9781133707592 pdf David R Anderson University of Cincinnati Dennis J Sweeney University of Cincinnati Thomas A Williams Rochester Institute of Technology Jeffrey D Camm University of Cincinnati James[.]
David R Anderson University of Cincinnati Dennis J Sweeney University of Cincinnati Thomas A Williams Rochester Institute of Technology Jeffrey D Camm University of Cincinnati James J Cochran Louisianna Tech University Michael J Fry University of Cincinnati Jeffrey W Ohlmann University of Iowa Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States 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 Quantitative Methods for Business, Twelfth Edition David R Anderson, Dennis J Sweeney, Thomas A Williams, Jeffrey D Camm, James J Cochran, Michael J Fry, Jeffrey W Ohlmann Vice President of Editorial, Business: Jack W Calhoun Editor-in-Chief: Joe Sabatino Senior Acquisitions Editor: Charles McCormick, Jr Developmental Editor: Maggie Kubale Editorial Assistant: Courtney Bavaro Marketing Manager: Adam Marsh Content Project Manager: Emily Nesheim © 2013, 2010 South-Western, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Media Editor: Chris Valentine Manufacturing Planner: Ron J Montgomery Senior Marketing Communications Manager: Libby Shipp Production Service: MPS Limited, a Macmillan Company Sr Art Director: Stacy Jenkins Shirley ExamView® is a registered trademark of eInstruction Corp Windows is a registered trademark of the Microsoft Corporation used herein under license Macintosh and Power Macintosh are registered trademarks of Apple Computer, Inc used herein under license © 2013 Cengage Learning All Rights Reserved Cengage Learning WebTutor™ is a trademark of Cengage Learning Internal Designer: Michael Stratton/ cmiller design Cover Designer: Craig Ramsdell Library of Congress Control Number: 2011936338 Cover Image: ©Tom Merton/Getty Images Package ISBN-13: 978-0-8400-6233-8 Package ISBN-10: 0-8400-6233-8 Book only ISBN-13: 978-0-8400-6234-5 Book only ISBN-10: 0-8400-6234-6 Rights Acquisitions Specialist: Amber Hosea South-Western 5191 Natorp Boulevard Mason, OH 45040 USA Cengage Learning products are represented in Canada by Nelson Education, Ltd For your course and learning solutions, visit www.cengage.com Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com Printed in the United States of America 15 14 13 12 11 To My Children Krista, Justin, Mark, and Colleen DRA To My Children Mark, Linda, Brad, Tim, Scott, and Lisa DJS To My Children Cathy, David, and Kristin TAW To My Family Karen, Jennifer, Stephanie, and Allison JDC To My Wife Teresa JJC To My Family Nicole and Ian MJF To My Family Amie and Willa JWO This page intentionally left blank Brief Contents Preface xvii About the Authors xxiv Chapter Introduction Chapter Introduction to Probability 27 Chapter Probability Distributions 62 Chapter Decision Analysis 101 Chapter Utility and Game Theory 157 Chapter Time Series Analysis and Forecasting 188 Chapter Introduction to Linear Programming 245 Chapter Linear Programming: Sensitivity Analysis and Interpretation of Solution 304 Chapter Linear Programming Applications in Marketing, Finance, and Operations Management 358 Chapter 10 Distribution and Network Models 419 Chapter 11 Integer Linear Programming 481 Chapter 12 Advanced Optimization Applications 530 Chapter 13 Project Scheduling: PERT/CPM 585 Chapter 14 Inventory Models 623 Chapter 15 Waiting Line Models 672 Chapter 16 Simulation 712 Chapter 17 Markov Processes 772 Appendix A Building Spreadsheet Models 798 Appendix B Binomial Probabilities 827 vi Brief Contents Appendix C Poisson Probabilities 834 Appendix D Areas for the Standard