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Case Study Report

Required to study and analyze Case 4.1 ========= Page 214 from the text book Practical Management Science (Attached)

A well-organized written report is required to be submitted.

write up an introduction summary of the case and discuss the type of industries it might be applicable. Additionally, you need to:

1-Develop the mathematical model formulation for the case. Then develop the spreadsheet model.

2-Provide any suggestions to improve the applicability of this case to a realistic situation.

3-Answer and elaborate on the given questions and the requests provided in the case.

4- do further sensitivity analysis either by Solver and/or Solver-Table.

5-Write general conclusion about the case.

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6th
Edition
Practical Management Science
Wayne L. Winston
Kelley School of Business, Indiana University
S. Christian Albright
Kelley School of Business, Indiana University
Australia Brazil Mexico Singapore United Kingdom United States
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Practical Management Science,
Sixth Edition
Wayne L. Winston,
S. Christian Albright
Senior Vice President: Erin Joyner
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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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About the Authors
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 statistics 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 Management Science, Data Analysis and Decision Making, Data Analysis for Managers, Spreadsheet 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.
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Brief Contents
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
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
407
MindTap Chapters
15 Project Management 15-1
16 Multiobjective Decision Making 16-1
17 Inventory and Supply Chain Models 17-1
vii
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Contents
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
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
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
Introduction  136
Advertising Models  137
Employee Scheduling Models  147
Aggregate Planning Models  155
Blending Models  166
Production Process Models  174
Financial Models  179
Data Envelopment Analysis (Dea)  191
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
5.2
5.3
5.4
5.5
5.6
5.7
Introduction  220
Transportation Models  221
Assignment Models  233
Other Logistics Models  240
Shortest Path Models  249
Network Models in the Airline Industry  258
Conclusion  267
Case 5.1 Optimized Motor Carrier Selection at
Westvaco  274
ix
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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
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
Introduction  340
Basic Ideas of Nonlinear Optimization  341
Pricing Models  347
Advertising Response and Selection Models  365
Facility Location Models  374
Models for Rating Sports Teams  378
Portfolio Optimization Models  384
Estimating the Beta of a Stock  394
Conclusion  398
Case 7.1 Gms Stock Hedging  405
Chapter 8 Evolutionary Solver: An Alternative
Optimization Procedure  407
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
Introduction  408
Introduction to Genetic Algorithms  411
Introduction to Evolutionary Solver  412
Nonlinear Pricing Models  417
Combinatorial Models  424
Fitting an S-Shaped Curve  435
Portfolio Optimization  439
Optimal Permutation Models  442
Conclusion  449
Case 8.1 Assigning Mba Students to Teams  454
Case 8.2 Project Selection at Ewing Natural Gas  455
x
Chapter 9 Decision Making under
Uncertainty  457
9.1
9.2
9.3
9.4
9.5
9.6
9.7
Introduction  458
Elements of Decision Analysis  460
Single-Stage Decision Problems  467
The PrecisionTree Add-In  471
Multistage Decision Problems  474
The Role of Risk Aversion  492
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
Contents
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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
12.2
12.3
12.4
12.5
12.6
12.7
Introduction  668
Elements of Queueing Models  670
The Exponential Distribution  673
Important Queueing Relationships  678
Analytic Steady-State Queueing Models  680
Queueing Simulation Models  699
Conclusion 709
Case 12.1 Catalog Company Phone Orders  713
Chapter 13 Regression and Forecasting Models  715
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
Introduction  716
Overview of Regression Models  717
Simple Regression Models  721
Multiple Regression Models  734
Overview of Time Series Models  745
Moving Averages Models  746
Exponential Smoothing Models  751
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
14.2
14.3
14.4
Introduction  772
Classification Methods  774
Clustering Methods  795
Conclusion  806
Case 14.1 Houston Area Survey  808
References 809
Index 815
MindTap Chapters
Chapter 15 Project Management  15-1
15.1
15.2
15.3
15.4
15.5
15.6
Introduction  15-2
The Basic CPM Model  15-4
Modeling Allocation of Resources  15-14
Models with Uncertain Activity Times  15-30
A Brief Look at Microsoft Project  15-35
Conclusion  15-39
Chapter 16 Multiobjective Decision Making  16-1
16.1
16.2
16.3
16.4
16.5
Introduction  16-2
Goal Programming  16-3
Pareto Optimality and Trade-Off Curves  16-12
The Analytic Hierarchy Process (AHP)  16-20
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
Contents
xi
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Preface
Practical Management Science provides a spreadsheetbased, 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:
â– 
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.
â– 
â– 
â– 
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
xiii
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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:
â– 
â– 
â– 
â– 
xiv
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
Preface
Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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.
â– 
â– 
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 scaleddown 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 problemoriented, 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:
â– 
â– 
â– 
â– 
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 program­ming
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
Preface
xv
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
development of interesting and nontrivial applications.
The sixth edition of Practical Manage­ment 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.
Acknowledgments
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:
â–  www.kelley.iu.edu/albrightbooks
â–  www.cengagebrain.com
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
S. Christian Albright (albright@indiana.edu)
Bloomington, Indiana
Wayne L. Winston (winston@indiana.edu)
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.
xvi
Preface
Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
CHAPTER
Introduction to Modeling
©michaeljung/Shutterstock.com
1
BUSINESS ANALYTICS PROVIDES INSIGHTS
AND IMPROVES PERFORMANCE
T
his book is all about using quantitative modeling to help companies
make better decisions and improve performance. We have been teaching 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,
1
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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 d
­ ifference
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 collaboration 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.
â– 
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 organization, achieving data quality is no small feat.
â– 
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.
â– 
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. â– 
2 Chapter 1 Introduction to Modeling
Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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 companies 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 latter, 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 represent, 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 optimization 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
1.2 A Capital Budgeting Example
3
Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Figure 1.1
Costs and NPVs for
Capital Budgeting
Model
1
2
3
4
5
6
7
A
B
Capital budgeting model
C
D
Input data on potential investments ($ millions)
2
3
1
Investment
$5.0
$2.4
$3.5
Cost
$5.6
$2.7
$3.9
NPV
12.0%
12.5%
11.4%
ROI
E
F
G
H
4
$5.9
$6.8
15.3%
5
$6.9
$7.7
11.6%
6
$4.5
$5.1
13.3%
7
$3.0
$3.3
10.0%
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 investment (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 calculations, 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 simple 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.
Figure 1.2
Relationships
among Elements of
the Model
Whether to
invest
Investment cost
Total cost of
investments
Investment NPV

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