37 Guidelines for Constructing LP Models 39 Mathematical Assumptions and Limitations of LP 51 Summary 53 Solved Problem 54 Review Questions 58 Problems 58 Bibliography 72 Solving LP Problems: Graphical Method 74 North American Van Lines, 74 Introduction 75 The Graphical Solution Method 75 Finding the Optimal Solution 81 Summary of the Graphical Solution Method 86 Graphical Solution of Minimization Problems 87 Special Cases in Solving LP Problems 90 Summary 94 Solved Problem 94 Review Questions 96 Problems 97 Bibliography 105 CONTENTS V >4 f f t f £ 'i / ! !■ Solving LP Problems: Simplex Method 106 American Airlines, Inc., 106 Introduction 107 Algebraic Overview of the Simplex Method 108 Basic Feasible Solutions 109 Incorporating the Objective Function 112 Using Elementary Row Operations to Transform the Equations 115 Basic Steps 117 The Simplex Tableau 118 The Basic Steps Applied 119 Minimization Problems 129 Handling Other Types of Constraints 130 Summary of Simplex Procedure 137 Special Cases in the Simplex Method 138 New Developments—Interior Point Methods 142 Using Spreadsheets in LP Analysis 145 Computer Implications 149 Summary 151 Solved Problem 152 Review Questions 154 Problems 154 Bibliography 164 Em5IEZEIII Sensitivity Analysis 165 Citgo Petroleum Corporation, 165 The Nature of Sensitivity Analysis 166 Sensitivity Analysis 168 Changes in the Objective Function Coefficients 169 RHS Ranging 172 Interpretation of Computer Output 175 Vi CONTENTS Shadow Prices 178 Simultaneous Changes 180 Adding a New Variable 181 Adding a Constraint 182 Sensitivity Analysis Based on Simplex Tableaus 184 Duality 190 Summary 197 Solved Problems 197 Review Questions 202 Problems 202 Bibliography 213 Distribution and Assignment Problems 214 , General Motors Corporation 214 Specialized LP Models 215 Rationale for Special-Purpose Algorithms 216 The Transportation Problem 217 Solving Transportation Problems Heuristically 220 Further Applications of Transportation Models 227 Transportation Problem Variations 229 The Transshipment Problem 230 The Assignment Problem 235 Computer Implications 238 Summary 238 Solved Problems 239 Review Questions 243 Problems 243 Bibliography 251 Supplement: Optimizing Transportation and Assignment Problems 252 CONTENTS Vii Network Models 279 E. I. du Pont de Nemours & Co., 279 Introduction 280 The Shortest-Route Problem 281 The Minimum Spanning Tree Problem 288 The Maximal Flow Problem 294 Computer Implications 298 Summary 300 Solved Problems 300 Review Questions 302 Problems 302 Bibliography 308 8 Project Scheduling 309 LTV Aerospace and Defense Company, 309 Introduction 310 Work Breakdown Structure 311 Gantt Charts 313 Deterministic Pert 315 Stochastic Pert 319 Evaluating Time-Cost Trade-Offs 324 Pert/Cost 326 Resource Constrained Pert 333 Computer Implications 337 Summary 338 Solved Problems 339 Review Questions 348 Problems 349 Bibliography 359 Viii CONTENTS Integer and Goal Programming 360 Mobil Oil Corporation, 360 Introduction 361 Integer Programming 362 Branch-and-Bound Method 366 Applications and Formulation Possibilities 373 Multiple-Criteria Decision Making 381 Pareto Optimality 382 Goal Programming 383 Multiple-Objective Linear Programming 392 Computer Implications 395 Summary 396 Solved Problems 397 Review Questions 399 Problems 400 Bibliography 408 rniommi Dynamic Programming 410 Phillips Petroleum Company, 410 Introduction 411 The Shortest-Route Problem Revisited 412 Fundamental Concepts and Notation 416 Computer Implications 428 Summary 429 Solved Problem 429 Review Questions 431 Problems 431 Bibliography 436 CONTENTS iX Decision Theory 437 Ohio Edison Company, 437 Introduction 438 Criteria for Decision Making When State-of-Nature Probabilities are Unknown 441 Criteria for Decision Making When State-of-Nature Probabilities are Known 444 The Decision Problem with an Opportunity to Obtain Additional Information 450 Decision Problem for Non-EMVers 459 The Analytic Hierarchy Process 467 Computer Implications 479 Summary 480 Solved Problems 480 Review Questions 486 Problems 487 Bibliography 499 Forecasting 500 The Manitoba Telephone System, 500 Introduction 501 Qualitative Techniques 505 Time-Series Analysis 507 Causal Methods 533 Forecast Error 538 Improving the Forecast 541 Computer Implications 542 Summary 543 Solved Problems 544 Review Questions 548 Problems 549 Bibliography 557 X CONTENTS Queuing Models 558 The Xerox Corporation, 558 Introduction 559 The Queuing System 560 Elementary Queuing Models 568 Application of Queuing Theory 580 Computer Implications 586 Summary 587 Solved Problems 587 Review Questions 594 Problems 595 Bibliography 600 Discrete Digital Simulation 601 United Airlines, 601 Introduction 602 Reasons for Using Simulation 603 Simulation Applications 603 Manual Simulation 604 Steps in a Simulation Study 613 Deterministic Simulation 623 Risk Analysis 625 Visual Interactive Modeling 629 When to Simulate 631 Computer Implications 633 Summary 634 Solved Problem 635 Review Questions 640 Problems 640 Bibliography 652