Practical management science excel files

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Practical Management Science

Wayne L. Winston Kelley School of Business, Indiana University

S. Christian Albright Kelley School of Business, Indiana University

6th Edition

Australia ● Brazil ● Mexico ● Singapore ● United Kingdom ● United States

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Practical Management Science, Sixth Edition

Wayne L. Winston, S. Christian Albright

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To Mary, my wonderful wife, best friend, and constant companion And to our Welsh Corgi, Bryn, who still just wants to play ball S.C.A.

To my wonderful family Vivian, Jennifer, and Gregory W.L.W.

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S. Christian Albright got his B.S. degree in Mathematics from Stanford in 1968 and his Ph.D. degree in Operations Research from Stanford in 1972. Until his retirement in 2011, he taught in the Operations & Decision Technologies Department in the Kelley School of Business at Indiana University. His teaching included courses in management science, computer simulation, and statis- tics to all levels of business students: undergraduates, MBAs, and doctoral students. He has published over 20 articles in leading operations research journals in the area of applied probability, and he has authored several books, including Practical Manage-

ment Science, Data Analysis and Decision Making, Data Analysis for Managers, Spread- sheet Modeling and Applications, and VBA for Modelers. He jointly developed StatTools, a statistical add-in for Excel, with the Palisade Corporation. In “retirement,” he continues to revise his books, and he has developed a commercial product, ExcelNow!, an extension of the Excel tutorial that accompanies this book. On the personal side, Chris has been married to his wonderful wife Mary for 46 years. They have a special family in Philadelphia: their son Sam, his wife Lindsay, and their two sons, Teddy and Archer. Chris has many interests outside the academic area. They include activities with his family (especially traveling with Mary), going to cultural events, power walking, and reading. And although he earns his livelihood from statistics and management science, his real passion is for playing classical music on the piano.

Wayne L. Winston is Professor Emeritus of Decision Sciences at the Kelley School of Business at Indiana University and is now a Professor of Decision and Information Sciences at the Bauer College at the University of Houston. Winston received his B.S. degree in Mathematics from MIT and his Ph.D. degree in Operations Research from Yale. He has written the successful textbooks Operations Research: Applications and Algorithms, Mathematical Programming: Applications and Algorithms, Simulation Modeling with @RISK, Practical Management Science, Data Analysis for Managers, Spreadsheet

Modeling and Applications, Mathletics, Data Analysis and Business Modeling with Excel 2013, Marketing Analytics, and Financial Models Using Simulation and Optimization. Winston has published over 20 articles in leading journals and has won more than 45 teaching awards, including the school-wide MBA award six times. His current interest is in showing how spreadsheet models can be used to solve business problems in all disciplines, particularly in finance, sports, and marketing. Wayne enjoys swimming and basketball, and his passion for trivia won him an appearance several years ago on the television game show Jeopardy, where he won two games. He is married to the lovely and talented Vivian. They have two children, Gregory and Jennifer.

About the Authors

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vii

Preface xiii 1 Introduction to Modeling 1 2 Introduction to Spreadsheet Modeling 19 3 Introduction to Optimization Modeling 71 4 Linear Programming Models 135 5 Network Models 219 6 Optimization Models with Integer Variables 277 7 Nonlinear Optimization Models 339 8 Evolutionary Solver: An Alternative Optimization Procedure 407 9 Decision Making under Uncertainty 457 10 Introduction to Simulation Modeling 515 11 Simulation Models 589 12 Queueing Models 667 13 Regression and Forecasting Models 715 14 Data Mining 771 References 809 Index 815

MindTap Chapters 15 Project Management 15-1 16 Multiobjective Decision Making 16-1 17 Inventory and Supply Chain Models 17-1

Brief Contents

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ix

Preface xiii

CHAPTER 1 Introduction to Modeling 1 1.1 Introduction 3 1.2 A Capital Budgeting Example 3 1.3 Modeling versus Models 6 1.4 A Seven-Step Modeling Process 7 1.5 A Great Source for Management Science

Applications: Interfaces 13 1.6 Why Study Management Science? 13 1.7 Software Included with This Book 15 1.8 Conclusion 17

