Giáo trình introduction to management sciecne a modeling and case studies appriach with speachsheets 5e by hillier

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INTRODUCTION TO MANAGEMENT SCIENCE: A MODELING AND CASE STUDIES

APPROACH WITH SPREADSHEETS, FIFTH EDITION

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Introduction to management science : modeling and case studies approach with spreadsheets / Frederick

S Hillier, Stanford University, Mark S Hillier, University of Washington ; cases developed by Karl

Schmedders, University of Zurich, Molly Stephens, Quinn, Emanuel, Urquhart, Sullivan LLP.—Fifth

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ISBN 978-0-07-802406-1 (alk paper)

1 Management science 2 Operations research—Data processing 3 Electronic spreadsheets I Hillier,

Mark S II Title.

T56.H55 2014

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The Internet addresses listed in the text were accurate at the time of publication The inclusion of a

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To the memory of

Christine Phillips Hillier

a beloved wife and daughter-in-law

Gerald J Lieberman

an admired mentor and one of the true giants

of our field

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vi

About the Authors

Frederick S Hillier is professor emeritus of operations research at Stanford University Dr

Hillier is especially known for his classic, award-winning text, Introduction to Operations

Research, co-authored with the late Gerald J Lieberman, which has been translated into well

over a dozen languages and is currently in its 9th edition The 6th edition won honorable tion for the 1995 Lanchester Prize (best English-language publication of any kind in the field) and Dr Hillier also was awarded the 2004 INFORMS Expository Writing Award for the 8th

men-edition His other books include The Evaluation of Risky Interrelated Investments, Queueing

Tables and Graphs, Introduction to Stochastic Models in Operations Research, and tion to Mathematical Programming He received his BS in industrial engineering and doctorate

Introduc-specializing in operations research and management science from Stanford University The winner of many awards in high school and college for writing, mathematics, debate, and music,

he ranked first in his undergraduate engineering class and was awarded three national lowships (National Science Foundation, Tau Beta Pi, and Danforth) for graduate study After receiving his PhD degree, he joined the faculty of Stanford University, where he earned tenure

fel-at the age of 28 and the rank of full professor fel-at 32 Dr Hillier’s research has extended into a variety of areas, including integer programming, queueing theory and its application, statistical quality control, and production and operations management He also has won a major prize for research in capital budgeting Twice elected a national officer of professional societies, he has served in many important professional and editorial capacities For example, he served The Institute of Management Sciences as vice president for meetings, chairman of the publications

committee, associate editor of Management Science, and co-general chairman of an

interna-tional conference in Japan He also is a Fellow of the Institute for Operations Research and the Management Sciences (INFORMS) He currently is continuing to serve as the founding series editor for a prominent book series, the International Series in Operations Research and Man-agement Science, for Springer Science  1  Business Media He has had visiting appointments at Cornell University, the Graduate School of Industrial Administration of Carnegie-Mellon Uni-versity, the Technical University of Denmark, the University of Canterbury (New Zealand), and the Judge Institute of Management Studies at the University of Cambridge (England)

Mark S Hillier, son of Fred Hillier, is associate professor of quantitative methods at the

Michael G Foster School of Business at the University of Washington Dr Hillier received his BS in engineering (plus a concentration in computer science) from Swarthmore College

He then received his MS with distinction in operations research and PhD in industrial neering and engineering management from Stanford University As an undergraduate, he won the McCabe Award for ranking first in his engineering class, won election to Phi Beta Kappa based on his work in mathematics, set school records on the men’s swim team, and was awarded two national fellowships (National Science Foundation and Tau Beta Pi) for gradu-ate study During that time, he also developed a comprehensive software tutorial package,

OR Courseware, for the Hillier–Lieberman textbook, Introduction to Operations Research

As a graduate student, he taught a PhD-level seminar in operations management at Stanford and won a national prize for work based on his PhD dissertation At the University of Wash-ington, he currently teaches courses in management science and spreadsheet modeling He has won several MBA teaching awards for the core course in management science and his elective course in spreadsheet modeling, as well as a universitywide teaching award for his work in teaching undergraduate classes in operations management He was chosen by MBA students in 2007 as the winner of the prestigious PACCAR award for Teacher of the Year (reputed to provide the largest monetary award for MBA teaching in the nation) He also has been awarded an appointment to the Evert McCabe Endowed Faculty Fellowship His research interests include issues in component commonality, inventory, manufacturing, and the design of production systems A paper by Dr Hillier on component commonality won an

award for best paper of 2000–2001 in IIE Transactions He currently is principal investigator

on a grant from the Bill and Melinda Gates Foundation to lead student research projects that apply spreadsheet modeling to various issues in global health being studied by the foundation

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About the Case Writers

Karl Schmedders is professor of quantitative business administration at the University

of Zurich in Switzerland and a visiting associate professor at the Kellogg School of agement of Northwestern University His research interests include management science, financial economics, and computational economics and finance In 2003, a paper by Dr

Man-Schmedders received a nomination for the Smith-Breeden Prize for the best paper in the

Jour-nal of Finance He received his PhD in operations research from Stanford University, where

he taught both undergraduate and graduate classes in management science, including a case studies course He received several teaching awards at Stanford, including the university-wide Walter J Gores Teaching Award After a post-doc at the Hoover Institution, a think tank

on the Stanford campus, he became assistant professor of managerial economics and decision sciences at the Kellogg School He was promoted to associate professor in 2001 and received tenure in 2005 In 2008 he joined the University of Zurich, where he currently teaches courses

in management science, spreadsheet modeling, and computational economics and finance At Kellogg he received several teaching awards, including the L G Lavengood Professor of the Year Award Most recently he won the best professor award of the Kellogg School’s Euro-pean EMBA program (2008, 2009, and 2011) and its Miami EMBA program (2011)

Molly Stephens is a partner in the Los Angeles office of Quinn, Emanuel, Urquhart &

Sullivan, LLP She graduated from Stanford with a BS in industrial engineering and an MS in operations research Ms Stephens taught public speaking in Stanford’s School of Engineer-ing and served as a teaching assistant for a case studies course in management science As a teaching assistant, she analyzed management science problems encountered in the real world and transformed these into classroom case studies Her research was rewarded when she won

an undergraduate research grant from Stanford to continue her work and was invited to speak

at INFORMS to present her conclusions regarding successful classroom case studies ing graduation, Ms Stephens worked at Andersen Consulting as a systems integrator, expe-riencing real cases from the inside, before resuming her graduate studies to earn a JD degree with honors from the University of Texas School of Law at Austin She is a partner in the largest law firm in the United States devoted solely to business litigation, where her practice focuses on complex financial and securities litigation

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Preface

We have long been concerned that traditional management science textbooks have not taken the best approach in introducing business students to this exciting field Our goal when ini-tially developing this book during the late 1990s was to break out of the old mold and present new and innovative ways of teaching management science more effectively We have been gratified by the favorable response to our efforts Many reviewers and other users of the first four editions of the book have expressed appreciation for its various distinctive features, as well as for its clear presentation at just the right level for their business students

Our goal for this fifth edition has been to build on the strengths of the first four editions

Co-author Mark Hillier has won several schoolwide teaching awards for his spreadsheet eling and management science courses at the University of Washington while using the first four editions, and this experience has led to many improvements in the current edition We also incorporated many user comments and suggestions Throughout this process, we took painstaking care to enhance the quality of the preceding edition while maintaining the distinc-tive orientation of the book

This distinctive orientation is one that closely follows the recommendations in the 1996 report of the operating subcommittee of the INFORMS Business School Education Task Force, including the following extract

There is clear evidence that there must be a major change in the character of the (introductory management science) course in this environment There is little patience with courses centered

on algorithms Instead, the demand is for courses that focus on business situations, include prominent non-mathematical issues, use spreadsheets, and involve model formulation and assessment more than model structuring Such a course requires new teaching materials

This book is designed to provide the teaching materials for such a course

In line with the recommendations of this task force, we believe that a modern introductory management science textbook should have three key elements As summarized in the subtitle

of this book, these elements are a modeling and case studies approach with spreadsheets

SPREADSHEETS

The modern approach to the teaching of management science clearly is to use spreadsheets

as a primary medium of instruction Both business students and managers now live with spreadsheets, so they provide a comfortable and enjoyable learning environment Modern spreadsheet software, including Microsoft Excel used in this book, now can be used to do real management science For student-scale models (which include many practical real-world models), spreadsheets are a much better way of implementing management science models than traditional algebraic solvers This means that the algebraic curtain that was so prevalent

in traditional management science courses and textbooks now can be lifted

However, with the new enthusiasm for spreadsheets, there is a danger of going board Spreadsheets are not the only useful tool for performing management science analy-ses Occasional modest use of algebraic and graphical analyses still have their place and

over-we would be doing a disservice to the students by not developing their skills in these areas when appropriate Furthermore, the book should not be mainly a spreadsheet cookbook that focuses largely on spreadsheet mechanics Spreadsheets are a means to an end, not an end

in themselves

A MODELING APPROACH

This brings us to the second key feature of the book, a modeling approach Model

formula-tion lies at the heart of management science methodology Therefore, we heavily emphasize the art of model formulation, the role of a model, and the analysis of model results We pri-marily (but not exclusively) use a spreadsheet format rather than algebra for formulating and presenting a model

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a spreadsheet Furthermore, by using the best spreadsheet modeling techniques (as presented

in this edition), formulating a spreadsheet model tends to be considerably more efficient and transparent than formulating an algebraic model Another benefit is that the spreadsheet model includes all the relationships that can be expressed in an algebraic form and we often will summarize the model in this format as well

Another break from tradition in this book (and several contemporary textbooks) is to virtually ignore the algorithms that are used to solve the models We feel that there is no good reason why typical business students should learn the details of algorithms executed by computers Within the time constraints of a one-term management science course, there are far more important lessons to be learned Therefore, the focus in this book is on what we believe are these far more important lessons High on this list is the art of modeling managerial problems on a spreadsheet

Formulating a spreadsheet model of a real problem typically involves much more than designing the spreadsheet and entering the data Therefore, we work through the process step by step: understand the unstructured problem, verbally develop some structure for the problem, gather the data, express the relationships in quantitative terms, and then lay out the spreadsheet model The structured approach highlights the typical components of the model (the data, the decisions to be made, the constraints, and the measure of performance) and the different types of spreadsheet cells used for each Consequently, the emphasis is on the mod-eling rather than spreadsheet mechanics

A CASE STUDIES APPROACH

However, all this still would be quite sterile if we simply presented a long series of brief examples with their spreadsheet formulations This leads to the third key feature of this

book—a case studies approach In addition to examples, nearly every chapter includes one or

two case studies patterned after actual applications to convey the whole process of applying management science In a few instances, the entire chapter revolves around a case study By drawing the student into the story, we have designed each case study to bring that chapter’s technique to life in a context that vividly illustrates the relevance of the technique for aiding managerial decision making This storytelling, case-centered approach should make the mate-rial more enjoyable and stimulating while also conveying the practical considerations that are key factors in applying management science

We have been pleased to have several reviewers of the first four editions express particular appreciation for our case study approach Even though this approach has received little use

in other management science textbooks, we feel that it is a real key to preparing students for the practical application of management science in all its aspects Some of the reviewers have highlighted the effectiveness of the dialogue/scenario enactment approach used in some of the case studies Although unconventional, this approach provides a way of demonstrating the process of managerial decision making with the help of management science It also enables previewing some key concepts in the language of management

Every chapter also contains full-fledged cases following the problems at the end of the chapter These cases usually continue to employ a stimulating storytelling approach, so they can be assigned as interesting and challenging projects Most of these cases were developed jointly by two talented case writers, Karl Schmedders (a faculty member at the University

of Zurich in Switzerland) and Molly Stephens (formerly a management science consultant with Andersen Consulting) The authors also have added some cases, including several shorter ones In addition, the University of Western Ontario Ivey School of Business (the second-largest producer of teaching cases in the world) has specially selected cases from their case collection that match the chapters in this textbook These cases are available on