Normal Distribution 840 Appendix E Values of eⴚλ 842 Appendix F References and Bibliography 843 Appendix G Self-Test Solutions and Answers to Even-Numbered Problems 845 Index 902 Contents Preface xvii About the Authors xxiv Chapter Introduction 1.1 1.2 1.3 Problem Solving and Decision Making Quantitative Analysis and Decision Making Quantitative Analysis Model Development Data Preparation 10 Model Solution 11 Report Generation 13 A Note Regarding Implementation 13 1.4 Models of Cost, Revenue, and Profit 14 Cost and Volume Models 14 Revenue and Volume Models 15 Profit and Volume Models 15 Breakeven Analysis 16 1.5 Quantitative Methods in Practice 17 Methods Used Most Frequently 17 Summary 19 Glossary 19 Problems 20 Case Problem Scheduling a Golf League 23 Appendix 1.1 Using Excel for Breakeven Analysis 23 Chapter 2.1 2.2 Introduction to Probability 27 Experiments and the Sample Space 29 Assigning Probabilities to Experimental Outcomes 31 Classical Method 31 Relative Frequency Method 32 Subjective Method 32 2.3 Events and Their Probabilities 33 2.4 Some Basic Relationships of Probability 34 Complement of an Event 34 Addition Law 35 Conditional Probability 38 Multiplication Law 42 2.5 Bayes’ Theorem 43 The Tabular Approach 46 2.6 Simpson’s Paradox 47 Summary 50 Glossary 50 viii Contents Problems 51 Case Problem Hamilton County Judges 59 Case Problem College Softball Recruiting 61 Chapter Probability Distributions 62 3.1 3.2 Random Variables 64 Discrete Random Variables 65 Probability Distribution of a Discrete Random Variable 65 Expected Value 67 Variance 68 3.3 Binomial Probability Distribution 69 Nastke Clothing Store Problem 70 Expected Value and Variance for the Binomial Distribution 73 3.4 Poisson Probability Distribution 73 An Example Involving Time Intervals 74 An Example Involving Length or Distance Intervals 74 3.5 Continuous Random Variables 76 Applying the Uniform Distribution 76 Area as a Measure of Probability 77 3.6 Normal Probability Distribution 79 Standard Normal Distribution 80 Computing Probabilities for Any Normal Distribution 84 Grear Tire Company Problem 85 3.7 Exponential Probability Distribution 87 Computing Probabilities for the Exponential Distribution 87 Relationship Between the Poisson and Exponential Distributions 89 Summary 89 Glossary 90 Problems 91 Case Problem Specialty Toys 97 Appendix 3.1 Computing Discrete Probabilities with Excel 98 Appendix 3.2 Computing Probabilities for Continuous Distributions with Excel 99 Chapter 4.1 4.2 4.3 4.4 Decision Analysis 101 Problem Formulation 103 Influence Diagrams 104 Payoff Tables 104 Decision Trees 105 Decision Making Without Probabilities 106 Optimistic Approach 106 Conservative Approach 107 Minimax Regret Approach 107 Decision Making With Probabilities 109 Expected Value of Perfect Information 112 Risk Analysis and Sensitivity Analysis 113 Risk Analysis 113 Sensitivity Analysis 114 Appendix G 897 Self-Test Solutions and Answers to Even-Numbered Problems © Cengage Learning 2013 FIGURE G16.14 WORKSHEET FOR THE MADEIRA MANUFACTURING COMPANY WORKSHEET FOR THE CONTRACTOR BIDDING © Cengage Learning 2013 FIGURE G16.18 898 Appendix G Self-Test Solutions and Answers to Even-Numbered Problems a $750,000 should win roughly 600 to 650 of the 1000 times; the probability of winning the bid should be between 0.60 and 0.65 b The probability of $775,000 winning should be roughly 0.82, and the probability of $785,000 winning should be roughly 0.88; a contractor’s bid of $775,000 is recommended b Rock 0.27 Rock 0.31 20 a Results vary with each simulation run Approximate results: 50,000 provided $230,000 60,000 provided $190,000 70,000 less than $100,000 