CHAPTER 2 Introduction to Spreadsheet Modeling 19

2.1 Introduction 20 2.2 Basic Spreadsheet Modeling:

Concepts and Best Practices 21 2.3 Cost Projections 25 2.4 Breakeven Analysis 31 2.5 Ordering with Quantity Discounts

and Demand Uncertainty 39 2.6 Estimating the Relationship between

Price and Demand 44 2.7 Decisions Involving the Time Value of

Money 54 2.8 Conclusion 59 Appendix Tips for Editing and

Documenting Spreadsheets 64 CASE 2.1 Project Selection at Ewing Natural

Gas 66 CASE 2.2 New Product Introduction at eTech 68

CHAPTER 3 Introduction to Optimization Modeling 71

3.1 Introduction 72 3.2 Introduction to Optimization 73 3.3 A Two-Variable Product Mix Model 75

Contents

3.4 Sensitivity Analysis 87 3.5 Properties of Linear Models 97 3.6 Infeasibility and Unboundedness 100 3.7 A Larger Product Mix Model 103 3.8 A Multiperiod Production Model 111 3.9 A Comparison of Algebraic

and Spreadsheet Models 120 3.10 A Decision Support System 121 3.11 Conclusion 123 Appendix Information on Optimization Software 130 CASE 3.1 Shelby Shelving 132

CHAPTER 4 Linear Programming Models 135 4.1 Introduction 136 4.2 Advertising Models 137 4.3 Employee Scheduling Models 147 4.4 Aggregate Planning Models 155 4.5 Blending Models 166 4.6 Production Process Models 174 4.7 Financial Models 179 4.8 Data Envelopment Analysis (DEA) 191 4.9 Conclusion 198 CASE 4.1 Blending Aviation Gasoline at Jansen

Gas 214 CASE 4.2 Delinquent Accounts at GE Capital 216 CASE 4.3 Foreign Currency Trading 217

CHAPTER 5 Network Models 219 5.1 Introduction 220 5.2 Transportation Models 221 5.3 Assignment Models 233 5.4 Other Logistics Models 240 5.5 Shortest Path Models 249 5.6 Network Models in the Airline Industry 258 5.7 Conclusion 267 CASE 5.1 Optimized Motor Carrier Selection at

Westvaco 274

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CHAPTER 9 Decision Making under Uncertainty 457

9.1 Introduction 458 9.2 Elements of Decision Analysis 460 9.3 Single-Stage Decision Problems 467 9.4 The PrecisionTree Add-In 471 9.5 Multistage Decision Problems 474 9.6 The Role of Risk Aversion 492 9.7 Conclusion 499 CASE 9.1 Jogger Shoe Company 510 CASE 9.2 Westhouser Paper Company 511 CASE 9.3 Electronic Timing System for

Olympics 512 CASE 9.4 Developing a Helicopter Component

for the Army 513

CHAPTER 10 Introduction to Simulation Modeling 515

10.1 Introduction 516 10.2 Probability Distributions for Input

Variables 518 10.3 Simulation and the Flaw of Averages 537 10.4 Simulation with Built-in Excel Tools 540 10.5 Introduction to @RISK 551 10.6 The Effects of Input Distributions on

Results 568 10.7 Conclusion 577 Appendix Learning More About @RISK 583 CASE 10.1 Ski Iacket Production 584 CASE 10.2 Ebony Bath Soap 585 CASE 10.3 Advertising Effectiveness 586 CASE 10.4 New Project Introduction at eTech 588

CHAPTER 11 Simulation Models 589 11.1 Introduction 591 11.2 Operations Models 591 11.3 Financial Models 607 11.4 Marketing Models 631 11.5 Simulating Games of Chance 646 11.6 Conclusion 652 Appendix Other Palisade Tools for Simulation 662

x Contents

CHAPTER 6 Optimization Models with Integer Variables 277

6.1 Introduction 278 6.2 Overview of Optimization with Integer

Variables 279 6.3 Capital Budgeting Models 283 6.4 Fixed-Cost Models 290 6.5 Set-Covering and Location-Assignment

Models 303 6.6 Cutting Stock Models 320 6.7 Conclusion 324 CASE 6.1 Giant Motor Company 334 CASE 6.2 Selecting Telecommunication Carriers to

Obtain Volume Discounts 336 CASE 6.3 Project Selection at Ewing Natural Gas 337

CHAPTER 7 Nonlinear Optimization Models 339 7.1 Introduction 340 7.2 Basic Ideas of Nonlinear Optimization 341 7.3 Pricing Models 347 7.4 Advertising Response and Selection Models 365 7.5 Facility Location Models 374 7.6 Models for Rating Sports Teams 378 7.7 Portfolio Optimization Models 384 7.8 Estimating the Beta of a Stock 394 7.9 Conclusion 398 CASE 7.1 GMS Stock Hedging 405

CHAPTER 8 Evolutionary Solver: An Alternative Optimization Procedure 407

8.1 Introduction 408 8.2 Introduction to Genetic Algorithms 411 8.3 Introduction to Evolutionary Solver 412 8.4 Nonlinear Pricing Models 417 8.5 Combinatorial Models 424 8.6 Fitting an S-Shaped Curve 435 8.7 Portfolio Optimization 439 8.8 Optimal Permutation Models 442 8.9 Conclusion 449 CASE 8.1 Assigning MBA Students to Teams 454 CASE 8.2 Project Selection at Ewing Natural Gas 455