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the Ivey website, cases.ivey.uwo.ca/cases , in the segment of the CaseMate area designated

for this book This website address is provided at the end of each chapter as well

We are, of course, not the first to incorporate any of these key features into a management science textbook However, we believe that the book currently is unique in the way that it fully incorporates all three key features together

OTHER SPECIAL FEATURES

We also should mention some additional special features of the book that are continued from the fourth edition

• Diverse examples, problems, and cases convey the pervasive relevance of management science

• A strong managerial perspective

• Learning objectives at the beginning of each chapter

• Numerous margin notes that clarify and highlight key points

• Excel tips interspersed among the margin notes

• Review questions at the end of each section

• A glossary at the end of each chapter

• Partial answers to selected problems in the back of the book

• Supplementary text material on the CD-ROM (as identified in the table of contents)

• An Excel-based software package (MS Courseware) on the CD-ROM and website that includes many add-ins, templates, and files (described below)

• Other helpful supplements on the CD-ROM and website (described later)

A NEW SOFTWARE PACKAGE

This edition continues to integrate Excel 2010 and its Solver (a product of Frontline Systems) throughout the book However, we are excited to also add to this edition an impressive more recent product of Frontline Systems called Risk Solver Platform for Education (or RSPE

for short) RSPE also is an Excel add-in and its Solver shares some of the features of the Excel Solver However, in addition to providing all the key capabilities of the Excel Solver, RSPE adds some major new functionalities as outlined below:

• A more interactive user interface, with the model parameters always visible alongside the main spreadsheet, rather than only in the Solver dialog box

• Parameter analysis reports that provide an easy way to see the effect of varying data in a model in a systematic way

• A model analysis tool that reveals the characteristics of a model (e.g., whether it is linear

or nonlinear, smooth or nonsmooth)

• Tools to build and solve decision trees within a spreadsheet

• The ability to build and run sophisticated Monte Carlo simulation models

• An interactive simulation mode that allows simulation results to be shown instantly ever a change is made to a simulation model

• The RSPE Solver can be used in combination with computer simulation to perform lation optimization

A CONTINUING FOCUS ON EXCEL AND ITS SOLVER

As with all the preceding editions, this edition continues to focus on spreadsheet modeling

in an Excel format Although it lacks some of the functionalities of RSPE, the Excel Solver continues to provide a completely satisfactory way of solving most of the spreadsheet models encountered in this book This edition continues to feature this use of the Excel Solver when-ever either it or the RSPE Solver could be used

Many instructors prefer this focus because it avoids introducing other complications that might confuse their students We agree

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Preface xi

However, the key advantage of introducing RSPE in this edition is that it provides an one complement to the Excel Solver There are some important topics in the book (including decision analysis and computer simulation) where the Excel Solver lacks the functionalities needed to deal with these kinds of problems Multiple Excel add-ins—Solver Table, Tree-Plan, SensIt, RiskSim, Crystal Ball, and OptQuest (a module of Crystal Ball)—were intro-duced in previous editions to provide the needed functionalities RSPE alone now replaces all

all-in-of these add-ins

OTHER SOFTWARE

Each edition of this book has provided a comprehensive Excel-based software package called

MS Courseware on the CD-ROM and website RSPE replaces various Excel add-ins in this

package Otherwise, the remainder of this package is being provided again with the current edition

This package includes Excel files that provide the live spreadsheets for all the various examples and case studies throughout the book In addition to further investigating the exam-ples and case studies, these spreadsheets can be used by either the student or instructor as tem-plates to formulate and solve similar problems The package also includes dozens of Excel templates for solving various models in the book

MS Courseware includes additional software as well

• Interactive Management Science Modules for interactively exploring certain

manage-ment science techniques in depth (including techniques presented in Chapters 1, 2, 5, 10,

11, 12, and 18)

• Queueing Simulator for performing computer simulations of queueing systems (used in

Chapter 12)

NEW FEATURES IN THIS EDITION

We have made some important enhancements to the fifth edition

• A Substantial Revision of Chapter 1 In addition to some updates and a new

end-of-chapter case, the example at the heart of the end-of-chapter has been modernized to better attract the interest of the students The example now deals with iWatches instead of grandfather clocks

• A New Section Introduces Risk Solver Platform for Education (RSPE) Section 2.6

presents the basics of how to use RSPE It is placed near the end of Chapter 2 to avoid disrupting the flow of the chapter, including the introduction of the Excel Solver

• Parameter Analysis Reports Are Introduced and Widely Used Parameter analysis

reports are introduced in Chapter 5 for performing sensitivity analysis systematically This key tool of RSPE also receives important use in Chapters 7, 8, and 13

• Chapter 8 Is Revised to Better Identify the Available Solving Methods for Nonlinear Programming The Excel Solver and the RSPE Solver share some solving methods for

nonlinear programming and then the RSPE Solver adds another one These solving ods and when each one should be used are better identified now

• A New Section on Using RSPE to Analyze a Model and Choose a Solving Method A

new Section 8.6 describes a key tool of RSPE for analyzing a model and choosing the best solving method

• A Substantial Revision of Chapter 9 (Decision Analysis) RSPE has outstanding

func-tionality for constructing and analyzing decision trees This funcfunc-tionality is thoroughly exploited in the revised Chapter 9

• A Key Revision of the First Computer Simulation Chapter Computer simulation commonly is used to analyze complicated queueing systems, so it is natural for Chapter

12 (Computer Simulation: Basic Concepts) to refer back to Chapter 11 (Queueing els) occasionally However, some instructors cover Chapter 12 but skip over Chapter 11

Mod-Therefore, we have revised Chapter 12 to make it as independent of Chapter 11 as possible while still covering this important kind of application of computer simulation

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xii Preface

• A Major Revision of the Second Computer Simulation Chapter Although the

exam-ples remain the same, the old Chapter 13 (Computer Simulation with Crystal Ball) has been thoroughly revised to replace Crystal Ball by Risk Solver Platform for Education (RSPE)

Most students already will be familiar with RSPE from preceding chapters, which should provide a gentler entry into this chapter More importantly, this impressive, relatively new software package has some significant advantages over Crystal Ball for performing and analyzing computer simulations However, an updated version of the old Chapter 13 still will be available on the CD-ROM (now Chapter 20) for instructors who wish to stick with Crystal Ball for the time being

• A New Section on Decision Making with Computer Simulations A key tool of RSPE is

its use of multiple simulation runs to generate parameter analysis reports and trend charts that can provide an important guide to managerial decision making Section 13.8 describes this approach to decision making

• A New Section on Optimizing with Computer Simulations Another key tool of RSPE

is that its Solver can use multiple simulation runs to automatically search for an mal solution for simulation models with any number of decision variables Section 13.9 describes this approach

• Additional Links to Articles that Describe Dramatic Real Applications The fourth

edition includes 23 application vignettes that describe in a few paragraphs how an actual application of management science had a powerful effect on a company or organization by using techniques like those being studied in that portion of the book The current edition adds seven more vignettes based on recent applications (while deleting two old ones) We also continue the practice of adding a link to the journal articles that fully describe these applications, through a special arrangement with the Institute for Operations Research and the Management Sciences (INFORMS ® ) Thus, the instructor now can motivate his or her lectures by having the students delve into real applications that dramatically demonstrate the relevance of the material being covered in the lectures The end-of-chapter problems also include an assignment after reading each of these articles

We continue to be excited about this partnership with INFORMS, our field’s preeminent professional society, to provide a link to these 28 articles describing spectacular applica-tions of management science INFORMS is a learned professional society for students, aca-demics, and practitioners in quantitative and analytical fields Information about INFORMS journals, meetings, job bank, scholarships, awards, and teaching materials is available at

www.informs.org

• Refinements in Each Chapter Each chapter in the fourth edition has been carefully

examined and revised as needed to update and clarify the material after also taking into account the input provided by reviewers and others

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Preface xiii

OTHER SUPPLEMENTS

The Instructor’s Edition of this book’s Online Learning Center, www.mhhe.com/hillier5e ,

is password-protected and a convenient place for instructors to access course supplements

Resources for professors include the complete solutions to all problems and cases, a test bank with hundreds of multiple-choice and true-false questions, and PowerPoint Presentation The PowerPoint slides include both lecture materials for nearly every chapter and nearly all the figures (including all the spreadsheets) in the book

The student’s CD-ROM bundled with the book provides most of the MS Courseware package It also includes a tutorial with sample test questions (different from those in the instructor’s test bank) for self-testing quizzes on the various chapters

The materials on the student CD-ROM can also be accessed on the Student’s Edition of the Online Learning Center, www.mhhe.com/hillier5e The website also provides the remain-

der of the MS Courseware package, as well as access to the INFORMS articles cited in the application vignettes and updates about the book, including errata In addition, the publisher’s operations management supersite at www.mhhe.com/pom/ links to many resources on the

Internet that you might find pertinent to this book

We invite your comments, suggestions, and errata You can contact either one of us at the e-mail addresses given below While giving these addresses, let us also assure instructors that

we will continue our policy of not providing solutions to problems and cases in the book to

anyone (including your students) who contacts us We hope that you enjoy the book

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Acknowledgments

This new edition has benefited greatly from the sage advice of many individuals To begin,

we would like to express our deep appreciation to the following individuals who provided formal reviews of the fourth edition:

Michael (Tony) Ratcliffe

James Madison University

John Wang

Montclair State University

Jinfeng Yue

Middle Tennessee State University

We also are grateful for the valuable input provided by many of our students as well as various other students and instructors who contacted us via e-mail

This book has continued to be a team effort involving far more than the two coauthors As

a third coauthor for the first edition, the late Gerald J Lieberman provided important initial impetus for this project We also are indebted to our case writers, Karl Schmedders and Molly Stephens, for their invaluable contributions Ann Hillier again devoted numerous hours to sitting with a Macintosh, doing word processing and constructing figures and tables They all were vital members of the team

McGraw-Hill/Irwin’s editorial and production staff provided the other key members of the team, including Douglas Reiner (Publisher), Beth Baugh (Freelance Developmental Editor), and Mary Jane Lampe (Project Manager) This book is a much better product because of their guidance and hard work It has been a real pleasure working with such a thoroughly profes-sional staff

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1 Introduction 1

2 Linear Programming: Basic Concepts 22

3 Linear Programming: Formulation

and Applications 64

4 The Art of Modeling with Spreadsheets 124

5 What-If Analysis for Linear

Programming 150

6 Network Optimization Problems 194

7 Using Binary Integer Programming to Deal

with Yes-or-No Decisions 232

8 Nonlinear Programming 267

9 Decision Analysis 322

10 Forecasting 384

11 Queueing Models 433

12 Computer Simulation: Basic Concepts 488

13 Computer Simulation with Risk Solver

SUPPLEMENTS ON THE CD-ROM

Supplement to Chapter 2: More about the Graphical Method for Linear Programming Supplement to Chapter 5: Reduced Costs

Supplement to Chapter 6: Minimum ning-Tree Problems

Supplement 1 to Chapter 7: Advanced mulation Techniques for Binary Integer Programming

Supplement 2 to Chapter 7: Some tives on Solving Binary Integer Program- ming Problems

Supplement 1 to Chapter 9: Decision Criteria

Supplement 2 to Chapter 9: Using TreePlan Software for Decision Trees

Supplement to Chapter 11: Additional Queueing Models

Supplement to Chapter 12: The Inverse Transformation Method for Generating Random Observations