b Recommend 50,000 units c Roughly 0.75 22 Very poor operation; some customers wait 30 minutes or more 0.42 Rock 0.36 0.42 Paper 0.15 Rock 0.49 Scissors 0.18 Chapter 17 0.55 a 0.82 b 1 0.5, 2 0.5 c 1 0.6, 2 0.4 a Given the opposing player last chose Rock, the transition matrix shows that she is most likely to choose Paper next (with probability 0.42) Therefore, you should choose Scissors (because Scissors beats Paper) Paper Rock 0.31 a 1 0.92, 2 0.08 b $85 Scissors 0.27 24 b Waiting time approximately 0.8 minutes c 30% to 35% of customers have to wait a 0.10 as given by the transition probability b 1 0.901 0.302 (1) 2 0.101 0.702 (2) 1 2 (3) Using (1) and (3), 0.101 0.302 0.101 0.30(1 1) 0.101 0.30 0.301 0.401 0.30 1 0.75 2 (1 1) 0.25 Paper Scissors 0.27 Paper Scissors c The one step probability matrix is 0.27 P £ 0.36 0.18 0.42 0.15 0.55 0.31 0.49 § 0.27 The probability your opponent will choose Paper in the second round is given by p2(2) This can be found from ß(2) by first finding ß(1) as follows: ß(1) [0 [0.36 0.27 0] £ 0.36 0.18 0.15 0.42 0.15 0.55 0.49] 0.27 ß(2) [0.36 0.15 0.49] £ 0.36 0.18 [0.24 0.44 0.32] So, p2(2) is 0.44 0.31 0.49 § 0.27 0.42 0.15 0.55 0.31 0.49 § 0.27 Appendix G a 1 0.851 0.202 0.153 2 0.101 0.752 0.103 3 0.051 0.052 0.753 1 2 3 (1) (2) (3) (4) Using (1), (2), and (4) provides three equations with three unknowns; solving provides 1 0.548, 2 0.286, and 3 0.166 b 16.6% as given by 3 c Quick Stop should take 667 0.548(1000) 119 Murphy’s customers and 333 0.286(1000) 47 Ashley’s customers Total 166 Quick Stop customers It will take customers from Murphy’s and Ashley’s 10 also 1 0.801 0.052 0.403 2 0.101 0.752 0.303 3 0.101 0.202 0.303 (1) (2) (3) 1 2 3 (4) Using equations 1, 2, and 4, we have 1 0.442, 2 0.385, and 3 0.173 The Markov analysis shows that Special B now has the largest market share In fact, its market share has increased by almost 11% The MDA brand will be hurt most by the introduction of the new brand, T-White People who switch from MDA to T-White are more likely to make a second switch back to MDA 12 (I Q) c 0 0.4 d c 0.1 N (I Q)1 c NR c 1.85 0.37 1.85 0.37 1.11 0.2 dc 2.22 0.2 899 Self-Test Solutions and Answers to Even-Numbered Problems 0.3 0.6 0.3 d c d 0.1 0.5 0.5 1.11 d 2.22 0.1 0.59 d c 0.2 0.52 13 I c 0 d (I Q) c 0.59 probability state units end up in state 1; 0.52 probability state units end up in state 0.25 d 0.25 1.3636 0.0909 0.4545 d 1.3636 0.4545 0.5 dc 1.3636 0.5 0.01 0.909 dc 0.5 0.727 0.091 d 0.273 0.909 0.727 Estimate $1729 in bad debts 0.091 d [7271 0.273 1729] NR c 1.3636 0.0909 0.25 0.05 0.25 d 0.75 0.75 0.05 N (I Q)1 c 5000] c BNR [4000 14 3580 will be sold eventually; 1420 will be lost 16 a The Injured and Retired states are absorbing states b Rearrange the transition probability matrix to the following: Injured Retired Backup Starter Injured Retired Backup Starter 0.1 0.15 0.1 0.25 0 0.4 0.1 0 0.4 0.5 (I Q) c 0.6 0.1 N (I Q)1 c NR c 0.41 d 0.48 Q c 0.423 0.385 0.4 d 0.5 1.923 0.385 1.538 d 2.308 0.577 d 0.615 38.5% of Starters will eventually be Injured and 61.5% will be Retired 0.426 0.577 d 0.385 0.615 7.691] c BNR [8 5] c [5.308 We expect that 5.308 players will end up injured and 7.691 will retire 900 Appendix G Self-Test Solutions and Answers to Even-Numbered Problems Appendix A F6*$F$3 Cell D14 E14 F14 G14 H14 I14 Formula C14*$B$3 C14*$B$7 C14*$B$9 $B$5 SUM(E14:G14) D14-H14 Appendix G Self-Test Solutions and Answers to Even-Numbered Problems 901 10 Error #1: Grade Count F D C C C B B B A A 1 1 Formulas: These formulas hold until the row after new payment 155 Payments 156–180 are after the old loan would have been repaid and hence