10-The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employees time is worth

21 Apr 10-The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employees time is worth

Posted at 13:00h in Mathematics by

10-The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour,
and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine
are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour?

32-A power company located in southern Alabama wants to predict the peak power load (i.e., the maximum amount of power that must be generated each day to meet demand) as a function of the daily high temperature (X). A random sample of 25 summer days is chosen, and the peak power load and the high temperature are recorded each day. The file P13_32.xlsx contains these observations.

Create a scatterplot for these data. Comment on the observed relationship between Y and X.
Estimate an appropriate regression equation to predict the peak power load for this power |company. Interpret the estimated regression coefficients.
Analyze the estimated equation’s residuals.
Do they suggest that the regression equation is adequate? If not, return to part b and revise your equation. Continue to revise the equation until the results are satisfactory.
Use your final equation to predict the peak power load on a summer day with a high temperature of 100 degrees.

35-The file P13_35.xlsx contains the amount of money spent advertising a product (in thousands of dollars) and the number of units sold (in millions) for eight months.

a. Assume that the only factor influencing monthly sales is advertising. Fit the following two curves to these data: linear (Y 5 a 1 bX) and power (Y 5 aXb). Which equation best fits the data?

b. Interpret the best-fitting equation.
c. Using the best-fitting equation, predict sales during a month in which $60,000 is spent on advertising.

Quantitative Assignment

Problem 10 – Page 696
Problem 32 – Page 764
Problem 35 – Page 764

Use of Excel in Forecasting Problems

Excel Analysis Tool Pack

The Excel Analysis Tool Pack is an Excel add-in that is typically included in the Excel screen tool bar after you select the DATA tab. The icon will be titled: “Data Analysis” and is located on the right side of the tool bar. If the tool pack is not appearing, go to the Excel add-ins to add the tool pack to your spreadsheet toolbar. This tool pack contains a number of basic data analysis tools that you may be familiar with; such as: Correlation, Descriptive Statistics, Exponential Smoothing, Histograms, Moving Averages, and so on.

I recommended that you access the tool pack by selecting the “Data Analysis” icon and review the various analysis tools. To get a detailed description of an analtyical tool, select the tool, select Help, and then scroll down the screen to select the function. For instance: Select “Data Analysis” icon à Select “Correlation” à Select “Help” à scroll to the later part of screen to select “Correlation” again à this will provide you with a definition of the function.

Informational video for your review: https://www.youtube.com/watch?v=4lAvbp-yVs8

This informational video will illustrate the use of the Excel data analysis tool for various statistical functions, such as: mean, median, hypothesis, regression analysis. The intent of this video is to ensure that you are aware of additional Excel analysis capabilities, how to access the Tool Pack and what some of the analytical capabilities are.

Hint: There are a number of interactive tutorials online…so, do not hesitate to search the web for additional information. A link for the Lynda tutorial site was provided earlier in the course. However, here is access information if you have not use Lynda as yet: To start using Lynda, go to -> www.esc.edu/lynda (you will need to put this link in your browser). When prompted, log in with your ESC College credentials (email address & password).

Creating Graphics and Including Analysis Results

When working on the two forecasting problems in this Module, it is important that you demonstrate the correct use of Excel analytics by creating: Scattergrams, adding Trendlines, including Regression data / Regression Equation, identifying R-squared value and the use of linear, exponential, power curves for Best Fit analysis, and on so. Finally, graphics should be appropriately labeled (x and y axis). All of these analysis functions can be found in the Excel tool bar after you insert the scattergram plot to your spreadsheet (based on the data that is provided). Once the basic graphic has been created, select the graphic and the tool bar will display the Chart tools: Design, Layout, Format. Select “Layout” to obtain access to the analytical tools required to complete your chart. When asked to interpret data – use your graphic display and analytical results to facilitate the interpretation. For instance: Interpret the estimated regression coefficients? Use the Regression Equation to identify the coefficients and then provide a brief discussion regarding the influence of the coeficients. Be sure it is a “Best Fit” solution. Check your R2 values.