CHAPTERS ON THE CD-ROM

14 Solution Concepts for Linear

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xvi

Contents

Chapter 1

Introduction 1

1.1 The Nature of Management Science 2

1.2 An Illustration of the Management Science

Approach: Break-Even Analysis 6

1.3 The Impact of Management Science 12

1.4 Some Special Features of This Book 14

Linear Programming: Basic Concepts 22

2.1 A Case Study: The Wyndor Glass Co

Product-Mix Problem 23

2.2 Formulating the Wyndor Problem on a

Spreadsheet 25

2.3 The Mathematical Model in the Spreadsheet 31

2.4 The Graphical Method for Solving Two-Variable

Problems 33

2.5 Using Excel’s Solver to Solve Linear

Program-ming Problems 38

2.6 Risk Solver Platform for Education (RSPE) 42

2.7 A Minimization Example—The Profit & Gambit

Co Advertising-Mix Problem 46

2.8 Linear Programming from a Broader

Case 2-1 Auto Assembly 60

Case 2-2 Cutting Cafeteria Costs 61

Case 2-3 Staffing a Call Center 62

Solved Problems 104 Problems 105 Case 3-1 Shipping Wood to Market 114 Case 3-2 Capacity Concerns 115 Case 3-3 Fabrics and Fall Fashions 116 Case 3-4 New Frontiers 118

Case 3-5 Assigning Students to Schools 119 Case 3-6 Reclaiming Solid Wastes 120 Case 3-7 Project Pickings 121

Chapter 4 The Art of Modeling with Spreadsheets 124

4.1 A Case Study: The Everglade Golden Years Company Cash Flow Problem 125

4.2 Overview of the Process of Modeling with Spreadsheets 126

4.3 Some Guidelines for Building “Good” sheet Models 135

4.4 Debugging a Spreadsheet Model 141

4.5 Summary 144

Glossary 145 Learning Aids for This Chapter in Your MS Courseware 145

Solved Problems 145 Problems 146 Case 4-1 Prudent Provisions for Pensions 148

Chapter 5 What-If Analysis for Linear Programming 150

5.1 The Importance of What-If Analysis to Managers 151

5.2 Continuing the Wyndor Case Study 153

5.3 The Effect of Changes in One Objective Function Coefficient 155

5.4 The Effect of Simultaneous Changes in Objective Function Coefficients 161

5.5 The Effect of Single Changes in a Constraint 169

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Case 5-1 Selling Soap 188

Case 5-2 Controlling Air Pollution 189

Case 5-3 Farm Management 191

Case 5-4 Assigning Students to

Schools (Revisited) 193

Chapter 6

Network Optimization Problems 194

6.1 Minimum-Cost Flow Problems 195

6.2 A Case Study: The BMZ Co Maximum Flow

Problem 202

6.3 Maximum Flow Problems 205

6.4 Shortest Path Problems 209

Case 6-1 Aiding Allies 224

Case 6-2 Money in Motion 227

Case 6-3 Airline Scheduling 229

Case 6-4 Broadcasting the Olympic

Games 230

Chapter 7

Using Binary Integer Programming to Deal

with Yes-or-No Decisions 232

7.1 A Case Study: The California Manufacturing Co

Problem 233

7.2 Using BIP for Project Selection: The Tazer Corp

Problem 239

7.3 Using BIP for the Selection of Sites for

Emer-gency Services Facilities: The Caliente City Problem 241

7.4 Using BIP for Crew Scheduling: The

Southwest-ern Airways Problem 246

7.5 Using Mixed BIP to Deal with Setup Costs for

Initiating Production: The Revised Wyndor Problem 250

Schools (Revisited) 266 Case 7-4 Broadcasting the Olympic Games

(Revisited) 266

Chapter 8 Nonlinear Programming 267

8.1 The Challenges of Nonlinear Programming 269

8.2 Nonlinear Programming with Decreasing Marginal Returns 277

8.3 Separable Programming 287

8.4 Difficult Nonlinear Programming Problems 297

8.5 Evolutionary Solver and Genetic Algorithms 299

8.6 Using RSPE to Analyze a Model and Choose a Solving Method 306

8.7 Summary 310

Glossary 311 Learning Aids for This Chapter in Your MS Courseware 312

Solved Problem 312 Problems 312 Case 8-1 Continuation of the Super Grain Case

Study 317 Case 8-2 Savvy Stock Selection 318 Case 8-3 International Investments 319

Chapter 9 Decision Analysis 322

9.1 A Case Study: The Goferbroke Company Problem 323

9.2 Decision Criteria 325

9.3 Decision Trees 330

9.4 Sensitivity Analysis with Decision Trees 333

9.5 Checking Whether to Obtain More Information 338

9.6 Using New Information to Update the Probabilities 340

9.7 Using a Decision Tree to Analyze the Problem with a Sequence of Decisions 344

9.8 Performing Sensitivity Analysis on the Problem with a Sequence of Decisions 351

9.9 Using Utilities to Better Reflect the Values of Payoffs 354

9.10 The Practical Application of Decision Analysis 365

9.11 Summary 366

Glossary 367

Rev Confirming Pages

Case 9-1 Who Wants to Be a Millionaire? 379

Case 9-2 University Toys and the Business Professor

Action Figures 379 Case 9-3 Brainy Business 380

Case 9-4 Smart Steering Support 382

Chapter 10

Forecasting 384

10.1 An Overview of Forecasting Techniques 385

10.2 A Case Study: The Computer Club Warehouse

(CCW) Problem 386

10.3 Applying Time-Series Forecasting Methods to

the Case Study 391

10.4 The Time-Series Forecasting Methods in

Perspective 410

10.5 Causal Forecasting with Linear Regression 413

10.6 Judgmental Forecasting Methods 418

10.7 Summary 419

Glossary 420

Summary of Key Formulas 421

Learning Aids for This Chapter in Your MS

11.1 Elements of a Queueing Model 434

11.2 Some Examples of Queueing Systems 440

11.3 Measures of Performance for Queueing

Systems 442

11.4 A Case Study: The Dupit Corp Problem 445

11.5 Some Single-Server Queueing Models 448

11.6 Some Multiple-Server Queueing Models 457

11.7 Priority Queueing Models 463

11.8 Some Insights about Designing Queueing

Case 11-1 Queueing Quandary 485

Case 11-2 Reducing In-Process Inventory 486

Chapter 12 Computer Simulation: Basic Concepts 488

12.1 The Essence of Computer Simulation 489

12.2 A Case Study: Herr Cutter’s Barber Shop (Revisited) 501

12.3 Analysis of the Case Study 508

12.4 Outline of a Major Computer Simulation Study 515

12.5 Summary 518

Glossary 518 Learning Aids for This Chapter in Your MS Courseware 519

Solved Problem 519 Problems 519 Case 12-1 Planning Planers 523 Case 12-2 Reducing In-Process Inventory

(Revisited) 524

Chapter 13 Computer Simulation with Risk Solver Platform 525

13.1 A Case Study: Freddie the Newsboy’s Problem 526

13.2 Bidding for a Construction Project: A Prelude to the Reliable Construction Co Case Study 536

13.3 Project Management: Revisiting the Reliable Construction Co Case Study 540

13.4 Cash Flow Management: Revisiting the glade Golden Years Company Case Study 546

13.5 Financial Risk Analysis: Revisiting the Big Development Co Problem 552

13.6 Revenue Management in the Travel Industry 557

13.7 Choosing the Right Distribution 562

13.8 Decision Making with Parameter Analysis Reports and Trend Charts 575

13.9 Optimizing with Computer Simulation Using RSPE’s Solver 583

13.10 Summary 590

Glossary 591 Learning Aids for This Chapter in Your MS Courseware 591

Solved Problem 591 Problems 592 Case 13-1 Action Adventures 596 Case 13-2 Pricing under Pressure 597

Appendix A Tips for Using Microsoft Excel for Modeling 599

Appendix B Partial Answers to Selected Problems 605

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Contents xix

Index 609

Supplements on the CD-ROM

Supplement to Chapter 2: More about the Graphical Method for Linear Programming Supplement to Chapter 5: Reduced Costs Supplement to Chapter 6: Minimum Spanning-Tree Problems

Supplement 1 to Chapter 7: Advanced tion Techniques for Binary Integer Programming Supplement 2 to Chapter 7: Some Perspectives on Solving Binary Integer Programming Problems Supplement 1 to Chapter 9: Decision Criteria Supplement 2 to Chapter 9: Using TreePlan Software for Decision Trees

Supplement to Chapter 11: Additional Queueing Models

Supplement to Chapter 12: The Inverse formation Method for Generating Random Observations

Chapters on the CD-ROM

Chapter 14

Solution Concepts for Linear Programming

14.1 Some Key Facts about Optimal Solutions

14.2 The Role of Corner Points in Searching for an

Optimal Solution

14.3 Solution Concepts for the Simplex Method

14.4 The Simplex Method with Two Decision

Variables

14.5 The Simplex Method with Three Decision

Variables

14.6 The Role of Supplementary Variables

14.7 Some Algebraic Details for the Simplex Method

14.8 Computer Implementation of the Simplex

Transportation and Assignment Problems

15.1 A Case Study: The P & T Company Distribution

Problem

15.2 Characteristics of Transportation Problems

15.3 Modeling Variants of Transportation Problems

15.4 Some Other Applications of Variants of

Trans-portation Problems

15.5 A Case Study: The Texago Corp Site Selection Problem

15.6 Characteristics of Assignment Problems

15.7 Modeling Variants of Assignment Problems

15.8 Summary

Glossary Learning Aids for This Chapter in Your MS Courseware

Problems Case 15-1 Continuation of the Texago Case Study

Chapter 16 PERT/CPM Models for Project Management

16.1 A Case Study: The Reliable Construction Co

Project

16.2 Using a Network to Visually Display a Project

16.3 Scheduling a Project with PERT/CPM

16.4 Dealing with Uncertain Activity Durations

16.5 Considering Time–Cost Trade-Offs

16.6 Scheduling and Controlling Project Costs

16.7 An Evaluation of PERT/CPM from a Managerial Perspective

16.8 Summary

Glossary Learning Aids for This Chapter in Your MS Courseware

Problems Case 16-1 Steps to Success Case 16-2 “School’s Out Forever  .  ”

Chapter 17 Goal Programming

17.1 A Case Study: The Dewright Co

Goal-Programming Problem

17.2 Weighted Goal Programming

17.3 Preemptive Goal Programming

17.4 Summary

Glossary Learning Aids for This Chapter in Your MS Courseware

Problems Case 17-1 A Cure for Cuba Case 17-2 Remembering September 11

Chapter 18 Inventory Management with Known Demand

18.1 A Case Study: The Atlantic Coast Tire Corp

(ACT) Problem

18.2 Cost Components of Inventory Models

18.3 The Basic Economic Order Quantity (EOQ) Model

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xx Contents

Problems Case 19-1 TNT: Tackling Newsboy’s Teachings Case 19-2 Jettisoning Surplus Stock

Chapter 20 Computer Simulation with Crystal Ball

20.1 A Case Study: Freddy the Newsboy’s Problem

20.2 Bidding for a Construction Project: A Prelude to the Reliable Construction Co Case Study

20.3 Project Management: Revisiting the Reliable Construction Co Case Study

20.4 Cash Flow Management: Revisiting the glade Golden Years Company Case Study

20.5 Financial Risk Analysis: Revisiting the Big Development Co Problem

20.6 Revenue Management in the Travel Industry

20.7 Choosing the Right Distribution

20.8 Decision Making with Decision Tables

20.9 Optimizing with OptQuest

20.10 Summary Glossary Learning Aids for This Chapter in Your MS Courseware

Solved Problem Problems Case 20-1 Action Adventures Case 20-2 Pricing under Pressure