are negative savings (that is, costs) of $1,521.84 per month from months 156 to180 The formula in cell C17 is: SUMPRODUCT(C8:G11,B22:F25) but should be SUMPRODUCT(C8:F11,B22:F25) Error #2: The formula in cell G22 is: SUM(B22:E22) but should be SUM(B22:F22) 12 Discounted savings net of out-of-pocket expense $17,791.44 Screen shots for this solution are included below Index a (alpha) smoothing constant, 208, 210–211 ! (factorial), 70 l (lambda), 74, 75 m (mu; mean) expected value of random variables, 67 s (sigma; standard deviation) variation from the mean, 68–69 s2 (sigma squared; variance), 68–69 z (standard normal random variable), 84 A Absorbing states, 782–783, 787 Accounts receivable analysis, Markov processes for, 781–786 Accuracy in forecasting, 199–204 of exponential smoothing, 210–211 of moving averages, 206–207 of weighted moving averages, 207–208 Activities, 586, 609 Activity identification with PERT/CPM, 587–588 Activity times with beta probability distribution, 598 crashing, 595, 604, 605–607 linear programming model for, 607–609 critical path, 588–593 estimates, 596, 597 shortening, 605–607 uncertain, 595–603 Addition law, 35–38, 51 Additivity in linear programming, 251 Advanced optimization applications See Optimization applications Airline industry crew scheduling for, 482–483 operations research usage, 18 overbooking simulation, 713 revenue management by, 2, 3, 531, 539–545 seat pricing, 539 Air New Zealand, 482–483 All-integer linear programs, 482, 484, 509 graphical and computer solutions, 485–489 Allowable decrease, 312–313 Allowable increase, 312 Alternative optimal solutions, 280 linear programming, 272 Aluminum can production, 484–485 American Airlines, 2, 539 Analog models, 7, 19 Ankor Company of The Netherlands, 746–747 Apollo 11 moon landing, Arcs, 422, 452, 587 Areas, measurements of probability, 77–78, 81–84 Arrival rates, 675, 701 distribution of, 674–676 finite calling populations, 696, 697 Asociación Latino-Iberoamericana de Investigatión Operativa (ALIO), 18 Asset allocation, 545–552 for risk avoiders, 546–549 Assigning products though linear programming, 305–306 Assignment problems, 435–440, 452 Excel solutions for, 478–480 linear programming model, 438–439 project manager assignments, 439–440 Association of Asian Pacific Operational Research Societies (APORS), 18 Association of European Operational Research Societies (EURO), 18 ATM (automatic teller machine) waiting times, 673–674 AT&T, restoration capacity optimization by, 448 Automobile environmental compliance, pricing for, 552–553 Averages, moving See Moving averages B Backorders, 637, 659 costs of, 641 inventory models, 637–640 Backward pass, 591, 610 Bank branch efficiency, 532 Bank location, 498–500 Baseball revenue management, 2–3 Base-case scenarios, 716, 747 Basic requirements of probability, 31, 50 Bayer Pharmaceuticals, 126 Bayes, Thomas, 45 Bayes’ theorem, 33, 43–47, 51, 134 branch probabilities, 129 Bernoulli processes, 69 Best-case scenarios, 716, 747 Beta probability distribution, 598, 610 Binary expansion, 504 Binary variables, 482 See also 0-1 variables Binomial experiments, 69 Binomial probability distribution, 69–73, 90 Blending problems, 389–393 Blocked arrivals, 694, 701 Bluegrass Farms, sensitivity analysis problem, 322–324 Bombardier Flexjet flight scheduling, 560–561 Boundary establishment, 488–489 Branch, defined, 134 Branch probabilities, computing, 129–133 Breakeven analysis, 16 Excel for, 23–26 Breakeven points, 16, 19 Excel for, 25–26 Bush, President George W., 552 Business analytics, C CAFE (Corporate Average Fuel Economy) standards, 552–553 Call center design, 714 Canadian curling, 786 