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# You can compare your work on those with the solut

## 16 Mar You can compare your work on those with the solut

You can compare your work on those with the solutions that are in the Student Solutions manual.  You should find the Conclusion page 267 a good review of what you should have learned in this module.

#### Quantitative Assignment

• Download and save a copy of the Excel Template File for the Assignment file found in this module to use with this assignment.
• Rename the file by adding your last name (for example change m04-qa.xlsx to m04-qa-roufaiel.xlsx).
• Assignment Problems: Use above file to solve the following problems. Note there are three worksheets in the file, one for each problem.
• Problem 43 – Page 268
• Problem 46 – Page 268
• Problem 52 – Page 269

I attach the scan copy of the book.

43-A truck must travel from New York to Los Angeles. As shown in Figure 5.44, several routes are available. The number associated with each arc is the number of gallons of fuel required by the truck to traverse the arc. Determine the route from New York to Los Angeles that uses the minimum amount of gas.

46-The government is auctioning off oil leases at two sites. At each site, 150,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bid- ding for the oil. Government rules state that no bidder can receive more than 45% of the land being auctioned. Cliff has bid \$2000 per acre for site 1 land and \$1000 per acre for site 2 land. Blake has bid \$1800 per acre for site 1 land and \$1500 per acre for site 2 land.

Alexis has bid \$1900 per acre for site 1 land and \$1300 per acre for site 2 land.

a)Determine how to maximize the government’s revenue with a transportation model.
b)Use SolverTable to see how changes in the government’s rule on 45% of all land being auctioned affect the optimal revenue. Why can the optimal revenue not decrease if this percentage required increases? Why can the optimal revenue not increase if this percentage required decreases?

52-A company is taking bids on four construction jobs. Three contractors have placed bids on the jobs. Their bids (in thousands of dollars) are given in the file P05_52.xlsx. (A blank indicates that the contractor did not bid on the given job.) Contractor 2 can do only one job, but contractors 1 and 3 can each do up to
two jobs. Determine the minimum cost assignment of contractors to jobs.

## P5-43

 Traveling from New York to LA Labeling of nodes City Index New York Cleveland St. Louis Nashville Phoenix Dallas Salt Lake City Los Angeles Network formulation Node balance constraints Origin Destination Gallons Flow Node Net inflow/outflow Required Gallons used

## P5-46

 Oil lease auction Bids for sites (dollars/acre) Site 1 Site 2 Ewing Barnes Pickens Max % that can be sold to any bidder Number of acres sold to bidders Site 1 Site 2 Total Max allowed Ewing Barnes Pickens Total Available Revenue (\$millions)

Problem 4.8

## P5-52

 Bidding on contracts Bids on contracts (in \$1000s) (large values mean contractor didn’t bid for that job) Job 1 Job 2 Job 3 Job 4 Contractor 1 Contractor 2 Contractor 3 Assignment of contractors to jobs Job 1 Job 2 Job 3 Job 4 Total Max Contractor 1 Contractor 2 Contractor 3 Total Required Total cost (\$1000s)

Problem 4.16

,

cengage.com/mindtap

Fit your coursework into your hectic life. Make the most of your time by learning your way. Access the resources you need to succeed wherever, whenever.

• �Stay�focused�with�an�all-in-one-place,�integrated� presentation�of�course�content.

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Break limitations. Create your own�potential,�and�be�unstoppable� with�MindTap.

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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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Printed in the United States of America Print Number: 01 Print Year: 2017

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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.

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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