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Contents xi

CASE 11.1 College Fund Investment 664 CASE 11.2 Bond Investment Strategy 665 CASE 11.3 Project Selection Ewing Natural Gas 666

CHAPTER 12 Queueing Models 667 12.1 Introduction 668 12.2 Elements of Queueing Models 670 12.3 The Exponential Distribution 673 12.4 Important Queueing Relationships 678 12.5 Analytic Steady-State Queueing Models 680 12.6 Queueing Simulation Models 699 12.7 Conclusion 709 CASE 12.1 Catalog Company Phone Orders 713

CHAPTER 13 Regression and Forecasting Models 715 13.1 Introduction 716 13.2 Overview of Regression Models 717 13.3 Simple Regression Models 721 13.4 Multiple Regression Models 734 13.5 Overview of Time Series Models 745 13.6 Moving Averages Models 746 13.7 Exponential Smoothing Models 751 13.8 Conclusion 762 CASE 13.1 Demand for French Bread at Howie’s

Bakery 768 CASE 13.2 Forecasting Overhead at Wagner

Printers 769 CASE 13.3 Arrivals at the Credit Union 770

CHAPTER 14 Data Mining 771 14.1 Introduction 772 14.2 Classification Methods 774 14.3 Clustering Methods 795 14.4 Conclusion 806 CASE 14.1 Houston Area Survey 808

References 809

Index 815

MindTap Chapters

CHAPTER 15 Project Management 15-1 15.1 Introduction 15-2 15.2 The Basic CPM Model 15-4 15.3 Modeling Allocation of Resources 15-14 15.4 Models with Uncertain Activity Times 15-30 15.5 A Brief Look at Microsoft Project 15-35 15.6 Conclusion 15-39

CHAPTER 16 Multiobjective Decision Making 16-1 16.1 Introduction 16-2 16.2 Goal Programming 16-3 16.3 Pareto Optimality and Trade-Off Curves 16-12 16.4 The Analytic Hierarchy Process (AHP) 16-20 16.5 Conclusion 16-25

CHAPTER 17 Inventory and Supply Chain Models 17-1 17.1 Introduction 17-2 17.2 Categories of Inventory and Supply Chain

Models 17-3 17.3 Types of Costs in Inventory and Supply Chain

Models 17-5 17.4 Economic Order Quantity (EOQ) Models 17-6 17.5 Probabilistic Inventory Models 17-21 17.6 Ordering Simulation Models 17-34 17.7 Supply Chain Models 17-40 17.8 Conclusion 17-50 CASE 17.1 Subway Token Hoarding 17-57

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xiii

Practical Management Science provides a spreadsheet- based, example-driven approach to management science. Our initial objective in writing the book was to reverse negative attitudes about the course by making the subject relevant to students. We intended to do this by imparting valuable modeling skills that students can appreciate and take with them into their careers. We are very gratified by the success of previous editions. The book has exceeded our initial objectives. We are especially pleased to hear about the success of the book at many other colleges and universities around the world. The acceptance and excitement that has been generated has motivated us to revise the book and make the current edition even better. When we wrote the first edition, management science courses were regarded as irrelevant or uninteresting to many business students, and the use of spreadsheets in management science was in its early stages of development. Much has changed since the first edition was published in 1996, and we believe that these changes are for the better. We have learned a lot about the best practices of spreadsheet modeling for clarity and communication. We have also developed better ways of teaching the materials, and we understand more about where students tend to have difficulty with the concepts. Finally, we have had the opportunity to teach this material at several Fortune 500 companies (including Eli Lilly, PricewaterhouseCoopers, General Motors, Tomkins, Microsoft, and Intel). These companies, through their enthusiastic support, have further enhanced the realism of the examples included in this book. Our objective in writing the first edition was very simple—we wanted to make management science relevant and practical to students and professionals. This book continues to distinguish itself in the market in four fundamental ways:

■ Teach by Example. The best way to learn modeling concepts is by working through examples and solving an abundance of problems. This active learning approach is not new, but our text has more fully developed this approach than any book in the field. The feedback we have received from many of you has confirmed the success of this pedagogical approach for management science.

■ Integrate Modeling with Finance, Marketing, and Operations Management. We integrate modeling into all functional areas of business. This is an important feature because the majority of business students major in finance and marketing. Almost all competing textbooks emphasize operations management–related examples. Although these examples are important, and many are included in the book, the application of modeling to problems in finance and marketing is too important to ignore. Throughout the book, we use real examples from all functional areas of business to illustrate the power of spreadsheet modeling to all of these areas. At Indiana University, this led to the development of two advanced MBA electives in finance and marketing that built upon the content in this book.