18.4 The Optimal Inventory Policy for the Basic EOQ

Model

18.5 The EOQ Model with Planned Shortages

18.6 The EOQ Model with Quantity Discounts

18.7 The EOQ Model with Gradual Replenishment

19.1 A Case Study for Perishable Products: Freddie

the Newsboy’s Problem

19.2 An Inventory Model for Perishable Products

19.3 A Case Study for Stable Products: The Niko

Camera Corp Problem

19.4 The Management Science Team’s Analysis

of the Case Study

19.5 A Continuous-Review Inventory Model for

Chapter One

Introduction

Learning Objectives

After completing this chapter, you should be able to

1 Define the term management science

2 Describe the nature of management science

3 Explain what a mathematical model is

4 Use a mathematical model to perform break-even analysis

5 Use a spreadsheet model to perform break-even analysis

6 Identify the levels of annual savings that management science sometimes can provide

to organizations

7 Identify some special features of this book

Welcome to the field of management science! We think that it is a particularly exciting and

interesting field Exciting because management science is having a dramatic impact on the profitability of numerous business firms around the world Interesting because the methods used to do this are so ingenious We are looking forward to giving you a guided tour to intro-duce you to the special features of the field

Some students approach a course (and textbook) about management science with a tain amount of anxiety and skepticism The main source of the anxiety is the reputation of the field as being highly mathematical This reputation then generates skepticism that such

cer-a theoreticcer-al cer-approcer-ach ccer-an hcer-ave much relevcer-ance for decer-aling with prcer-acticcer-al mcer-ancer-agericer-al lems Most traditional courses (and textbooks) about management science have only rein-forced these perceptions by emphasizing the mathematics of the field rather than its practical application

Rest easy This is not a traditional management science textbook We realize that most readers of this book are aspiring to become managers, not mathematicians Therefore, the emphasis throughout is on conveying what a future manager needs to know about manage-ment science Yes, this means including a little mathematics here and there, because it is a major language of the field The mathematics you do see will be at the level of high school algebra plus (in the later chapters) basic concepts of elementary probability theory We think you will be pleasantly surprised by the new appreciation you gain for how useful and intuitive mathematics at this level can be However, managers do not need to know any of the heavy mathematical theory that underlies the various techniques of management science Therefore, the use of mathematics plays only a strictly secondary role in the book

One reason we can deemphasize mathematics is that powerful spreadsheet software now is

available for applying management science Spreadsheets provide a comfortable and familiar environment for formulating and analyzing managerial problems The spreadsheet takes care

of applying the necessary mathematics automatically in the background with only a minimum

of guidance by the user This has begun to revolutionize the use of management science

In the past, technically trained management scientists were needed to carry out significant management science studies for management Now spreadsheets are bringing many of the tools and concepts of management science within the reach of managers for conducting their own analyses Although busy managers will continue to call upon management science teams

to conduct major studies for them, they are increasingly becoming direct users themselves

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2 Chapter One Introduction

through the medium of spreadsheet software Therefore, since this book is aimed at future managers (and management consultants), we will emphasize the use of spreadsheets for applying management science

What does an enlightened future manager need to learn from a management science course?

1 Gain an appreciation for the relevance and power of management science (Therefore, we

include many application vignettes throughout the book that give examples of actual

appli-cations of management science and the impact they had on the organizations involved.)

2 Learn to recognize when management science can (and cannot) be fruitfully applied

(Therefore, we will emphasize the kinds of problems to which the various management

science techniques can be applied.)

3 Learn how to apply the major techniques of management science to analyze a variety of agerial problems (Therefore, we will focus largely on how spreadsheets enable many such applications with no more background in management science than provided by this book.)

4 Develop an understanding of how to interpret the results of a management science study

(Therefore, we will present many case studies that illustrate management science studies

and how their results depend on the assumptions and data that were used.) The objectives just described are the key teaching goals of this book

We begin this process in the next two sections by introducing the nature of management science and the impact that it is having on many organizations (These themes will continue throughout the remaining chapters as well.) Section 1.4 then points out some of the special features of this book that you can look forward to seeing in the subsequent chapters

1.1 THE NATURE OF MANAGEMENT SCIENCE

What is the name management science (sometimes abbreviated MS) supposed to convey?

It does involve management and science or, more precisely, the science of management, but

this still is too vague Here is a more suggestive definition

Management science is a discipline that attempts to aid managerial decision making by applying

a scientific approach to managerial problems that involve quantitative factors

Now let us see how elaborating upon each of the italicized terms in this definition conveys much more about the nature of management science

Management Science Is a Discipline

As a discipline, management science is a whole body of knowledge and techniques that are based on a scientific foundation For example, it is analogous in some ways to the medical field A medical doctor has been trained in a whole body of knowledge and techniques that are based on the scientific foundations of the medical field After receiving this training and entering practice, the doctor must diagnose a patient’s illness and then choose the appropriate medical procedures to apply to the illness The patient then makes the final decision on which medical procedures to accept For less serious cases, the patient may choose not to consult

a doctor and instead use his own basic knowledge of medical principles to treat himself

Similarly, a management scientist must receive substantial training (albeit considerably less than for a medical doctor) This training also is in a whole body of knowledge and techniques that are based on the scientific foundations of the discipline After entering practice, the management scientist must diagnose a managerial problem and then choose the appropriate management science techniques to apply in analyzing the problem The cognizant manager then makes the final decision as to which conclusions from this analysis to accept For less extensive managerial problems where management science can be helpful, the manager may choose not to consult a management scientist and instead use his or her own basic knowledge

of management science principles to analyze the problem

Although it has considerably longer roots, the rapid development of the discipline began

in the 1940s and 1950s The initial impetus came early in World War II, when large numbers

of scientists were called upon to apply a scientific approach to the management of the war

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1.1 The Nature of Management Science 3

effort for the allies Another landmark event was the discovery in 1947 by George Dantzig

of the simplex method for solving linear programming problems (Linear programming is the

subject of several early chapters.) Another factor that gave great impetus to the growth of the discipline was the onslaught of the computer revolution

The traditional name given to the discipline (and the one that still is widely used today

outside of business schools) is operations research This name was applied because the

teams of scientists in World War II were doing research on how to manage military

opera-tions The abbreviation OR also is widely used This abbreviation often is combined with the

one for management science (MS), thereby referring to the discipline as OR/MS According

to projections from the U.S Bureau of Labor Statistics for the year 2013, there are mately 65,000 individuals working as operations research analysts in the United States with

approxi-an average approxi-annual salary of about $79,000

Another discipline that is closely related to management science is business analytics

Like management science, business analytics attempts to aid managerial decision making but

with particular emphasis on three types of analysis: (1) descriptive analytics —the use of data (sometimes massive amounts of data) to analyze trends, (2) predictive analytics —the use of

data to predict what will happen in the future (perhaps by using the forecasting techniques

described in Chapter 10), and (3) prescriptive analytics —the use of data to prescribe the best

course of action (frequently by using the optimization techniques described throughout this book) Broadly speaking, the techniques of the management science discipline provide the firepower for prescriptive analytics and, to a lesser extent, for predictive analytics, but not so much for descriptive analytics

One major international professional society for the management science discipline

(as well as for business analytics) is the Institute for Operations Research and the

Man-agement Sciences (INFORMS) Headquartered in the United States, with over 10,000

members, this society holds major conferences in the United States each year (including

an annual Conference for Business Analytics and Operations Research) plus occasional

conferences elsewhere It also publishes several prominent journals, including

Manage-ment Science, Operations Research, Analytics, and Interfaces (Articles describing actual

applications of management science are featured in Interfaces, so you will see many

refer-ences and links to this journal throughout the book.) In addition, a few dozen countries around the world have their own national operations research societies (More about this

in Section 1.3.) Thus, operations research/management science (OR/MS) is a truly international discipline

(We hereafter will just use the name management science or the abbreviation MS.)

Management Science Aids Managerial Decision Making

The key word here is that management science aids managerial decision making

Manage-ment scientists don’t make managerial decisions Managers do A manageManage-ment science study only provides an analysis and recommendations, based on the quantitative factors involved in the problem, as input to the cognizant managers Managers must also take into account vari-ous intangible considerations that are outside the realm of management science and then use their best judgment to make the decision Sometimes managers find that qualitative factors are as important as quantitative factors in making a decision

A small informal management science study might be conducted by just a single

individ-ual, who may be the cognizant manager However, management science teams normally are used for larger studies (We often will use the term team to cover both cases throughout the

book.) Such a team often includes some members who are not management scientists but who provide other types of expertise needed for the study Although a management science team

often is entirely in-house (employees of the company), part or all of the team may instead

be consultants who have been hired for just the one study Consulting firms that partially or

entirely specialize in management science currently are a growing industry

Management Science Uses a Scientific Approach

Management science is based strongly on some scientific fields, including mathematics and computer science It also draws on the social sciences, especially economics Since the field

operations research

Management science began

its rapid development

dur-ing World War II with the

name operations research.

Confirming Pages

4 Chapter One Introduction

is concerned with the practical management of organizations, a management scientist should have solid training in business administration, including its various functional areas, as well

To a considerable extent, a management science team will attempt to use the scientific

method in conducting its study This means that the team will emphasize conducting a tematic investigation that includes careful data gathering, developing and testing hypotheses

sys-about the problem (typically in the form of a mathematical model), and then applying sound logic in the subsequent analysis

When conducting this systematic investigation, the management science team typically will follow the (overlapping) steps outlined and described below

Step 1: Defi ne the problem and gather data In this step, the team consults with

man-agement to clearly identify the problem of concern and ascertain the appropriate tives for the study The team then typically spends a surprisingly large amount of time gathering relevant data about the problem with the assistance of other key individuals in the organization A common frustration is that some key data are either very rough or completely unavailable This may necessitate installing a new computer-based manage-ment information system

Another increasingly common problem is that there may be too much data available to

be easily analyzed Dramatic advances in computerized data capture, processing power, data transmission, and storage capabilities are enabling organizations to integrate their

various databases into massive data warehouses This has led to the development of

data-mining software for extracting hidden predictive information, correlations, and patterns

from large databases

Fortunately, the rapid development of the information technology (IT) fi eld in recent

years is leading to a dramatic improvement in the quantity and quality of data that may be available to the management science (MS) team Corporate IT now is often able to provide the computational resources and databases, as well as any helpful data mining, that are needed by the MS team Thus, the MS team often will collaborate closely with the IT group

mod-or chemical reactions, graphs, mod-organization charts, and industrial accounting systems

Such models are invaluable for abstracting the essence of the subject of inquiry, showing interrelationships, and facilitating analysis

Mathematical models are also approximate representations, but they are expressed

in terms of mathematical symbols and expressions Such laws of physics as F   5   ma and

E   5   mc 2 are familiar examples Similarly, the mathematical model of a business problem

is the system of equations and related mathematical expressions that describes the sence of the problem

With the emergence of powerful spreadsheet technology, spreadsheet models now

are widely used to analyze managerial problems A spreadsheet model lays out the evant data, measures of performance, interrelationships, and so forth, on a spreadsheet in

rel-an orgrel-anized way that facilitates fruitful rel-analysis of the problem It also frequently porates an underlying mathematical model to assist in the analysis, but the mathematics is kept in the background so the user can concentrate on the analysis

The modeling process is a creative one When dealing with real managerial problems

(as opposed to some cut-and-dried textbook problems), there normally is no single rect” model but rather a number of alternative ways to approach the problem The mod-eling process also is typically an evolutionary process that begins with a simple “verbal model” to defi ne the essence of the problem and then gradually evolves into increasingly more complete mathematical models (perhaps in a spreadsheet format)

We further describe and illustrate such mathematical models in the next section

Step 3: Develop a computer-based procedure for deriving solutions to the problem from the model The beauty of a well-designed mathematical model is that it enables the

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1.1 The Nature of Management Science 5

use of mathematical procedures to fi nd good solutions to the problem These procedures usually are run on a computer because the calculations are too extensive to be done by hand In some cases, the management science team will need to develop the procedure In others, a standard software package already will be available for solving the model When the mathematical model is incorporated into a spreadsheet, the spreadsheet software nor-mally includes a Solver that usually will solve the model

Step 4: Test the model and refi ne it as needed Now that the model can be solved,

the team needs to thoroughly check and test the model to make sure that it provides a suffi ciently accurate representation of the real problem A number of questions should be addressed, perhaps with the help of others who are particularly familiar with the problem

Have all the relevant factors and interrelationships in the problem been accurately porated into the model? Does the model seem to provide reasonable solutions? When it is applied to a past situation, does the solution improve upon what was actually done? When assumptions about costs and revenues are changed, do the solutions change in a plausible manner?