Canadian Operational Research Society (CORS), 18 Capacitated transportation problem, 426, 452 Capacitated transshipment problem, 433, 452 Capital budgeting problems, 490–491, 509 Categorical variables, 216, 223 CB Predictor, 241–244 exponential smoothing, 243–244 moving averages, 242–243 Centre for Operations Excellence (COE), 743 Certain event, 28, 50 Chance events, 103, 133 Chance nodes, 104, 134 Chilean mine cave-in, 28–29 Citibank, 673–674 Clean Energy Act of 2007, 552 Coefficients of constraints, 316–317 903 Index Collectively exhaustive, 103 Complements of events, 34–35, 51 Completion time variability, 601–603 Computer-generated random numbers, 719–721 Computers, linear programming solutions, 265–267 simulations by, 744 Concave functions, 557–558, 566 Conditional constraints, 506–507, 510 Conditional probabilities, 38–41, 51, 134 branch probabilities, 129–131 Consequence nodes, 104, 134 Consequences, 103, 133 Conservative approach to decision making, 107, 134 Conservative portfolios, 546–549 Constant demand rate, 625, 659 Constant service time, 693 Constant supply rate, 634, 659 Constrained problems, 554–557 Constraints, 8, 19, 506–507, 510 coefficients, changes in, 316–317 defined, 279 in linear programming, 247 nonnegativity, 250 redundant, 263 slack variables, 262–263 Contingency tables, 39 Continuous probability distributions, Excel for, 99–100 Continuous random variables, 64–65, 90 Excel, computing probabilities with, 99–100 probability distributions, 76–78 Continuous review inventory systems, 654, 660 Controllable inputs, 9–10, 19 defined, 713, 747 Convex functions, 558, 566 Cook, Thomas M., Corequisite constraints, 506–507, 510 Corporate Average Fuel Economy (CAFE) standards, 552–553 Costs of backorders, 641 of capital, 626, 659 of inventories, 625 and volume models, 14–15 CPM (critical path method), 586, 609 Crashing, 605, 610 activity times, 604, 605–607 critical path, 595, 604 linear programming model for, 607–609 Crew scheduling, 482–483 Critical activities, 589, 593, 610 Critical path method (CPM), 586, 609 Critical paths, 589, 609 algorithm, 593 crashing, 595, 604 expected activity times, 588–593, 594 PERT/CPM procedure, 594 project scheduling expected activity times, 588–593, 594 uncertain activity times, 599–601 Crosstabulations, 39 Crystal Ball, simulations with, 727, 744, 761–767 Cumulative probabilities, 81–83, 90 using Excel, 621–622 Curling, 786 Customer arrival time simulation, 733–734 Customer order allocation model, 507–508 Customer service time simulation, 734–735 CVS Corporation, 624 Cycle service levels, 654 Cycle times, 631, 659 Cyclical patterns, 197, 223 D Dantzig, George, 2, 247 Data envelopment analysis (DEA), 313, 531–539 defined, 531, 566 hospital performance evaluation, 532–539 linear programming model, 534–538 summary of approach, 538–539 Data preparation in quantitative analysis, 10–11 Decision alternatives, 103, 133 Decision analysis, 17, 102–103 branch probabilities, 129–133 decision making with probabilities, 109–113 without probabilities, 106–109 problem formulation, 103–106 risk analysis, 113–114 with sample information, 118–129 sensitivity analysis, 113, 114–118 TreePlan for, 150–156 Decision making, 19 conservative approach, 107 expected value approach, 109–111 expected value of perfect information, 112–113 linear programming, 246 minimax regret approach, 107–109 optimistic approach, 106–107 with probabilities, 109–113 and problem solving, 3–5 and utility, 160–165 without probabilities, 106–109 conservative approach, 107 minimax regret approach, 107–109 optimistic approach, 106–107 Decision nodes, 104, 134 Decisions, 4, 19 Decision science, Decision Sciences