■ Teach Modeling, Not Just Models. Poor attitudes among students in past management science courses can be attributed to the way in which they were taught: emphasis on algebraic formulations and memorization of models. Students gain more insight into the power of management science by developing skills in modeling. Throughout the book, we stress the logic associated with model development, and we discuss solutions in this context. Because real problems and real models often include limitations or alternatives, we include several “Modeling Issues” sections to discuss these important matters. Finally, we include “Modeling Problems” in most chapters to help develop these skills.

■ Provide Numerous Problems and Cases. Whereas all textbooks contain problem sets for students to practice, we have carefully and judiciously crafted the problems and cases contained in this book. Each chapter contains four types of problems: easier Level A Problems, more difficult Level B Problems, Modeling Problems, and Cases. Most of the problems following sections of chapters ask students to extend the examples in the preceding section. The end-of-chapter problems then ask students to explore new models. Selected solutions are available to students through MindTap and are

Preface

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xiv Preface

denoted by the second-color numbering of the problem. Solutions for all of the problems and cases are provided to adopting instructors. In addition, shell files (templates) are available for many of the problems for adopting instructors. The shell files contain the basic structure of the problem with the relevant formulas omitted. By adding or omitting hints in individual solutions, instructors can tailor these shell files to best meet the specific needs of students.

New to the Sixth Edition The immediate reason for the sixth edition was the introduction of Excel 2016. Admittedly, this is not really a game changer, but it does provide new features that ought to be addressed. In addition, once we were motivated by Excel 2016 to revise the book, we saw the possibility for other changes that will hopefully improve the book. Important changes to the sixth edition include the following:

■ The book is now entirely geared to Excel 2016. In particular, all screenshots are from this newest version of Excel. However, the changes are not dramatic, and users of Excel 2013, Excel 2010, and even Excel 2007 should have no trouble following. Also, the latest changes in the accompanying @RISK, PrecisionTree, and StatTools add-ins have been incorporated into the text.

■ Many of the problems (well over 100) have new data. Even though these problems are basically the same as before, the new data results in different solutions. Similarly, the time series data in several of the chapter examples have been updated.

■ A new chapter on Data Mining has been added. It covers classification problems (including a section on neural networks) and clustering. To keep the size of the physical book roughly the same as before, the chapter on Inventory and Supply Chain Models has been moved online as Chapter 17.

■ Probably the single most important change is that the book is now incorporated into Cengage’s MindTap platform. This provides an enhanced learning environment for both instructors and students. Importantly, dozens of new multiple choice questions are included in MindTap. These are not of the memorization variety. Instead, they

require students to understand the material, and many of them require students to solve problems similar to those in the book. They are intended to help instructors where grading in large classes is a serious issue.

MindTap: Empower Your Students MindTap is a platform that propels students from memorization to mastery. It gives you the instructor complete control of your course, so you can provide engaging content, challenge every learner, and build student confidence. You can customize interactive syllabi to emphasize priority topics, then add your own material or notes to the eBook as desired. This outcomes-driven application gives you the tools needed to empower your students and boost both understanding and performance.

Access Everything You Need in One Place MindTap’s preloaded and organized course materials, including interactive multimedia, assignments, quizzes, and more, allow you to cut down on prep time and teach more efficiently. In addition, the full textbook is available for smartphone via the MindTap mobile app. This gives your students the power to read, listen, and study on their phones, so that they can learn in the way best suited to them.

Empower Students to Reach their Potential Twelve distinct metrics give you actionable insights into student engagement. You can identify topics troubling your entire class and instantly communicate with those struggling. Students can track their scores to stay motivated towards their goals.

Control Your Course—and Your Content MindTap gives you the flexibility to reorder textbook chapters, add your own notes, and embed a variety of content, including Open Educational Resources (OER). You can personalize course content to your students’ needs. Students can even read your notes, add their own, and highlight key text to aid their learning.

Get a Dedicated Team, Whenever You Need Them MindTap isn’t just a tool. It is backed by a personalized team eager to support you. We can help set up your

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Preface xv

course and tailor it to your specific objectives, so you will be ready to make an impact from day one. You can be confident that we will be standing by to help you and your students until the final day of the term.

Student Website Access to the companion site for this text can be found at cengage.com/login. Students will need to set up a free account and then search for this text and edition by author name, title, and/or ISBN. The site includes access to the student problem files, example files, case files, an Excel tutorial, and SolverTable. In addition, a link to access download instructions for Palisade’s DecisionTools Suite is available. Note: An access code is not needed to access this software; only the index that is in the back of this textbook is needed to download the Decision Tools Suite.