If the model is to be applied repeatedly to help guide decisions on an ongoing basis,

the team might also develop a decision support system This is an interactive

computer-based system that aids managerial decision making The system draws

current data from databases or management information systems and then solves the

various versions of the model specifi ed by the manager

With this in mind, the team monitors the initial experience with the system and seeks to identify any modifi cations that should be made in the future

Management Science Considers Quantitative Factors

Many managerial problems revolve around such quantitative factors as production quantities, revenues, costs, the amounts available of needed resources, and so on By incorporating these

quantitative factors into a mathematical model and then applying mathematical procedures to

solve the model, management science provides a uniquely powerful way of analyzing such managerial problems Although management science is concerned with the practical manage-ment of organizations, including taking into account relevant qualitative factors, its special contribution lies in this unique ability to deal with the quantitative factors

The Special Products Company example discussed below will illustrate how management science considers quantitative factors

1 When did the rapid development of the management science discipline begin?

2 What is the traditional name given to this discipline that still is widely used outside of business schools?

3 What does a management science study provide to managers to aid their decision making?

4 Upon which scientific fields and social sciences is management science especially based?

5 What is a decision support system?

6 What are some common quantitative factors around which many managerial problems revolve?

Review

Questions

Confirming Pages

6 Chapter One Introduction

BREAK-EVEN ANALYSIS

The Special Products Company produces expensive and unusual gifts to be sold in stores

that cater to affluent customers who already have everything The latest new-product posal to management from the company’s Research Department is a first-of-its-kind iWatch

pro-This iWatch would combine the features of a top-of-the-line atomic wristwatch and a generation smartphone, including the ability to respond to voice commands or questions with voice responses It also would connect to the Internet wirelessly to provide weather, sports scores, stock quotes, and more An extensive research-and-development project would be needed to develop the iWatch The proposal is to provide a generous budget of $10 million for this project in order to provide as many desirable features as possible within this budget

next-It is clear that the production costs for the iWatch would be very large because of the extreme miniaturization that would be required, so the selling price would need to be far beyond the reach of middle-class customers Therefore, the marketing of the iWatch would be aimed at wealthy customers who want the most advanced products regardless of cost

Management needs to decide whether to develop and market this new product and, if so, how many of these watches to produce Before making these decisions, a sales forecast will

be obtained to estimate how many watches can be sold Since most of these sales would occur quickly during the relatively brief time before the “next big thing” arrives to take over the market, there would be only one production run for the iWatch and the number produced would be set equal to the sales forecast Following the production run, the iWatch would be marketed as aggressively as needed to sell this entire inventory if possible Management now needs a management science study to be conducted to determine how large this sales potential needs to be to make the iWatch profitable after considering all the prospective revenues and costs, so let’s next look at the estimates of these financial figures

If the company goes ahead with this product, the research-and-development cost of

$10 million is referred to as a fixed cost because it remains the same regardless of how many watches are produced and sold (However, note that this cost would not be incurred

if management decides not to introduce the product since the research-and-development project then would not be undertaken.)

In addition to this fixed cost, there is a production cost that varies with the number of

watches produced This variable cost is $1,000 per watch produced, which adds up to $1,000 times the number of watches produced (The cost for each additional unit produced, $1,000,

is referred to as the marginal cost ) Each watch sold would generate a unit revenue of $2,000

for the company

Spreadsheet Modeling of the Problem

You will see throughout this book that spreadsheets provide a very convenient way of using

a management science approach for modeling and analyzing a wide variety of managerial problems This certainly is true for the Special Products Company problem as well, as we now will demonstrate

Figure 1.1 shows a spreadsheet formulation of this problem after obtaining a sales forecast that indicates 30,000 watches can be sold The data have been entered into cells C4 to C7 Cell C9 is used to record a trial value for the decision as to how many watches to produce As one of the many possibilities that eventually might be tried, Figure 1.1 shows the specific trial value of 20,000

Cells F4 to F7 give the resulting total revenue, total costs, and profit (loss) by using the Excel equations shown under the spreadsheet in Figure 1.1 The Excel equations could have been written using cell references (e.g., F6  5  C6*C9) However, the spreadsheet model

is made clearer by giving “range names” to key cells or blocks of cells (A range name

is a descriptive name given to a cell or range of cells that immediately identifies what is there Appendix A provides details about how to incorporate range names into a spreadsheet model.) To define a name for a selected cell (or range of cells), click on the name box (on the left of the formula bar above the spreadsheet) and type a name These cell names then can

be used in other formulas to create an equation that is easy to decipher (e.g., Cost  5  MarginalCost*ProductionQuantity rather than the more cryptic F6  5  C6*C9) Note

TotalVariable-A cost that remains the

same regardless of the

pro-duction volume is referred

to as a fixed cost, whereas

a cost that varies with the

production volume is called

a variable cost.

Excel Tip: To update

formulas throughout the

spreadsheet to incorporate a

newly defined range name,

choose Apply Names from

the Define Name menu on

the Formulas tab

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1.2 An Illustration of the Management Science Approach: Break-Even Analysis 7

that spaces are not allowed in range names When a range name has more than one word, we have used capital letters to distinguish the start of each new word (e.g., ProductionQuantity)

The lower left-hand corner of Figure 1.1 lists the names of the quantities in the spreadsheet

in alphabetical order and then gives cell references where the quantities are found Although this isn’t particularly necessary for such a small spreadsheet, you should find it helpful for the larger spreadsheets found later in the book

This same spreadsheet is provided for you live in your MS Courseware on the CD-ROM

(All the spreadsheets in the book are included in your MS Courseware.) As you can see for yourself by bringing up and playing with the spreadsheet, it provides a straightforward way of

performing what-if analysis on the problem What-if analysis involves addressing such

ques-tions as what happens if the sales forecast should have been considerably lower? What pens if some of the cost and revenue estimates are wrong? Simply enter a variety of new values for these quantities in the spreadsheet and see what happens to the profit shown in cell F7

The lower right-hand corner of Figure  1.1 introduces two useful Excel functions, the

MIN( a, b ) function and the IF( a, b, c ) function The equation for cell F4 uses the MIN( a, b ) function, which gives the minimum of a and b In this case, the estimated number of watches

that will be sold is the minimum of the sales forecast and the production quantity, so

F4 5 UnitRevenue*MIN(SalesForecast, ProductionQuantity) enters the unit revenue (from cell C4) times the minimum of the sales forecast (from C7) and the production quantity (from C9) into cell F4

Also note that the equation for cell F5 uses the IF( a, b, c ) function, which does the ing: If statement a is true, it uses b; otherwise, it uses c Therefore,

follow-F5 5 IF(ProductionQuantity 0, FixedCost, 0) says to enter the fixed cost (C5) into cell F5 if the production quantity (C9) is greater than zero, but otherwise enter 0 (the fixed cost is avoided if production is not initiated)

The spreadsheet in Figure 1.1 , along with its equations for the results in column F,

con-stitutes a spreadsheet model for the Special Products Company problem You will see many

examples of such spreadsheet models throughout the book

Excel Tip: A list of all the

defined names and their

corresponding cell

refer-ences can be pasted into a

spreadsheet by choosing

Paste Names from the Use

in Formula menu on the

Formulas tab, and then

clicking on Paste List.

A spreadsheet is a

conve-nient tool for performing

what-if analysis.

The Excel function MIN

(a, b) gives the minimum

of the numbers in the cells

whose addresses are a and

b.

The Excel function IF

(a, b, c) tests if a is true

If so, it uses b; otherwise

it uses c.

2 3 4 5 6 7 8 9

Unit Revenue Fixed Cost Marginal Cost Sales Forecast

$40,000,000

$10,000,000

$20,000,000

Total Revenue Total Fixed Cost Total Variable Cost Profit (Loss)

Production Quantity

3

4 5 6 7

Results

Total Revenue Total Fixed Cost Total Variable Cost Profit (Loss)

=UnitRevenue * MIN(SalesForecast, ProductionQuantity)

=IF(ProductionQuantity > 0, FixedCost, 0)

=MarginalCost * ProductionQuantity

=TotalRevenue – (TotalFixedCost + TotalVariableCost)

Range Name FixedCost MarginalCost ProductionQuantity Profit

SalesForecast TotalFixedCost TotalRevenue TotalVariableCost UnitRevenue

Cell C5 C6 C9 F7 C7 F5 F4 F6 C4

$2,000

$10,000,000

$1,000 30,000

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8 Chapter One Introduction

This particular spreadsheet model is based on an underlying mathematical model that uses

algebra to spell out the equations in cells F4:F7 and then to derive some additional useful information Let us take a look at this mathematical model next

Expressing the Problem Mathematically

The issue facing management is to make the following decision

Decision to be made: Number of watches to produce (if any)

Since this number is not yet known, we introduce an algebraic variable Q to represent this

quantity Thus,

Q 5 Number of watches to produce,

where Q is referred to as a decision variable Naturally, the value chosen for Q should not

exceed the sales forecast for the number of watches that can be sold Choosing a value of 0 for

Q would correspond to deciding not to introduce the product, in which case none of the costs

or revenues described in the preceding paragraph would be incurred

The objective is to choose the value of Q that maximizes the company’s profit from this

new product The management science approach is to formulate a mathematical model to represent this problem by developing an equation that expresses the profit in terms of the

decision variable Q To get there, it is necessary first to develop equations in terms of Q for

the total cost and revenue generated by the watches

If Q   5  0, no cost is incurred However, if Q  > 0, there is both a fixed cost and a variable cost

Fixed cost 5 $10 million (if Q 0)

Therefore, the total cost would be

Total cost 5 e0$10 million 1 $1,000Q if Q 5 0 if Q 0 Since each watch sold would generate a revenue of $2,000 for the company, the total rev-

enue from selling Q watches would be

Total revenue 5 $2,000Q Consequently, the profit from producing and selling Q watches would be

Profit 5 Total revenue 2 Total cost

5 e0$2,000Q 2 ($10 million 1 $1,000Q) if Q 5 0 if Q 0

Thus, since $2,000 Q   2  $1,000 Q   5  $1,000 Q

Analysis of the Problem

This last equation shows that the attractiveness of the proposed new product depends greatly

on the value of Q, that is, on the number of watches that can be produced and sold A small value of Q means a loss (negative profit) for the company, whereas a sufficiently large value

would generate a positive profit for the company For example, look at the difference between

Q   5  2,000 and Q   5  20,000

Profit 5 2$10 million 1 $1,000 (2,000) 5 2$8 million if Q 5 20

Figure  1.2 plots both the company’s total cost and total revenue for the various values

of Q Note that the cost line and the revenue line intersect at Q   5  10,000 For any value of

Q  < 10,000, cost exceeds revenue, so the gap between the two lines represents the loss to the company For any Q  > 10,000, revenue exceeds cost, so the gap between the two lines now

Variable cost 5 $1,000 Q

Profit 5 2$10 million 1 $1,000Q if Q 0

Profit 5 2$10 million 1 $1,000 (20,000) 5 $10 million if Q 5 200

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1.2 An Illustration of the Management Science Approach: Break-Even Analysis 9

shows positive profit At Q   5  10,000, the profit is 0 Since 10,000 units is the production and

sales volume at which the company would break even on the proposed new product, this

vol-ume is referred to as the break-even point This is the point that must be exceeded to make

it worthwhile to introduce the product Therefore, the crucial question is whether the sales forecast for how many watches can be sold is above or below the break-even point

Figure 1.2 illustrates the graphical procedure for finding the break-even point Another alternative is to use an algebraic procedure to solve for the point Because the profit is 0 at this point, the procedure consists of solving the following equation for the unknown Q

Profit 5 2$10 million 1 $1,000Q 5 0

Thus,

$1,000Q 5 $10 million

A Complete Mathematical Model for the Problem

The preceding analysis of the problem made use of a basic mathematical model that consisted

of the equation for profit expressed in terms of Q However, implicit in this analysis were some

additional factors that can be incorporated into a complete mathematical model for the problem

Two of these factors concern restrictions on the values of Q that can be considered One of

these is that the number of watches produced cannot be less than 0 Therefore,

Q $ 0

is one of the constraints for the complete mathematical model Another restriction on the

value of Q is that it should not exceed the number of watches that can be sold A sales forecast has not yet been obtained, so let the symbol s represent this currently unknown value

s 5 Sales forecast (not yet available) of the number of watches that can be sold

mathemat-ical model is an inequality

or equation that expresses

some restrictions on the

values that can be assigned

to the decision variables.