Institute (DSI), 18 Decision strategy, 123–125, 134 Decision trees, 105–106, 120–122, 134 Decision variables, 9, 19 defined, 249, 279 in linear programming, 319–325 Decomposition methods, 560 Deere & Company, 658 Degeneracy, 314–315 Degree of belief, 32 De Moivre, Abraham, 79 Dependent events, 40–41, 51 Dependent variables, 211, 223 Destination nodes, 427 Deterministic inventory models, 624, 644, 659 economic production lot size model, 634–637 See also Economic order quantity (EOQ) model Deterministic models, 10, 19 Deviation, 68 Discrete event simulation models, 733, 743, 748 Discrete probability distributions, 65–67, 90 Excel, computing with, 98–99 Discrete random variables, 64–69, 90 probability distribution of, 65–67 Divisibility in linear programming, 251 Dominated strategies, 177, 179 Doubtful accounts allowances, 784–786 Drug development, 102, 126 Dual values or dual prices, 314, 417 See also Shadow prices Dummy origin, 424, 452 Dummy variables, 217 Duncan Industries Limited, 331 Dynamic simulation models, 733, 747 E Earliest finish time, 589–593, 610 Earliest start time, 589–593, 610 Eastman Kodak, 305–306 Economic analysis of waiting line models, 689–690 Economic order quantity (EOQ), 659 Economic order quantity (EOQ) formula, 629 904 Index Economic order quantity (EOQ) model, 625–633 assumptions of, 633 Excel solutions of, 632–633 how-much-to-order decision, 629–630 optimal order quantity, 670–671 quantity discounts for, 642–644 sensitivity analysis of, 631–632 when-to-order decision, 630–631 Economic production lot size model, 634–637 optimal lot size formula, 671 total cost model, 635–637 Edmonton Folk Festival, 505 Efficiency evaluation, 313 Efficiency index, 536, 566 Efficiency of sample information, 129, 134 Eisner, Mark, 18 Electronic Communications, 325–330 Energy needs forecasts, 189 Environmental compliance of the auto industry, 552–553 Erlang, A.K., 673 Events, 50 complements of, 34–35, 51 defined, 733, 747 dependent, 40–41, 51 independent, 41, 42, 51 intersection of, 35–36, 51 mutually exclusive, 37–38, 42 probability of, 33–34 union of, 35, 51 Excel assignment problems, 478–480 for breakeven analysis, 23–26 continuous distributions, 99–100 cumulative probabilities, 621–622 discrete probabilities, 98–99 economic order quantity (EOQ) models, 632–633 exponential smoothing, 234–235, 236 financial planning problems, 414–418 integer linear program solving with, 489, 525–528 inventory models, 632–633 inventory simulation, 730–731 linear program solving with, 298–301 linear trends, 237–238, 239, 240 matrix inversion, 796 moving averages, 233–234, 235 nonlinear optimization problems, 582–584 seasonality, models with, 238–241 no trend, 238–240 trend, 240–241 sensitivity analysis with, 353–354, 355 simulations, 761–767 risk analysis, 725–726 waiting line, 738–739, 742 transportation problems, 474–475 transshipment problems, 475–478 TreePlan add-in, 150–156 trend projection, 235–238, 239, 240 waiting line models, 681–682, 699 simulations, 738–739, 742 Expected activity times, 586–595, 597 Expected loss (EL), 646–647 Expected utility, 163, 179 Expected utility approach, 162–164 Expected value approach, 109–111, 134 Expected values, 67–68, 90, 134 binomial probability distribution, 73 decision analysis, 109 of perfect information, 112–113, 134 of sample information, 128, 134 Experiments, 29–30, 50 binomial, 69 outcomes of, 31–33, 64 Exponential probability distribution, 87–89, 90 and the Poisson distribution, 89 waiting line models, 676, 678, 682, 701 Exponential smoothing, 208–211, 223 CB Predictor, 243–244 Excel, 234–235, 236 Extreme points, 264–265, 280 exponential smoothing, 208–211 moving