Software We continue to be very excited about offering the most comprehensive suite of software ever available with a management science textbook. The commercial value of the software available with this text exceeds $1,000 if purchased directly. This software is available free with new copies of the sixth edition. The following Palisade software is available from www.cengagebrain.com.

■ Palisade’s DecisionTools™ Suite, including the award-winning @RISK, PrecisionTree, StatTools, TopRank, NeuralTools, Evolver, and BigPicture. This software is not available with any competing textbook and comes in an educational version that is only slightly scaled- down from the expensive commercial version. (StatTools replaces Albright’s StatPro add-in that came with the second edition. Although it is no longer maintained, StatPro is still freely available from www.kelley.iu.edu/albrightbooks.) For more information about the Palisade Corporation and the DecisionTools Suite, visit Palisade’s website at www.palisade.com.

■ To make sensitivity analysis for optimization models useful and intuitive, we continue to provide Albright’s SolverTable add-in (which is also freely available from www.kelley.iu.edu /albrightbooks). SolverTable provides data table– like sensitivity output for optimization models that is easy to interpret.

Example Files, Data Sets, Problem Files, and Cases Also on the student website are the Excel files for all of the examples in the book, as well as many data files required for problems and cases. As in previous editions, there are two versions of the example files: a completed version and a template to get students started. Because this book is so example- and problem- oriented, these files are absolutely essential. There are also a few extra example files, in Extra Examples folders, that are available to instructors and students. These extras extend the book examples in various ways.

Ancillaries Instructor Materials Adopting instructors can obtain all resources online. Please go to login.cengage.com to access the following resources:

■ PMS6e Problem Database.xlsx file, which contains information about all problems in the book and the correspondence between them and those in the previous edition

■ Solution files (in Excel format) for all of the problems and cases in the book and solution shells (templates) for selected problems

■ PowerPoint® presentation files ■ Test Bank in Word format and also in the online

testing service, Cognero

Albright also maintains his own website at www .kelley.iu.edu/albrightbooks. Among other things, the instructor website includes errata for each edition.

Companion VBA Book Soon after the first edition appeared, we began using Visual Basic for Applications (VBA), the program ming language for Excel, in some of our management science courses. VBA allows you to develop decision support systems around the spreadsheet models. (An example appears near the end of Chapter 3.) This use of VBA has been popular with our students, and many instructors have expressed interest in learning how to do it. For additional support on this topic, a companion book by Albright, VBA for Modelers, 5e (ISBN 9781285869612) is available. It assumes no prior experience in computer programming, but it progresses rather quickly to the

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xvi Preface

development of interesting and nontrivial applications. The sixth edition of Practical Manage ment Science depends in no way on this companion VBA book, but we encourage instructors to incorporate some VBA into their management science courses. This is not only fun, but students quickly learn to appreciate its power. If you are interested in adopting VBA for Modelers, contact your local Cengage Learning representative.

Mac Users We are perfectly aware that more students, maybe even the majority of students, are now using Macs. This is a fact of life, and we can no longer assume that we’re targeting only Windows users. There are two possible solutions for you Mac users. First, you can use a Windows emulation program such as Boot Camp or Parallels. Our Mac users at IU have been doing this for years with no problems. Second, you can use Excel for the Mac, with the latest 2016 version highly recommended. Its user interface is now very similar to the Windows version, so it should be easy to get used to. However, you should be aware that not everything will work. Specifically, the Palisade and SolverTable add-ins will not work with Excel for Mac, and this is not likely to change in the future. Also, some features of Excel for Windows (mostly advanced features not covered in this book such as pivot charts and histograms) have not yet been incorporated in Excel for the Mac.

Acknowledgments This book has gone through several stages of reviews, and it is a much better product because of them. The majority of the reviewers’ suggestions were very

good ones, and we have attempted to incorporate them. We would like to extend our appreciation to:

Mohammad Ahmadi, University of Tennessee at Chattanooga

Ehsan Elahi, University of Massachusetts–Boston Kathryn Ernstberger, Indiana University Southeast Levon R. Hayrapetyan, Houston Baptist University Bradley Miller, University of Houston Sal Agnihothri, Binghamton University, SUNY Ekundayo Shittu, The George Washington

University Yuri Yatsenko, Houston Baptist University We would also like to thank three special people. First, we want to thank our original editor Curt Hinrichs. Curt’s vision was largely responsible for the success of the early editions of Practical Management Science. Second, we were then lucky to move from one great editor to another in Charles McCormick. Charles is a consummate professional. He was both patient and thorough, and his experience in the publishing business ensured that the tradition Curt started was carried on. Third, after Charles’s retirement, we were fortunate to be assigned to one more great editor, Aaron Arnsparger, for the current edition. We hope to continue working with Aaron far into the future. We would also enjoy hearing from you—we can be reached by e-mail. And please visit either of the following websites for more information and occasional updates: ■ www.kelley.iu.edu/albrightbooks ■ www.cengagebrain.com