FIGURE 1.2

Break-even analysis for

the Special Products

Company shows that the

cost line and revenue line

intersect at Q 5 10,000

watches, so this is the

break-even point for the

proposed new product.

Revenue/Cost

in $millions

Production Quantity (thousands)

Total revenue = $2000Q

Total cost = $10 million + $1000Q if Q > 0

Break-even point = 10,000 watches

Confirming Pages

10 Chapter One Introduction

Q # s

is another constraint, where s is a parameter of the model whose value has not yet been chosen.

The final factor that should be made explicit in the model is the fact that management’s objective is to make the decision that maximizes the company’s profit from this new product

Therefore, the complete mathematical model for this problem is to find the value of the

where the algebraic expression given for Profit is called the objective function for the

model The value of Q that solves this model depends on the value that will be assigned to the parameter s (the future forecast of the number of units that can be sold) Because the break- even point is 10,000 here is how the solution for Q depends on s

Solution for Mathematical Model

Break-even point 5 Fixed cost

Unit revenue 2 Marginal cost5

Therefore, the company should introduce the product and produce the number of units that

can be sold only if this production and sales volume exceeds the break-even point

What-if Analysis of the Mathematical Model

A mathematical model is intended to be only an approximate representation of the problem

For example, some of the numbers in the model inevitably are only estimates of quantities that cannot be determined precisely at this time

The above mathematical model is based on four numbers that are only estimates—the fixed cost of $10 million, the marginal cost of $1,000, the unit revenue of $2,000, and the sales forecast (after it is obtained) A management science study usually devotes consider-able time to investigating what happens to the recommendations of the model if any of the

estimates turn out to considerably miss their targets This is referred to as what-if analysis

To assist you in performing what-if analysis on this kind of model in a straightforward

and enjoyable way, we have provided a Break-Even Analysis module in the Interactive

Man-agement Science Modules at www.mhhe.com/hillier5e (All of the modules in this software

package also are included on your CD-ROM.) By following the simple directions given there, you can drag either the cost line or the revenue line to change the fixed cost, the marginal cost, or the unit revenue This immediately enables you to see the effect on the break-even point if any of these cost or revenue numbers should turn out to have values that are some-what different than their estimates in the model

Incorporating the Break-Even Point into the Spreadsheet Model

A key finding of the above mathematical model is its formula for the break-even point,

Break-even point 5 Fixed cost

Unit revenue 2 Marginal cost Therefore, once both the quantities in this formula and the sales forecast have been carefully estimated, the solution for the mathematical model specifies what the production quantity should be

By contrast, although the spreadsheet in Figure 1.1 enables trying a variety of trial values for the production quantity, it does not directly indicate what the production quantity should be

Figure 1.3 shows how this spreadsheet can be expanded to provide this additional guidance

parameter

The constants in a

math-ematical model are referred

to as the parameters of the

that gives the measure of

performance for the

prob-lem in terms of the decision

variables.

what-if analysis

Since estimates can be

wrong, what-if analysis is

used to check the effect on

the recommendations of a

model if the estimates turn

out to be wrong.

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1.2 An Illustration of the Management Science Approach: Break-Even Analysis 11

Suppose that a sales forecast of 30,000 has been obtained, as shown in cell C7 As indicated

by its equation at the bottom of the figure, cell F9 calculates the break-even point by dividing the fixed cost ($10 million) by the net profit per watch sold ($1,000), where this net profit is

the unit revenue ($2,000) minus the marginal cost ($1,000) Since the sales forecast of 30,000

exceeds the break-even point of 10,000 this forecast has been entered into cell C9

If desired, the complete mathematical model for break-even analysis can be fully

incorpo-rated into the spreadsheet by requiring that the model solution for the production quantity be entered into cell C9 This would be done by using the equation

C9 5 IF(SalesForecast BreakEvenPoint, SalesForecast, 0) However, the disadvantage of introducing this equation is that it would eliminate the pos-sibility of trying other production quantities that might still be of interest For example, if management does not have much confidence in the sales forecast and wants to minimize the danger of producing more watches than can be sold, consideration would be given to production quantities smaller than the forecast For example, the trial value shown in cell C9

of Figure 1.1 might be chosen instead As in any application of management science, a ematical model can provide useful guidance but management needs to make the final decision after considering factors that may not be included in the model

2 3 4 5 6 7 8 9

Data

30,000

Results

Unit Revenue Fixed Cost Marginal Cost Sales Forecast

$60,000,000

$10,000,000

$30,000,000

Total Revenue Total Fixed Cost Total Variable Cost Profit (Loss)

Break-Even Point Production Quantity

3

4 5 6 7 8 9

Results

Total Revenue Total Fixed Cost Total Variable Cost Profit (Loss)

=UnitRevenue * MIN(SalesForecast, ProductionQuantity)

=IF(ProductionQuantity > 0, FixedCost, 0)

=MarginalCost * ProductionQuantity

=TotalRevenue – (TotalFixedCost + TotalVariableCost)

Break-Even Point =FixedCost/(UnitRevenue – MarginalCost)

Range Name BreakEvenPoint FixedCost MarginalCost ProductionQuantity Profit

SalesForecast TotalFixedCost TotalRevenue TotalVariableCost UnitRevenue

Cell F9 C5 C6 C9 F7 C7 F5 F4 F6 C4

An expansion of the spreadsheet in Figure 1.1 that uses the solution for the mathematical model to calculate the break-even point.

1 How do the production and sales volume of a new product need to compare to its break-even point to make it worthwhile to introduce the product?

2 What are the factors included in the complete mathematical model for the Special Products Company problem, in addition to an equation for profit?

3 What is the purpose of what-if analysis?

4 How can a spreadsheet be used to perform what-if analysis?

5 What does the MIN( a, b ) Excel function do?

6 What does the IF( a, b, c ) Excel function do?

Review

Questions

Confirming Pages

12

1.3 THE IMPACT OF MANAGEMENT SCIENCE

Management science (or operations research as it is commonly called by practitioners) has

had an impressive impact on improving the efficiency of numerous organizations around the world In the process, management science has made a significant contribution to increasing the productivity of the economies of various countries There now are a few dozen member countries in the International Federation of Operational Research Societies (IFORS), with each country having a national operations research society Both Europe and Asia have fed-erations of such societies to coordinate holding international conferences and publishing international journals in those continents In addition, we described in Section 1.1 how the Institute for Operations Research and the Management Sciences (INFORMS) is a particularly

prominent international society in this area Among its various journals is one called

Inter-faces that regularly publishes articles describing major management science studies and the

impact they had on their organizations

Management science (MS) has had numerous applications of various types in business and industry, sometimes resulting in annual savings of millions, or even hundreds of millions, of dollars As an example, many hundreds of management scientists work on such airline prob-lems as how to most effectively assign airplanes and crews to flights and how to develop fare structures that maximize revenue For decades, financial services firms have used portfolio selection techniques that were developed by management scientists who won the Nobel Prize

in Economics for their work Management science models have become a core component of the marketing discipline Multinational corporations rely on MS for guiding the management

of their supply chains There are numerous other examples of MS applications that are having

a dramatic impact on the companies involved

Management science also is widely used outside business and industry For example, it

is having an increasing impact in the health care area, with applications involving improved management of health care delivery and operations, disease modeling, clinical diagnosis and decision making, radiation therapy, and so on Applications of MS also abound at various levels of government, ranging from dealing with national security issues at the federal level to managing the delivery of emergency services at the municipal level Other key governmental applications involve the use of MS modeling to help guide energy, environmental, and global warming policies Some of the earliest MS applications were military applications, including logistical planning and war gaming, and these continue today

These are just a sampling of the numerous applications of management science that are having a major impact on the organizations involved The list goes on and on

The most important

appli-cations of management

science in business and

industry have resulted in

annual savings in the

hun-dreds of millions of dollars.

Management science also

has had a major impact

in the health care area, in

guiding key governmental

policies, and in military

applications.

Federal Express (FedEx) is the world’s largest express

trans-portation company Every working day, it delivers more

than 6.5 million documents, packages, and other items

throughout the United States and more than 220 countries

and territories around the world In some cases, these

ship-ments can be guaranteed overnight delivery by 10:30 AM

the next morning.

The logistical challenges involved in providing this

ser-vice are staggering These millions of daily shipments must

be individually sorted and routed to the correct general

location (usually by aircraft) and then delivered to the exact

destination (usually by motorized vehicle) in an amazingly

short period of time How is this possible?

Management science (which usually is referred to as

oper-ations research within FedEx) is the technological engine

that drives this company Ever since the company’s

found-ing in 1973, management science (MS) has helped make its

major business decisions, including equipment investment,

route structure, scheduling, finances, and location of ties After MS was credited with literally saving the company during its early years, it became the custom to have MS rep- resented at the weekly senior management meetings and, indeed, several of the senior corporate vice presidents have come up from the outstanding FedEx MS group.

facili-FedEx has come to be acknowledged as a world-class company It routinely ranks among the top companies on

Fortune magazine’s annual listing of the “World’s Most

Admired Companies.” It also was the first winner (in 1991)

of the prestigious prize now known as the INFORMS Prize, which is awarded annually for the effective and repeated integration of management science into organizational deci- sion making in pioneering, varied, novel, and lasting ways.

Source: R O Mason, J L McKenney, W Carlson, and D Copeland,

“Absolutely, Positively Operations Research: The Federal Express

Story,” Interfaces 27, no 2 (March–April 1997), pp 17–36 (A link to

this article is provided on our Website, www.mhhe.com/hillier5e.)

An Application Vignette

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1.3 The Impact of Management Science 13

To give you a better notion of the wide applicability of management science, we list some actual applications in Table 1.1 Note the diversity of organizations and applications in the first two columns The third column identifies the section where an “application vignette”

devotes several paragraphs to describing the application and also references an article that provides full details (You can see the first of these application vignettes in this section.) The last column indicates that these applications typically resulted in annual savings in the many millions of dollars Furthermore, additional benefits not recorded in the table (e.g., improved service to customers and better managerial control) sometimes were considered to be even more important than these financial benefits (You will have an opportunity to investigate these less tangible benefits further in Problems 1.9 and 1.10.)