averages, 206–207 weighted, 207–208 seasonality, 216–222 See also Time series patterns Forecasts, 189 Forward pass, 591, 610 Freight car assignment optimization, 427 Frequency band auction, 158 Fuel conservation by the U.S Navy, 279 Fundamental matrix, 783–784, 787 G Game theory, 170–173, 179 frequency band auction, 158 mixed strategy, 174–178 Gantt, Henry L., 586 Gantt Chart, 586 General Electric, 370 General Electric Plastics (GEP), 320 General Motors, 553 Global optima, 557, 566 Goodwill costs, 638, 659 Governmental agencies waiting lines, 690 Graphical solutions linear programming, 251–263 integer, 485–489 lines, 260–261 slack variables, 262–263 summary of procedures for, 261–262 F Factorial, 70 Failure of a trial, 69 False positives and false negatives, 131 FCFS (first-come, first-served), 677 Feasible decision alternatives, 11 Feasible region, 255, 279 Feasible solutions, 19, 255, 279 transportation problem, 423 Financial applications of linear programming, 366–373 Financial planning, 369–373 Excel, solutions with, 414–418 Finite calling populations, 696–699, 701 First-come, first-served (FCFS), 677, 701 Fixed cost problems, 491, 509 Fixed costs, 14, 19 0-1 variables, 491–493 Flight manuals production, 377–378 Flight scheduling optimization, 560–561 Flow capacity, 444, 452 Forecast error, 199–200, 223 Forecasting, 17 accuracy, 199–204 exponential smoothing, 210–211 H Harmonic averages, 578–579 Harrah’s Cherokee Casino & Hotel, 540 Harris, F W., 629 Harsanui, John, 178 Health care services, 773 Heery International, 439–440 Hepatitis B treatment, 132–133 Holding costs, 626–628, 659 Horizontal time series pattern, 190–192 Hospital performance evaluation, 532–539 Hospital revenue bond, 595 How-much-to-order decision, 629–630, 651 Hypothetical composite, 533, 566 I Iconic models, 7, 19 Immedicate predecessors, 587, 609 Impossible events, 28, 50 Incremental analysis, 646, 659 905 Index Independent events, 41, 51 vs mutually exclusive events, 42 Independent variables, 212, 223 Index funds, 561, 566 construction of, 561–565 Infeasibility, 272, 280 linear programming of, 272–274, 276 Infeasible decision alternatives, 11 Infeasible solutions, 19 Infinite calling populations, 696, 701 Influence diagrams, 104, 119–120, 134 Inputs for mathematical models, 9–10 Institute for Operations Research and the Management Sciences (INFORMS), 14, 18 Integer linear programming, 17, 482–483 defined, 482, 484, 509 Excel solutions for, 525–528 graphical and computer solutions, 485–489 LINGO solutions, 528–529 models, 484–485 sensitivity analysis, 508 Intensive care unit (ICU), 732 Interarrival times, 733 International Federation of Operational Research Societies (IFORS), 18 Intersection of events, 35–36, 51 Inventories, 624 cost of, 625 opportunity costs, 626 simulation, 727–732 Excel solutions for, 730–731 Inventory and production application, 448–451 Inventory models, 17, 624 backorders, 637–640 economic order quantity (EOQ) model, 625–633 assumptions of, 633 Excel solutions for, 632–633 how-much-to-order decision, 629–630 optimal order quantity, 670–671 quantity discounts for, 642–644 sensitivity analysis of, 631–632 when-to-order decision, 630–631 economic production lot size model, 634–637 economic production lot size, 637 optimal lot size formula, 671 total cost model, 635–637 expected loss (EL), 646–647 how-much-to-order decision, 629–630, 651 optimal lot size formula, 671 optimal order quantity, 670–671 order-quantity, reorder point model with probabilistic demand, 650–654, 657 how-much-to-order decision, 651 when-to-order decision, 652–654 periodic review model with probabilistic demand, 654–657 with planned