Video – Trend Lines and Regression Analysis in Excel (12 min):

https://www.youtube.com/watch?v=6rOlGbLeQxI

The intent of the following video is to provide you with an overview of adding a trend line to a chart along with the Excel regression analysis. (Note: Video is actually 12 min versus a stated run time of 15 min.)

Again, There are a number of good tutorials online…so, do not hesitate to search the web for additional information. A link for the Lynda tutorial site was provided earlier in the course.

P696-10-Slow

Renting a copier
Inputs (for slow system)
Unit of time	hour
Arrival rate	1	customers/hour
Service rate	2	customers/hour
Outputs
Direct outputs from inputs			Distribution of number in system		Distribution of time in queue
Mean time between arrivals	1.000	hours	n (customers)	P(n in system)	t (in hours)	P(wait > t)
Mean time per service	0.500	hours	4	0.031	2.000	0.068
Traffic intensity	0.500
Summary measures
Expected number in system	1.000	customers
Expected number in queue	0.500	customers
Expected time in system	1.000	hours
Expected time in queue	0.500	hours
Percentage who don't wait in queue	50.0%
Cost analysis
Employee cost/hr
Rental cost/hour
Waiting cost/hour
Total Cost/hour

Problem 11.11

P696-10-Fast

Renting a copier
Inputs (for slow system)
Unit of time	hour
Arrival rate	1	customers/hour
Service rate	2	customers/hour
Outputs
Direct outputs from inputs			Distribution of number in system		Distribution of time in queue
Mean time between arrivals	1.000	hours	n (customers)	P(n in system)	t (in hours)	P(wait > t)
Mean time per service	0.500	hours	4	0.031	2.000	0.068
Traffic intensity	0.500
Summary measures
Expected number in system	1.000	customers
Expected number in queue	0.500	customers
Expected time in system	1.000	hours
Expected time in queue	0.500	hours
Percentage who don't wait in queue	50.0%
Cost analysis
Employee cost/hr
Rental cost/hour
Waiting cost/hour
Total Cost/hour

Problem 11.11

P764-32

Day	Peak Load Christopher J. Zappe, Ph.D.: In megawatts.	Daily High Temperature Christopher J. Zappe, Ph.D.: In degrees F.
1	118.5	89
2	136.0	94
3	143.6	100
4	153.2	97
5	140.7	95
6	151.9	100
7	135.1	92
8	178.2	106
9	101.6	67
10	96.5	67
11	103.9	74
12	113.4	84
13	106.2	79
14	111.4	85
15	116.5	89
16	96.3	68
17	150.1	98
18	105.1	86
19	114.7	87
20	189.3	108
21	131.7	96
22	100.9	76
23	92.5	71
24	132.0	90
25	116.4	88

P764-35

Month	Advertising	Units Sold
1	$1,000	4,000,000
2	$2,000	4,800,000
3	$3,000	5,000,000
4	$20,000	7,500,000
5	$30,000	8,000,000
6	$50,000	9,000,000
7	$80,000	9,900,000
8	$100,000	10,200,000

cengage.com/mindtap

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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.

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06659_fm_ptg01_i-xvi.indd 2 11/09/17 7:33 PM

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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06659_fm_ptg01_i-xvi.indd 2 11/09/17 7:33 PM

This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest.

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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

06659_fm_ptg01_i-xvi.indd 4 11/09/17 8:25 PM

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

06659_fm_ptg01_i-xvi.indd 6 11/09/17 7:33 PM

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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06659_fm_ptg01_i-xvi.indd 8 11/09/17 7:33 PM

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

06659_fm_ptg01_i-xvi.indd 9 11/09/17 7:33 PM

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, Pricewaterh

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21 Apr 10-The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employees time is worth

Use of Excel in Forecasting Problems

P696-10-Slow

P696-10-Fast

P764-32

P764-35

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