S. Christian Albright (albright@indiana.edu) Bloomington, Indiana Wayne L. Winston (winston@indiana.edu)

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1

Introduction to Modeling

C H A P T E R

BUSINESS ANALYTICS PROVIDES INSIGHTS AND IMPROVES PERFORMANCE

This book is all about using quantitative modeling to help companies make better decisions and improve performance. We have been teach- ing management science for decades, and companies have been using the management science methods discussed in this book for decades to improve performance and save millions of dollars. Indeed, the applied journal Interfaces, discussed later in this chapter, has chronicled management science success stories for years. Therefore, we were a bit surprised when a brand new term, Business Analytics (BA), became hugely popular several years ago. All of a sudden, BA promised to be the road to success. By using quantitative BA methods—data analysis, optimization, simulation, prediction, and others—companies could drastically improve business performance. Haven’t those of us in management science been doing this for years? What is different about BA that has made it so popular, both in the academic world and even more so in the business world?

The truth is that BA does use the same quantitative methods that have been the hallmark of management science for years, the same methods you will learn in this book. BA has not all of a sudden invented brand new quantitative methods to eclipse traditional management science methods. The main difference is that BA uses big data to solve business problems and provide insights. Companies now have access to huge sources of data,

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and better/faster algorithms and technology are now available to use huge data sets for statistical and quantitative analysis, predictive modeling, optimization, and simulation. In short, the same quantitative methods that have been available for years can now be even more effective by utilizing big data and the corresponding algorithms and technology.

For a quick introduction to BA, you should visit the BA Wikipedia site (search the Web for “business analytics”). Among other things, it lists areas where BA plays a prominent role, including the following: retail sales analytics; financial services analytics; risk and credit analytics; marketing analytics; pricing analytics; supply chain analytics; and transportation analytics. If you glance through the examples and problems in this book, you will see that most of them come from these same areas. Again, the difference is that we use relatively small data sets to get you started—we do not want to overwhelm you with gigabytes of data—whereas real applications of BA use huge data sets to advantage.

A more extensive discussion of BA can be found in the Fall 2011 research report, Analytics: The Widening Divide, published in the MIT Sloan Management Review in collabo- ration with IBM, a key developer of BA software (search the Web for the article’s title). This 22-page article discusses what BA is and provides several case studies. In addition, it lists three key competencies people need to compete successfully in the BA world—and hopefully you will be one of these people.

■ Competency 1: Information management skills to manage the data. This competency involves expertise in a variety of techniques for managing data. Given the key role of data in BA methods, data quality is extremely important. With data coming from a number of disparate sources, both internal and external to an organi- zation, achieving data quality is no small feat.

■ Competency 2: Analytics skills and tools to understand the data. We were not surprised, but rather very happy, to see this competency listed among the requirements because these skills are exactly the skills we cover throughout this book—optimization with advanced quantitative algorithms, simulation, and others.

■ Competency 3: Data-oriented culture to act on the data. This refers to the culture within the organization. Everyone involved, especially top management, must believe strongly in fact-based decisions arrived at using analytical methods.

The article argues persuasively that the companies that have these competencies and have embraced BA have a distinct competitive advantage over companies that are just starting to use BA methods or are not using them at all. This explains the title of the article. The gap between companies that embrace BA and those that do not will only widen in the future.

One final note about the relationship between BA and management science is that the journal Management Science published a special issue in June 2014 with an emphasis on BA. The following is an excerpt from the Call for Papers for this issue (search the Web for “management science business analytics special issue”).

“We envision business analytics applied to many domains, including, but surely not limited to: digital market design and operation; network and social-graph analysis; pricing and revenue management; targeted marketing and customer relationship management; fraud and security; sports and entertainment; retailing to healthcare to financial services to many other industries. We seek novel modeling and empirical work which includes, among others, probability modeling, structural empirical models, and/or optimization methods.”

This is even more confirmation of the tight relationship between BA and management science. As you study this book, you will see examples of most of the topics listed in this quote. ■

2 Chapter 1 Introduction to Modeling

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1.2 A Capital Budgeting Example 3

1.1 INTRODUCTION The purpose of this book is to expose you to a variety of problems that have been solved successfully with management science methods and to give you experience in modeling these problems in the Excel spreadsheet package. The subject of management science has evolved for more than 60 years and is now a mature field within the broad category of applied mathematics. This book emphasizes both the applied and mathematical aspects of management science. Beginning in this chapter and continuing throughout the rest of the book, we discuss many successful management science applications, where teams of highly trained people have implemented solutions to the problems faced by major com- panies and have saved these companies millions of dollars. Many airlines, banks, and oil companies, for example, could hardly operate as they do today without the support of management science. In this book, we will lead you through the solution procedure for many interesting and realistic problems, and you will experience firsthand what is required to solve these problems successfully. Because we recognize that most of you are not highly trained in mathematics, we use Excel spreadsheets to solve problems, which makes the quantitative analysis much more understandable and intuitive.

