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Introduction to

Management Science

Bernard W. Taylor III

Virginia Polytechnic Institute and State University

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printed in initial caps or all caps. 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

1Management Science1

2Linear Programming:

Model Formulation and

Graphical Solution30

3Linear Programming:

Computer Solution and

Sensitivity Analysis72

4Linear Programming:

Modeling Examples111

5Integer Programming184

6Transportation,

Transshipment, and

Assignment Problems233

7Network Flow Models289

8Project Management339

9Multicriteria Decision

Making407

10Nonlinear Programming477

11Probability and Statistics502

12Decision Analysis537

13Queuing Analysis597

14Simulation637

15Forecasting689

16Inventory Management752

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 Modules

Module 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

1Management Science1

The Management Science Approach to Problem

Solving 2

Time Out:for Pioneers in Management

Science 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 Science

Techniques 18

Management Science Application:

Management Science in Health Care 19

Management Science Models in Decision Support

Systems 20

Summary 21 • Problems 22 • Case Problems 28

2Linear Programming:

Model Formulation and

Graphical Solution30

Model Formulation 31

A Maximization Model Example 31

Time Out:for George B. Dantzig 32

Management Science Application:

Allocating Seat Capacity on Indian Railways

Using Linear Programming 35

Graphical Solutions of Linear Programming

Models 35

Management Science Application:

Improving Customer Service at

Amazon.com 47

A Minimization Model Example 47

Management Science Application:

Determining Optimal Fertilizer Mixes

at Soquimich (South America) 51

Irregular Types of Linear Programming

Problems 53

Characteristics of Linear Programming

Problems 56

Summary 57 • Example Problem Solution 57 •

Problems 61 € Case Problems 70

3Linear Programming:

Computer Solution and

Sensitivity Analysis72

Computer Solution 73

Management Science Application:

Optimizing Production Quantities at GE

Plastics 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

CONTENTSvii

4Linear Programming:

Modeling Examples111

A Product Mix Example 112

Time Out:for George B. Dantzig 117

A Diet Example 117

An Investment Example 120

Management Science Application:A Linear

Programming Model for Optimal Portfolio

Selection 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 Management

Science 140

A Data Envelopment Analysis Example 142

Management Science Application:

Evaluating American Red Cross Chapters Using

DEA 144

Summary 146 • Example Problem Solution 147 •

Problems 149 • Case Problems 179

5Integer Programming184

Integer Programming Models 185

Management Science Application:Allocating

Operating Room Time at Toronto"s Mount Sinai

Hospital 188

Integer Programming Graphical Solution 188

Computer Solution of Integer Programming

Problems 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:Forming

Business Case Student Teams at Indiana

University 199

0-1 Integer Programming Modeling

Examples 199

Management Science Application:Planning

Next-Day Air Shipments at UPS 208

Summary 208 • Example Problem Solution 209 •

Problems 209 • Case Problems 225

6Transportation,

Transshipment, and

Assignment Problems233

The Transportation Model 234

Time Out:for Frank L. Hitchcock and Tjalling

C. Koopmans 236

Management Science Application:

Transportation Models at Nu-kote

International 237

Computer Solution of a Transportation

Problem 237

Management Science Application:Matching

Wineries with Distributors 242

The Transshipment Model 243

Management Science Application:

Transporting Mail at the U.S. Postal

Service 246

The Assignment Model 247

Computer Solution of an Assignment Problem 247

Management Science Application:Supplying

Empty Freight Cars at Union Pacific

Railroad 250

Management Science Application:Assigning

Umpire Crews at Professional Tennis

Tournaments 251

Summary 252 • Example Problem Solution 252 •

Problems 253 • Case Problems 281

7Network Flow

Models289

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 viiiCONTENTS

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

8Project Management339

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 T5

Project 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 Linear

Programming Model 374

Summary 381 • Example Problem Solution 382 •

Problems 384 • Case Problems 404

9Multicriteria Decision

Making407

Goal Programming 408

Graphical Interpretation of Goal

Programming 412

Computer Solution of Goal Programming Problems

with QM for Windows and Excel 415

Management Science Application:

Developing Television Advertising Sales Plans

at NBC 415

Time Out:for Abraham Charnes and William

W. Cooper 419

The Analytical Hierarchy Process 422

Management Science Application:Selecting

Students for Graduate Studies Abroad at Dar

Al-Hekma Women"s College 422

Management Science Application:Analyzing

Advanced-Technology Projects at NASA 428

Management Science Application:Ranking

Twentieth-Century Army Generals 430

Scoring Models 433

Management Science Application:A Scoring

Model for Determining U.S. Army Installation

Regions 435

Summary 435 • Example Problem Solutions 436 •

Problems 439 • Case Problems 472

10Nonlinear

Programming477

Nonlinear Profit Analysis 478

Constrained Optimization 481

Solution of Nonlinear Programming Problems with

Excel 483

Management Science Application:Making

Supplier Decisions at Ford with Nonlinear

Programming 487

A Nonlinear Programming Model with Multiple

Constraints 488

Nonlinear Model Examples 490

Summary 494 • Example Problem Solution 495 •

Problems 495 • Case Problems 500

11Probability and

Statistics502

Types of Probability 503

Fundamentals of Probability 505

Management Science Application:Treasure

Hunting with Probability and Statistics 507

Statistical Independence and Dependence 508

Expected Value 515

Management Science Application:

A Probability Model for Analyzing Coast Guard

Patrol Effectiveness 516

CONTENTSix

The Normal Distribution 517

Summary 527 • Example Problem Solution 527 •

Problems 529 • Case Problem 535

12Decision Analysis537

Components of Decision Making 538

Decision Making Without Probabilities 539

Management Science Application:

Planning for Terrorist Attacks and Epidemics

in Los Angeles County with Decision

Analysis 546

Decision Making with Probabilities 546

Management Science Application:

Evaluating Electric Generator Maintenance

Schedules Using Decision Tree Analysis 557

Decision Analysis with Additional Information 560

Management Science Application:

Scheduling Refueling at the Indian Point 3

Nuclear Power Plant 566

Utility 567

Summary 568 • Example Problem Solution 569 •

Problems 572 • Case Problems 592

13Queuing Analysis597

Elements of Waiting Line Analysis 598

The Single-Server Waiting Line System 599

Time Out:for Agner Krarup Erlang 600

Management Science Application:Reducing

Perceived Waiting Time at Bank of

America 607

Undefined and Constant Service Times 608

Finite Queue Length 611

Management Science Application:Providing

Telephone Order Service in the Retail Catalog

Business 613

Finite Calling Population 614

The Multiple-Server Waiting Line 617

Management Science Application:Making

Sure 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

14Simulation637

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:Planning

for 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

15Forecasting689

Forecasting Components 690

Management Science Application:

Forecasting Advertising Demand

at NBC 692

Time Series Methods 693

Management Science Application:

Forecasting at Goodyear Tire and Rubber

Company 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 for

Windows 712

Regression Methods 713

Management Science Application:

An Airline Passenger Forecasting Model 717

Summary 722 • Example Problem Solutions 722 •

Problems 725 • Case Problems 748

xCONTENTS

16Inventory Management752

Elements of Inventory Management 753

Management Science Application:

Evaluating Inventory Costs at Hewlett-

Packard 755

Inventory Control Systems 756

Time Out:for Ford Harris 757

Economic Order Quantity Models 757

The Basic EOQ Model 758

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