Table Of Contentth 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
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Marketing Manager: Sandra Steiner
Copy Editor: Keith Faivre
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Cover Designer: Rosemarie Paccione
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Supplements Editor: Lisamarie Brassini
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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
