Introduction toManagement Science

Bernard W. Taylor IIIVirginia Polytechnic Institute and State University

E D I T I O N

11

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Library of Congress Cataloging-in-Publication Data

Taylor, Bernard W.

Introduction to management science / Bernard W. Taylor III.—Ed. 11.

p. cm.

ISBN-13: 978-0-13-275191-9

ISBN-10: 0-13-275191-7

1. Management science. I. Title.

T56.T38 2011

658.5—dc23

2011031153

10 9 8 7 6 5 4 3 2 1

ISBN-10: 0-13-275191-7

ISBN-13: 978-0-13-275191-9

To Diane, Kathleen, and Lindsey

To the memory of my grandfather,

Bernard W. Taylor, Sr.

This page intentionally left blank

Brief Contents

Preface xi

1 Management Science 1

2 Linear Programming:Model Formulation andGraphical Solution 30

3 Linear Programming:Computer Solution andSensitivity Analysis 72

4 Linear Programming:Modeling Examples 111

5 Integer Programming 184

6 Transportation,Transshipment, andAssignment Problems 233

7 Network Flow Models 289

8 Project Management 339

9 Multicriteria DecisionMaking 407

10 Nonlinear Programming 477

11 Probability and Statistics 502

12 Decision Analysis 537

13 Queuing Analysis 597

14 Simulation 637

15 Forecasting 689

16 Inventory Management 752

Appendix A

Normal and Chi-Square Tables 794

Appendix B

Setting Up and Editing a Spreadsheet 796

Appendix C

The Poisson and Exponential Distributions 800

Solutions to Selected Odd-Numbered Problems 802

Glossary 810

Index 815

The following items can be found on the Companion Web

site that accompanies this text:

Web Site ModulesModule A: The Simplex Solution

Method A-1

Module B: Transportation and Assignment Solution

Methods B-1

Module C: Integer Programming: The Branch and

Bound Method C-1

Module D: Nonlinear Programming Solution

Techniques D-1

Module E: Game Theory E-1

Module F: Markov Analysis F-1

v

Contents

Preface xi

1 Management Science 1

The Management Science Approach to ProblemSolving 2

Time Out: for Pioneers in ManagementScience 5

Management Science Application:Room Pricing with Management Science at Marriott 6

Model Building: Break-Even Analysis 7

Computer Solution 12

Management Science Application:The Application of Management Science with Spreadsheets 14

Management Science Modeling Techniques 15

Business Usage of Management ScienceTechniques 18

Management Science Application:Management Science in Health Care 19

Management Science Models in Decision SupportSystems 20

Summary 21 • Problems 22 • Case Problems 28

2 Linear Programming:Model Formulation andGraphical Solution 30

Model Formulation 31

A Maximization Model Example 31

Time Out: for George B. Dantzig 32

Management Science Application:Allocating Seat Capacity on Indian RailwaysUsing Linear Programming 35

Graphical Solutions of Linear ProgrammingModels 35

Management Science Application:Improving Customer Service atAmazon.com 47

A Minimization Model Example 47

Management Science Application:Determining Optimal Fertilizer Mixes at Soquimich (South America) 51

Irregular Types of Linear ProgrammingProblems 53

Characteristics of Linear ProgrammingProblems 56

Summary 57 • Example Problem Solution 57 •Problems 61 • Case Problems 70

3 Linear Programming:Computer Solution andSensitivity Analysis 72

Computer Solution 73

Management Science Application:Optimizing Production Quantities at GEPlastics 77

Management Science Application:Improving Profitability at Norske Skog with Linear Programming 79

Sensitivity Analysis 80

Summary 91 • Example Problem Solution 91 •Problems 94 • Case Problems 108

vi

CONTENTS vii

4 Linear Programming:Modeling Examples 111

A Product Mix Example 112

Time Out: for George B. Dantzig 117

A Diet Example 117

An Investment Example 120

Management Science Application: A LinearProgramming Model for Optimal PortfolioSelection at GE Asset Management 125

A Marketing Example 126

A Transportation Example 130

A Blend Example 133

A Multiperiod Scheduling Example 137

Management Science Application:Linear Programming Blending Applications in the Petroleum Industry 138

Management Science Application:Employee Scheduling with ManagementScience 140

A Data Envelopment Analysis Example 142

Management Science Application:Evaluating American Red Cross Chapters UsingDEA 144

Summary 146 • Example Problem Solution 147 •Problems 149 • Case Problems 179

5 Integer Programming 184

Integer Programming Models 185

Management Science Application: AllocatingOperating Room Time at Toronto’s Mount SinaiHospital 188

Integer Programming Graphical Solution 188

Computer Solution of Integer ProgrammingProblems with Excel and QM for Windows 190

Time Out: for Ralph E. Gomory 191

Management Science Application:College of Business Class Scheduling at Ohio University 194

Management Science Application: FormingBusiness Case Student Teams at IndianaUniversity 199

0–1 Integer Programming Modeling Examples 199

Management Science Application: PlanningNext-Day Air Shipments at UPS 208

Summary 208 • Example Problem Solution 209 •Problems 209 • Case Problems 225

6 Transportation,Transshipment, andAssignment Problems 233

The Transportation Model 234

Time Out: for Frank L. Hitchcock and TjallingC. Koopmans 236

Management Science Application:Transportation Models at Nu-koteInternational 237

Computer Solution of a TransportationProblem 237

Management Science Application: MatchingWineries with Distributors 242

The Transshipment Model 243

Management Science Application:Transporting Mail at the U.S. PostalService 246

The Assignment Model 247

Computer Solution of an Assignment Problem 247

Management Science Application: SupplyingEmpty Freight Cars at Union PacificRailroad 250