The key to virtually every management science application is a mathematical model. In simple terms, a mathematical model is a quantitative representation, or idealization, of a real problem. This representation might be phrased in terms of mathematical expressions (equations and inequalities) or as a series of related cells in a spreadsheet. We prefer the lat- ter, especially for teaching purposes, and we concentrate primarily on spreadsheet models in this book. However, in either case, the purpose of a mathematical model is to represent the essence of a problem in a concise form. This has several advantages. First, it enables managers to understand the problem better. In particular, the model helps to define the scope of the problem, the possible solutions, and the data requirements. Second, it allows analysts to use a variety of the mathematical solution procedures that have been developed over the past half century. These solution procedures are often computer-intensive, but with today’s cheap and abundant computing power, they are usually feasible. Finally, the modeling process itself, if done correctly, often helps to “sell” the solution to the people who must work with the system that is eventually implemented.

In this introductory chapter, we begin by discussing a relatively simple example of a mathematical model. Then we discuss the distinction between modeling and a collection of models. Next, we discuss a seven-step modeling process that can be used, in essence if not in strict conformance, in most successful management science applications. Finally, we discuss why the study of management science is valuable, not only to large corporations, but also to students like you who are about to enter the business world.

1.2 A CAPITAL BUDGETING EXAMPLE As indicated earlier, a mathematical model is a set of mathematical relationships that rep- resent, or approximate, a real situation. Models that simply describe a situation are called descriptive models. Other models that suggest a desirable course of action are called optimi- zation models. To get started, consider the following simple example of a mathematical model. It begins as a descriptive model, but it then becomes an optimization model.

A Descriptive Model A company faces capital budgeting decisions. (This type of model is discussed in detail in Chapter 6.) There are seven potential investments. Each has an investment cost and a

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corresponding stream of cash flows (including the investment cost) summarized by a net present value (NPV). These are listed in Figure 1.1. Row 7 also lists the return on invest- ment (ROI) for each investment, the ratio of NPV to cost, minus 1.

The company must decide which of these seven investments to make. There are two constraints that affect the decisions. First, each investment is an all-or-nothing decision. The company either invests entirely in an investment, or it ignores the investment completely. It is not possible to go part way, incurring a fraction of the cost and receiving a fraction of the revenues. Second, the company is limited by a budget of $15 million. The total cost of the investments it chooses cannot exceed this budget. With these constraints in mind, the company wants to choose the investments that maximize the total NPV.

A descriptive model can take at least two forms. One form is to show all of the elements of the problem in a diagram, as in Figure 1.2. This method, which will be used extensively in later chapters, helps the company to visualize the problem and to better understand how the elements of the problem are related. Our conventions are to use red ovals for decisions, blue rectangles for given inputs, yellow rounded rectangles for calcu- lations, and gray-bordered rectangles for objectives to optimize. (These colors are visible when you open the files in Excel.)

Although the diagram in Figure 1.2 helps the company visualize the problem, it does not provide any numeric information. This can be accomplished with the second descriptive form of the model in Figure 1.3. Any set of potential decisions, 0/1 values, can be entered in row 10 to indicate which of the investments are undertaken. Then sim- ple Excel formulas that relate the decisions to the inputs in rows 5 and 6 can be used to calculate the total investment cost and the total NPV in cells B14 and B17. For example, the formula in cell B14 is

=SUMPRODUCT(B5:H5,B10:H10)

(If you don’t already know Excel’s SUMPRODUCT function, you will learn it in the next chapter and then use it extensively in later chapters.) The company can use this model to investigate various decisions. For example, the current set of decisions looks good in terms of total NPV, but it is well over budget. By trying other sets of 0/1 values in row 10, the company can play “what-if” to attempt to find a good set of decisions that stays within budget.