A link to the articles in Interfaces that describes these applications in detail is included

on our Website, www.mhhe.com/hillier5e We are grateful to INFORMS for our special

partnership to make these articles available to you through this link We think you will find these articles interesting and enlightening in illustrating the dramatic impact that management science sometimes can have on the success of a variety of organizations

You also will see a great variety of applications of management science throughout the book in the form of case studies, examples, and end-of-chapter cases Some of the applica-tions are similar to ones described in application vignettes, but many others are quite differ-ent However, they all generally fall into one of three broad categories, namely, applications

Annual Savings

Federal Express Logistical planning of shipments 1.3 Not estimated Swift & Company Improve sales and manufacturing performance 2.1 $12 million Samsung Electronics Reduce manufacturing times and inventory levels 2.6 $200 million

more revenue INDEVAL Settle all securities transactions in Mexico 3.2 $150 million United Airlines Plan employee work schedules at airports and reservations offices 3.3 $6 million Procter & Gamble Redesign the production and distribution system 3.5 $200 million Welch’s Optimize use and movement of raw materials 4.3 $150,000 Pacific Lumber Company Long-term forest ecosystem management 5.4 $398 million NPV Hewlett-Packard Product portfolio management 6.1 $180 million Norwegian companies Maximize flow of natural gas through offshore pipeline network 6.3 $140 million Canadian Pacific Railway Plan routing of rail freight 6.4 $100 million Waste Management Develop a route-management system for trash collection and disposal 7.1 $100 million MISO Administer the transmission of electricity in 13 states 7.2 $700 million Netherlands Railways Optimize operation of a railway network 7.4 $105 million Continental Airlines Reassign crews to flights when schedule disruptions occur 7.5 $40 million Bank Hapoalim Group Develop a decision-support system for investment advisors 8.2 $31 million more

revenue DHL Optimize the use of marketing resources 8.4 $22 million Workers’ Compensation

Board

Manage high-risk disability claims and rehabilitation 9.3 $4 million

Westinghouse Evaluate research and development projects 9.7 Not estimated Conoco-Phillips Evaluate petroleum exploration projects 9.9 Not estimated

L L Bean Forecast staffing needs at call centers 10.2 $300,000 Taco Bell Forecast the level of business throughout the day 10.3 $13 million

General Motors Improve the throughput of its production lines 11.5 $200 million KeyCorp Improve efficiency of bank teller service 11.6 $20 million Federal Aviation

Administration

Manage air traffic flows in severe weather 12.2 $200 million

Sasol Improve the efficiency of its production processes 12.4 $23 million Merrill Lynch Pricing analysis for providing financial services 13.5 $50 million

more revenue

TABLE 1.1 Applications of Management Science to Be Described in Application Vignettes

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14 Chapter One Introduction

in the areas of operations management, finance, and marketing Tables 1.2 , 1.3 , and 1.4 list these applications in these three respective areas, where the first column identifies where the application is described In the second column of each table, note the many different ways in which management science can have a real impact in helping improve managerial decisions

Even these long lists of applications in Tables 1.1 to 1.4 are just a sample of the ous important ways in which management science is applied in organizations around the world We do not have enough space to provide a more comprehensive compilation of the important applications (Other applications are included in the supplementary chapters on the CD-ROM.) A hallmark of management science is its great flexibility in dealing with new managerial problems as they arise

1.4 SOME SPECIAL FEATURES OF THIS BOOK

The focus of this book is on teaching what an enlightened future manager needs to learn from

a management science course It is not on trying to train technical analysts This focus has led

us to include a number of special features that we hope you enjoy

Location Type of Application

Sec 2.1 onward A case study: What is the most profitable mix of products?

Case 2-1 Which mix of car models should be produced?

Case 2-2 Which mix of ingredients should go into the casserole in a university cafeteria?

Case 2-3 Which mix of customer–service agents should be hired to staff a call center?

Sec 3.3 Personnel scheduling of customer–service agents Sec 3.5 Minimize the cost of shipping a product from factories to customers Sec 3.7 Optimize the assignment of personnel to tasks

Case 3-1 How should a product be shipped to market?

Case 3-3 Which mix of women’s clothing should be produced for next season?

Cases 3-5, 5-4, 7-3 Develop a plan for assigning students to schools so as to minimize busing costs Case 3-6 Which mixes of solid waste materials should be amalgamated into different grades

of a salable product?

Case 3-7 How should qualified managers be assigned to new R&D projects?

Case 5-2 Develop and analyze a steel company’s plan for pollution abatement Case 5-3 Plan the mix of livestock and crops on a farm with unpredictable weather Sec 6.1 Minimize the cost of operating a distribution network

Secs 6.2, 6.3 A case study: Maximize the flow of goods through a distribution network Sec 6.4 Find the shortest path from an origin to a destination

Case 6-1 Logistical planning for a military campaign Case 6-3 Develop the most profitable flight schedules for an airline Cases 6-4, 7-4 Operate and expand a private computer network Sec 7.2 Choose the best combination of R&D projects to pursue Sec 7.3 Select the best sites for emergency services facilities Sec 7.4 Airline crew scheduling

Sec 7.5 Production planning when setup costs are involved Case 7-2 Make inventory decisions for a retailer’s warehouse Sec 8.3 Production planning when overtime is needed Sec 8.5 Find the shortest route to visit all the American League ballparks Sec 11.2 Many examples of commercial service systems, internal service systems, and trans-

portation service systems that can be analyzed with queueing models Sec 11.4 onward A case study: An analysis of competing proposals for more quickly providing main-

tenance services to customers Cases 11-2, 12-2 Analysis of proposals for reducing in-process inventory Sec 12.1 Comparison of whether corrective maintenance or preventive maintenance is

better Secs 12.2, 12.3 A case study: Would it be profitable for the owner of a small business to add an

Case Studies and

Examples in the Area of

Operations Management

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1.4 Some Special Features of this Book 15

One special feature is that the entire book revolves around modeling as an aid to

mana-gerial decision making This is what is particularly relevant to a manager Although they may not use this term, all managers often engage in at least informal modeling (abstracting the essence of a problem to better analyze it), so learning more about the art of modeling is important Since managers instigate larger management science studies done by others, they also need to be able to recognize the kinds of managerial problems where such a study might

be helpful Thus, a future manager should acquire the ability both to recognize when a agement science model might be applicable and to properly interpret the results from analyz-ing the model Therefore, rather than spending substantial time in this book on mathematical theory, the mechanics of solution procedures, or the manipulation of spreadsheets, the focus

man-is on the art of model formulation, the role of a model, and the analysman-is of model results

A wide range of model types is considered

Location Type of Application

Sec 1.2 Break-even analysis Case 1-1 Break-even analysis and what-if analysis Sec 3.2 An airline choosing which airplanes to purchase Sec 3.2 Capital budgeting of real-estate development projects Case 3-2 Develop a schedule for investing in a company’s computer equipment Sec 4.1 onward A case study: Develop a financial plan for meeting future cash flow needs Case 4-1 Develop an investment and cash flow plan for a pension fund

Sec 6.4 Minimize the cost of car ownership Case 6-2 Find the most cost-effective method of converting various foreign currencies

into dollars Sec 7.1 A case study: Determine the most profitable combination of investments Case 7-1 Develop an investment plan for purchasing art

Sec 8.2 Portfolio selection that balances expected return and risk Sec 8.5 Select a portfolio to beat the market as frequently as possible Case 8-2 Determine an optimal investment portfolio of stocks Case 8-3 Develop a long-range plan to purchase and sell international bonds Sec 9.1 onward A case study: Choose whether to drill for oil or sell the land instead Case 9-1 Choose a strategy for the game show, “Who Wants to Be a Millionaire?”

Sec 12.1 Analysis of a new gambling game Sec 13.2 Choose the bid to submit in a competitive bidding process Sec 13.4 Develop a financial plan when future cash flows are somewhat unpredictable Sec 13.5 Risk analysis when assessing financial investments

Sec 13.6 How much overbooking should be done in the travel industry?

Case 13-1 Analysis of how a company’s cash flows might evolve over the next year Case 13-2 Calculate the value of a European call option

TABLE 1.3

Case Studies and

Examples in the Area of

Finance

Location Type of Application

Secs 2.6, 3.3 Determine the best mix of advertising media Case 2-1 Evaluate whether an advertising campaign would be worthwhile Secs 3.1, 3.4 A case study: Which advertising plan best achieves managerial goals?

Case 3-4 Develop a representative marketing survey Case 5-1 Analysis of the trade-off between advertising costs and the resulting increase

in sales of several products Sec 6.4 Balance the speed of bringing a new product to market and the associated

costs Sec 8.3 Deal with nonlinear marketing costs Case 8-1 Refine the advertising plan developed in the case study presented in Sections

3.1 and 3.4 Case 9-2 Should a company immediately launch a new product or test-market it first?

Case 9-3 Should a company buy additional marketing research before deciding whether

to launch a new product?

Case 9-4 Plan a sequence of decisions for a possible new product Sec 10.2 onward A case study: Manage a call center for marketing goods over the telephone Case 10-1 Improve forecasts of demand for a call center

Case 11-1 Estimate customer waiting times for calling into a call center

TABLE 1.4

Case Studies and

Examples in the Area of

Marketing

Confirming Pages

16 Chapter One Introduction

Another special feature is a heavy emphasis on case studies to better convey these ideas in

an interesting way in the context of applications Every subsequent chapter includes at least one case study that introduces and illustrates the application of that chapter’s techniques in a realistic setting In a few instances, the entire chapter revolves around a case study Although consider-ably smaller and simpler than most real studies (to maintain clarity), these case studies are pat-terned after actual applications requiring a major management science study Consequently, they convey the whole process of such a study, some of the pitfalls involved, and the complementary roles of the management science team and the manager responsible for the decisions to be made

To complement these case studies, every chapter also includes major cases at the end

These realistic cases can be used for individual assignments, team projects, or case studies in class In addition, the University of Western Ontario Ivey School of Business (the second larg-est producer of teaching cases in the world) also has specially selected cases from its case col-lection that match the chapters in this textbook These cases are available on the Ivey Website,

www.cases.ivey.uwo.ca/cases , in the segment of the CaseMate area designated for this book

The book also places heavy emphasis on conveying the impressive impact that ment science is having on improving the efficiency of numerous organizations around the world Therefore, you will see many examples of actual applications throughout the book

manage-in the form of boxed application vignettes, such as the one already shown manage-in Section 1.3

You then will have the opportunity to learn more about these actual applications by reading the articles fully describing them that are accessed by a link on our Website As indicated in Table 1.1 , these applications sometimes resulted in annual savings of millions, tens of mil-lions, or even hundreds of millions of dollars

In addition, we try to provide you with a broad perspective about the nature of the real world of management science in practice It is easy to lose sight of this world when cranking through textbook exercises to master the mechanics of a series of techniques Therefore, we shift some emphasis from mastering these mechanics to seeing the big picture The case stud-ies, cases, and descriptions of actual applications are part of this effort

Another feature is the inclusion of one or more solved problems for each chapter to help

you get started on your homework for that chapter The statement of each solved problem is given just above the Problems section of the chapter, and then the complete solution is given

on both the CD-ROM and the Website for the book

The last, but certainly not the least, of the special features of this book is the ing software We will describe and illustrate how to use today’s premier spreadsheet package, Microsoft Excel, to formulate many management science models in a spreadsheet format

accompany-Excel 2007 implemented a significant overhaul of the user interface accompany-Excel 2010 brought other significant changes and improvements Many of the models considered in this book can

be solved using standard Excel Some Excel add-ins also are available to solve other models

Appendix A provides a primer on the use of Excel

Included with the book is an extensive collection of software that we collectively refer

to as MS Courseware This collection includes spreadsheet files, Frontline Systems’ Risk

Solver Platform for Education, and a package of Interactive Management Science Modules

Each of these is briefly described below

MS Courseware includes numerous spreadsheet files for every chapter in this book Each time a spreadsheet example is presented in the book, a live spreadsheet that shows the for-mulation and solution for the example also is available in MS Courseware This provides a convenient reference, or even useful templates, when you set up spreadsheets to solve similar problems Also, for many models in the book, template spreadsheet files are provided that already include all the equations necessary to solve the model You simply enter the data for the model and the solution is immediately calculated

Included with standard Excel is an add-in, called Solver, which is used to solve most of the optimization models considered in the first half of this book Solver is a product of Frontline Systems, Inc New with this edition of the textbook is a very powerful software package from Frontline Systems, Inc., called Risk Solver Platform for Education (RSPE) Some special fea-tures of RSPE are a significantly enhanced version of the basic Solver included with Excel, the ability to build decision trees within Excel, as covered in Chapter 9, and tools to build computer simulation models within Excel, as covered in Chapter 13

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Most of the software used in this book is compatible with both Excel for Windows PCs and Excel for Macintosh computers (Macs) Some software (e.g., Risk Solver Platform for Education) is not directly compatible with Macs, although it works well on any recent (Intel) Mac with Boot Camp or virtualization software For the most up-to-date information on soft-ware compatibility and relevant differences between Windows PC versions and Mac ver-sions, please refer to the Software Compatibility link at www.mhhe.com/hillier5e

We should point out that Excel is not designed for dealing with the really large ment science models that occasionally arise in practice More powerful software packages that are not based on spreadsheets generally are used to solve such models instead How-ever, management science teams, not managers, primarily use these sophisticated packages

manage-(including using modeling languages to help input the large models) Since this book is aimed

mainly at future managers rather than future management scientists, we will not have you use these packages

To alert you to relevant material in MS Courseware, the end of each chapter has a list entitled “Learning Aids for This Chapter in Your MS Courseware.”