Management Science Application: AssigningUmpire Crews at Professional TennisTournaments 251

Summary 252 • Example Problem Solution 252 •Problems 253 • Case Problems 281

7 Network Flow Models 289

Network Components 290

The Shortest Route Problem 291

The Minimal Spanning Tree Problem 298

Management Science Application:Determining Optimal Milk Collection Routes in Italy 302

viii CONTENTS

The Maximal Flow Problem 303

Time Out: for E. W. Dijkstra, L. R. Ford, Jr.,and D. R. Fulkerson 304

Management Science Application:Distributing Railway Cars to Customers at CSX 306

Summary 310 • Example Problem Solution 310 •Problems 312 • Case Problems 332

8 Project Management 339

The Elements of Project Management 340

Management Science Application:Managing Projects in China 342

Time Out: for Henry Gantt 346

Management Science Application:An Interstate Highway Construction Project in Virginia 348

CPM/PERT 349

Time Out: for Morgan R. Walker, James E.Kelley, Jr., and D. G. Malcolm 350

Probabilistic Activity Times 357

Management Science Application: The T5Project at Heathrow Airport 364

Microsoft Project 365

Project Crashing and Time–Cost Trade-Off 369

Management Science Application:Reconstructing the Pentagon After 9/11 373

Formulating the CPM/PERT Network as a LinearProgramming Model 374

Summary 381 • Example Problem Solution 382 •Problems 384 • Case Problems 404

9 Multicriteria DecisionMaking 407

Goal Programming 408

Graphical Interpretation of GoalProgramming 412

Computer Solution of Goal Programming Problemswith QM for Windows and Excel 415

Management Science Application:Developing Television Advertising Sales Plans at NBC 415

Time Out: for Abraham Charnes and WilliamW. Cooper 419

The Analytical Hierarchy Process 422

Management Science Application: SelectingStudents for Graduate Studies Abroad at DarAl-Hekma Women’s College 422

Management Science Application: AnalyzingAdvanced-Technology Projects at NASA 428

Management Science Application: RankingTwentieth-Century Army Generals 430

Scoring Models 433

Management Science Application: A ScoringModel for Determining U.S. Army InstallationRegions 435

Summary 435 • Example Problem Solutions 436 •Problems 439 • Case Problems 472

10 NonlinearProgramming 477

Nonlinear Profit Analysis 478

Constrained Optimization 481

Solution of Nonlinear Programming Problems withExcel 483

Management Science Application: MakingSupplier Decisions at Ford with NonlinearProgramming 487

A Nonlinear Programming Model with MultipleConstraints 488

Nonlinear Model Examples 490

Summary 494 • Example Problem Solution 495 •Problems 495 • Case Problems 500

11 Probability andStatistics 502

Types of Probability 503

Fundamentals of Probability 505

Management Science Application: TreasureHunting with Probability and Statistics 507

Statistical Independence and Dependence 508

Expected Value 515

Management Science Application:A Probability Model for Analyzing Coast GuardPatrol Effectiveness 516

CONTENTS ix

The Normal Distribution 517

Summary 527 • Example Problem Solution 527 •Problems 529 • Case Problem 535

12 Decision Analysis 537

Components of Decision Making 538

Decision Making Without Probabilities 539

Management Science Application:Planning for Terrorist Attacks and Epidemics in Los Angeles County with DecisionAnalysis 546

Decision Making with Probabilities 546

Management Science Application:Evaluating Electric Generator MaintenanceSchedules Using Decision Tree Analysis 557

Decision Analysis with Additional Information 560

Management Science Application:Scheduling Refueling at the Indian Point 3Nuclear Power Plant 566

Utility 567

Summary 568 • Example Problem Solution 569 •Problems 572 • Case Problems 592

13 Queuing Analysis 597

Elements of Waiting Line Analysis 598

The Single-Server Waiting Line System 599

Time Out: for Agner Krarup Erlang 600

Management Science Application: ReducingPerceived Waiting Time at Bank ofAmerica 607

Undefined and Constant Service Times 608

Finite Queue Length 611

Management Science Application: ProvidingTelephone Order Service in the Retail CatalogBusiness 613

Finite Calling Population 614

The Multiple-Server Waiting Line 617

Management Science Application: MakingSure 911 Calls Get Through at AT&T 620

Additional Types of Queuing Systems 622

Summary 623 • Example Problem Solution 623 •Problems 625 • Case Problems 633

14 Simulation 637

The Monte Carlo Process 638

Time Out: for John Von Neumann 643

Computer Simulation with Excel Spreadsheets 643

Simulation of a Queuing System 648

Management Science Application: Planningfor Health Emergencies Created by Terrorist Attacks 651

Continuous Probability Distributions 652

Statistical Analysis of Simulation Results 657

Management Science Application:A Monte Carlo Simulation Model for Managing Liquidity Risk at Merrill Lynch Bank USA 658

Crystal Ball 659

Verification of the Simulation Model 666

Areas of Simulation Application 666

Summary 667 • Example Problem Solution 668 •Problems 671 • Case Problems 685

15 Forecasting 689

Forecasting Components 690

Management Science Application:Forecasting Advertising Demand at NBC 692

Time Series Methods 693

Management Science Application:Forecasting at Goodyear Tire and RubberCompany 697

Management Science Application:Forecasting at Heineken USA 702

Forecast Accuracy 705

Management Science Application:Forecasting at Bayer Consumer Care 709

Time Series Forecasting Using Excel 709

Time Series Forecasting Using QM forWindows 712

Regression Methods 713

Management Science Application:An Airline Passenger Forecasting Model 717

Summary 722 • Example Problem Solutions 722 •Problems 725 • Case Problems 748