4 Chapter 1 Introduction to Modeling

Figure 1.1 Costs and NPVs for Capital Budgeting Model

1 2 3 4 5 6 7

HGFEDCB Capital budgeting model

Input data on potential investments ($ millions) Investment

A

1 $5.0 $5.6

12.0%

$2.4 $2.7

12.5%

$3.5 $3.9

11.4%

$5.9 $6.8

15.3%

$6.9 $7.7

11.6%

$4.5 $5.1

13.3%

$3.0 $3.3

10.0%

2 3 4 5 6 7 Cost NPV ROI

Figure 1.2 Relationships among Elements of the Model

Whether to invest

Investment cost

Investment NPV

Budget< =Total cost ofinvestments

Maximize total NPV

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1.2 A Capital Budgeting Example 5

Because there are two possible values for each cell in row 10, 0 or 1, there are 27 5 128 possible sets of decisions, some of which will be within the budget and some of which will be over the budget. This is not a huge number, so the company could potentially try each of these to find the optimal investment strategy. However, you can probably see that this “exhaustive search” strategy can easily become overwhelming. For example, if there were 14 potential investments, the number of possible sets of decisions would increase to 214 5 16,384. The company would probably not want to search through all of these, which is why the optimization model discussed next is so useful.

An Optimization Model The company’s dream at this point is to have software that can quickly search through all potential sets of decisions and find the one that maximizes total NPV while staying within the budget. Fortunately, this software exists, and you own it! It is called Solver, an add-in to Excel, and it is discussed in detail in Chapters 3 to 8. All the company needs to do, after creating the descriptive model in Figure 1.3, is to invoke Solver. This opens a dialog box (not shown here) where the company can specify the objective cell, the range of decision variable cells, and any constraints. Then Solver finds the optimal solution, usually in a matter of seconds.

The optimal solution for this particular model appears in Figure 1.4. The company should undertake investments 3, 5, and 6, and it should ignore the others. Although not quite all of the budget is used, the company is guaranteed that no other set of decisions can obtain a higher total NPV and stay within the budget.

Optimal solutions are sometimes surprising. You might have expected the company to choose the investments with the largest ROIs, at least until the budget runs out. However, this is not what the optimal solution prescribes. For example, investment 4 has the largest ROI, but it is not chosen, and investment 5, which is chosen, has a lower ROI than three of the investments that are not chosen. As this example illustrates, an optimization model often provides insights that your intuition alone cannot provide.

Incorporating Uncertainty Most of the optimization models in this book are deterministic, meaning that there is no uncertainty about any of the model inputs. Specifically, the NPVs in row 6 of the capital budgeting model are assumed to be known when the company makes its investment

Figure 1.3 Descriptive Model for What-If Analysis

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17

HGFEDCB Capital budgeting model

Decisions: whether to invest

Budget constraint

Objective to maximize

Input data on potential investments ($ millions) Investment 1

$5.0 $5.6

12.0%

0

Total cost $17.3

$19.4

Budget $15

1 1 0 1 1 0

$2.4 $2.7

12.5%

$3.5 $3.9

11.4%

$5.9 $6.8

15.3%

$6.9 $7.7

11.6%

$4.5 $5.1

13.3%

$3.0 $3.3

10.0%

2 3 4 5 6 7 Cost

A

NPV ROI

1 if yes, 0 if no

Total NPV

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decisions. This is clearly a strong assumption; uncertainties about future revenues almost surely exist. This uncertainty can be built into the model by replacing fixed input values by probability distributions. This takes us into the realm of simulation models, which are dis- cussed in detail in Chapters 10 and 11. Simulation lets the company see how an output such as total NPV varies, for any given set of decisions, as uncertain inputs vary over their ranges of possible values. Fortunately, another Excel add-in called @RISK for performing simulations is available with this book, and it is used extensively in Chapters 10 and 11. @RISK even has a tool called RISKOptimizer that can be used to find the optimal set of decisions in the face of uncertainty. We discuss RISKOptimizer only briefly, but it is very powerful software.

1.3 MODELING VERSUS MODELS Management science, at least as it has been taught in many traditional courses, has evolved as a collection of mathematical models. These include various linear program- ming models (the transportation model, the product mix model, the shortest route model, and others), inventory models, queueing models, and more. Much time has been devoted to teaching the intricacies of these particular models. Management science practitio- ners, however, have justifiably criticized this emphasis on specific models. They argue that the majority of real-world management science problems cannot be neatly cate- gorized as one of the handful of models typically included in a management science textbook. That is, there is often no “off-the-shelf” model that can be used, at least not without modification, to solve a company’s real problem. Unfortunately, management science students might get the impression that all problems must be “shoe-horned” into one of the textbook models.

The good news is that this emphasis on specific models has been changing in the past decade or two, and our goal in this book is to embrace this change. Specifically, this book stresses modeling, not models. The distinction between modeling and models will become clear as you proceed through the book. Learning specific models is essentially a memori- zation process—memorizing the details of a particular model, such as the transportation model, and possibly learning how to “trick” other problems into looking like a transporta- tion model. Modeling, on the other hand, is a process in which you abstract the essence of a real problem into a model, spreadsheet or otherwise. Although many problems fall naturally into several categories, successful modelers do not try to shoe-horn each problem into one