1.5 Summary Management science is a discipline area that attempts to aid managerial decision making by applying a

scientific approach to managerial problems that involve quantitative factors The rapid development of this discipline began in the 1940s and 1950s The onslaught of the computer revolution has since continued to give great impetus to its growth Further impetus now is being provided by the widespread use of spread- sheet software, which greatly facilitates the application of management science by managers and others

A major management science study involves conducting a systematic investigation that includes careful data gathering, developing and testing hypotheses about the problem (typically in the form of

a mathematical model), and applying sound logic in the subsequent analysis The management science team then presents its recommendations to the managers who must make the decisions about how to resolve the problem Smaller studies might be done by managers themselves with the aid of spreadsheets

A major part of a typical management science study involves incorporating the quantitative factors into

a mathematical model (perhaps incorporated into a spreadsheet) and then applying mathematical

proce-dures to solve the model Such a model uses decision variables to represent the quantifiable decisions to be made An objective function expresses the appropriate measure of performance in terms of these decision variables The constraints of the model express the restrictions on the values that can be assigned to the decision variables The parameters of the model are the constants that appear in the objective function and the constraints An example involving break-even analysis was used to illustrate a mathematical model

Management science has had an impressive impact on improving the efficiency of numerous zations around the world In fact, many award-winning applications have resulted in annual savings in the millions, tens of millions, or even hundreds of millions of dollars

The focus of this book is on emphasizing what an enlightened future manager needs to learn from

a management science course Therefore, the book revolves around modeling as an aid to managerial decision making Many case studies (within the chapters) and cases (at the end of chapters) are used to better convey these ideas

Glossary break-even point The production and sales

volume for a product that must be exceeded to achieve a profit (Section 1.2), 9

business analytics A discipline closely related

to management science that makes extensive use

of data to analyze trends, make forecasts, and apply optimization techniques (Section 1.1), 3

constraint An inequality or equation in a

math-ematical model that expresses some restrictions

on the values that can be assigned to the decision variables (Section 1.2), 9

decision support system An interactive

com-puter-based system that aids managerial decision making (Section 1.1), 5

Confirming Pages

18 Chapter One Introduction

Chapter 1 Excel Files:

Special Products Co Example

Interactive Management Science Modules:

Module for Break-Even Analysis

Learning Aids for This Chapter in Your MS Courseware

Solved Problem (See the CD-ROM or Website for the Solution)

1.S1 Make or Buy?

Power Notebooks, Inc., plans to manufacture a new line of

notebook computers Management is trying to decide whether

to purchase the LCD screens for the computers from an outside

supplier or to manufacture the screens in-house The screens

cost $100 each from the outside supplier To set up the

assem-bly process required to produce the screens in-house would cost

$100,000 The company could then produce each screen for $75

The number of notebooks that eventually will be produced ( Q ) is

unknown at this point

a Set up a spreadsheet that will display the total cost of both tions for any value of Q Use trial and error with the spread-

op-sheet to determine the range of production volumes for which each alternative is best

b Use a graphical procedure to determine the break-even point for Q (i.e., the quantity at which both options yield the same

cost)

c Use an algebraic procedure to determine the break-even point for Q

Problems

1.1 The manager of a small firm is considering whether to

pro-duce a new product that would require leasing some special

equip-ment at a cost of $20,000 per month In addition to this leasing cost,

a production cost of $10 would be incurred for each unit of the

product produced Each unit sold would generate $20 in revenue

Develop a mathematical expression for the monthly profit

that would be generated by this product in terms of the number

of units produced and sold per month Then determine how large

this number needs to be each month to make it profitable to

pro-duce the product

1.2 Refer to Problem 1.1 A sales forecast has been obtained

that indicates that 4,000 units of the new product could be sold

This forecast is considered to be quite reliable, but there is

consid-erable uncertainty about the accuracy of the estimates given for the

leasing cost, the marginal production cost, and the unit revenue

Use the Break-Even Analysis module in the Interactive

Man-agement Science Modules to perform what-if analysis on these

estimates.

a How large can the leasing cost be before this new

product ceases to be profitable?

b How large can the marginal production cost be

before this new product ceases to be profitable?

c How small can the unit revenue be before this new

product ceases to be profitable?

1.3 Management of the Toys R4U Company needs to decide whether to introduce a certain new novelty toy for the upcom- ing Christmas season, after which it would be discontinued

The total cost required to produce and market this toy would

be $500,000 plus $15 per toy produced The company would receive revenue of $35 for each toy sold.

a Assuming that every unit of this toy that is

pro-duced is sold, write an expression for the profit in terms of the number produced and sold Then find the break-even point that this number must exceed

to make it worthwhile to introduce this toy

decision variable An algebraic variable that

represents a quantifiable decision to be made

(Section 1.2), 8

mathematical model An approximate

repre-sentation of, for example, a business problem that

is expressed in terms of mathematical symbols and expressions (Section 1.1), 4

model An approximate representation of

some-thing (Section 1.1), 4

MS Courseware The name of the software

package that is shrinkwrapped with the book or is

on its Website (Section 1.4), 16

objective function A mathematical expression

in a model that gives the measure of performance for a problem in terms of the decision variables

(Section 1.2), 10

operations research The traditional name for

management science that still is widely used side of business schools (Section 1.1), 3

parameter One of the constants in a

mathemat-ical model (Section 1.2), 10

range name A descriptive name given to a cell

or range of cells that immediately identifies what

is there (Section 1.2), 6

spreadsheet model An approximate

represen-tation of, for example, a business problem that is laid out on a spreadsheet in a way that facilitates analysis of the problem (Section 1.1), 4

what-if analysis Analysis of how the

recom-mendations of a model might change if any of the estimates providing the numbers in the model eventually need to be corrected (Section 1.2), 10 www.downloadslide.net

Chapter 1 Problems 19

b Now assume that the number that can be sold might

be less than the number produced Write an sion for the profit in terms of these two numbers

c Formulate a spreadsheet that will give the profit in

part b for any values of the two numbers

d Write a mathematical expression for the constraint

that the number produced should not exceed the number that can be sold

1.4 A reliable sales forecast has been obtained indicating

that the Special Products Company (see Section 1.2) would be

able to sell 30,000 iWatches, which appears to be enough to

justify introducing this new product However, management is

concerned that this conclusion might change if more accurate

estimates were available for the research-and-development cost,

the marginal production cost, and the unit revenue Therefore,

before a final decision is made, management wants what-if

anal-ysis done on these estimates

Use the spreadsheet from Figure 1.3 (see this chapter’s Excel

files) and trial-and-error to perform what-if analysis by

indepen-dently investigating each of the following questions.

a How large can the research-and-development cost

be before the watches cease to be profitable?

b How large can the marginal production cost be

before the watches cease to be profitable?

c How small can the unit revenue be before the

watches cease to be profitable?

1.5 Reconsider the problem facing the management of the

Special Products Company as presented in Section 1.2

A more detailed investigation now has provided better mates of the data for the problem The research-and-development

esti-cost still is estimated to be $10 million, but the new estimate of

the marginal production cost is $1,300 The revenue from each

watch sold now is estimated to be $1,700.

a Use a graphical procedure to find the new

break-even point

b Use an algebraic procedure to find the new

break-even point

c State the mathematical model for this problem with

the new data

d Incorporate this mathematical model into a

spread-sheet with a sales forecast of 30,000 Use this spreadsheet model to find the new break-even point, and then determine the production quantity and the estimated total profit indicated by the model

e Suppose that management fears that the sales

fore-cast may be overly optimistic and so does not want

to consider producing more than 20,000 watches

Use the spreadsheet from part d to determine what

the production quantity should be and the estimated total profit that would result

1.6 The Best-for-Less Corp supplies its two retail outlets

from its two plants Plant A will be supplying 30 shipments next

month Plant B has not yet set its production schedule for next

month but has the capacity to produce and ship any amount up

to a maximum of 50 shipments Retail outlet 1 has submitted

its order for 40 shipments for next month Retail outlet 2 needs

a minimum of 25 shipments next month but would be happy

to receive more The production costs are the same at the two

plants but the shipping costs differ The shipping cost per ment from each plant to each retail outlet is given below, along with a summary of the other data

ship-The distribution manager, Jennifer Lopez, now needs to develop a plan for how many shipments to send from each plant

to each of the retail outlets next month Her objective is to mize the total shipping cost.

mini-Unit Shipping Cost Retail Outlet 1 Retail Outlet 2 Supply Plant A $700 $400 5 30 shipments

Plant B $800 $600 ≤ 50 shipments

Needed 5 40 shipments $ 25 shipments

a Identify the individual decisions that Jennifer needs

to make For each of these decisions, define a sion variable to represent the decision

b Write a mathematical expression for the total

ship-ping cost in terms of the decision variables

c Write a mathematical expression for each of the

constraints on what the values of the decision ables can be

d State a complete mathematical model for Jennifer’s

problem

e What do you think Jennifer’s shipping plan should

be? Explain your reasoning Then express your shipping plan in terms of the decision variables

1.7 The Water Sports Company soon will be producing and marketing a new model line of motor boats The production

manager, Michael Jensen, now is facing a make-or-buy decision

regarding the outboard motor to be installed on each of these boats Based on the total cost involved, should the motors be produced internally or purchased from a vendor? Producing them internally would require an investment of $1 million in new facilities as well as a production cost of $1,600 for each motor produced If purchased from a vendor instead, the price would be $2,000 per motor

Michael has obtained a preliminary forecast from the pany’s marketing division that 3,000 boats in this model line will be sold.

a Use spreadsheets to display and analyze Michael’s

two options Which option should be chosen?

b Michael realizes from past experience that

prelimi-nary sales forecasts are quite unreliable, so he wants

to check on whether his decision might change if a more careful forecast differed significantly from the

preliminary forecast Determine a break-even point

for the production and sales volume below which the buy option is better and above which the make option is better

1.8 Reconsider the Special Products Company problem sented in Section 1.2

Although the company is well qualified to do most of the work in producing the iWatch, it currently lacks much expertise

in one key area, namely, developing and producing a miniature camera to be embedded into the iWatch Therefore, management