shortages, 637–641 quantity discounts, 642–644 service level, 654 single period model with probabilistic demand, 644–649 total cost model, 635–637 when-to-order decision, 630–631, 652–654 Inventory planning, 658 Inventory policy simulations, 713–714 Inventory position, 630, 659 Inversion, matrix, 795–796 with Excel, 796 J Jeppesen Sanderson, 377–378 Joint probabilities, 39–40, 51, 134 branch probabilities, 131 K Kellogg Company, 384–385 Kendall, D.G., 691 Kendall notation for waiting line models, 691 Ketron Management Science, 507–508 Koopmans, Tjalling, 247 K out of n alternatives constraints, 506, 510 L Latest finish time, 591, 610 Latest start time, 589, 591, 610 Lead-time demand distribution, 651, 652, 659 Lead-time demands, 630–631, 633, 659 Lead times, 630, 633, 659 and periodic review systems, 657 Likelihood of an event, 28 Linear functions, 251, 279 Linear programming, 17, 250, 251, 279 alternative optimal solutions, 272 applications of, 246, 359 assignment problem, 438–439 constraints, 247 decision making, 246 decision variables, 319–325 Excel solutions for, 298–301 extreme points, 264–265 financial applications See Financial applications of linear programming general notation for, 276–278 graphical solutions, 251–263 infeasibility, 272–274, 276 integer See Integer linear programming lines, 260–261 LINGO solutions, 301–303 marketing applications See Marketing applications of linear programming mathematical models, 250–251 maximal flow problem, 444–448 maximization problem, 247–251 minimization problem, 267–272 network models, 420, 446, 451 objective function coefficients, 307–310 operations management See Operations management applications of linear programming optimal solutions, 264–265 optimization applications See Optimization applications production and inventory application, 448–451 profit lines, 257–258 right-hand sides, 310–315 sensitivity analysis, 305–307 decision variables, more than two, 319–325 objective function coefficients, 307–310 right-hand sides, 310–315 shortest-route problem, 440–444 slack variables, 262–263 transportation problem, 420–426 transshipment problem, 427–433 production and inventory application, 448–451 unbounded solutions, 274–276 Linear trends, 211–215 with Excel, 237–238, 239, 240 LINGO integer linear programming, 528–529 linear program solving with, 301–303 nonlinear optimization problems, 580–582 sensitivity analysis with, 353–354 Little, John D C., 687 Little’s flow equations, 687–688 Local optima, 557, 566 Location problem, 498, 509 0-1 variables, 498–500 Lot size, 634, 659 Lottery, 160, 179 LP Relaxation, 484, 509 boundary establishment, 488–489 graphical solution of, 486–487 906 Index M Machine repair problem, 698 Maintenance time scheduling, 603 Make-or-buy decision, 373–377 Management science (MS), Marathon Oil, 359 Marginal costs, 15, 19 Marginal probabilities, 40, 51 Marginal revenues, 15, 19 Marketing applications of linear programming, 360–365 marketing research, 363–365 media selection, 360–363 Marketing planning model, 359 Marketing research, 363–365 Market share analysis of, 774–781 competing for, 171–173 Markov chains with stationary transition probabilities, 773, 787 Markov decision processes, 781 Markov processes, 773, 780 accounts receivable analysis, 781–786 doubtful accounts allowance, 784–786 fundamental matrix, 783–784 doubtful accounts allowance, 784–786 fundamental matrix, 783–784 market share analysis, 774–781 Markov-process models, 17 Markowitz, Harry, 545, 551 Mathematical models, 7, 19, 248, 279 inputs, 9–10 for a linear program, 250–251 Mathematical programming models, 251 Matrices fundamental, 783, 787 Markov processes, 783–784 inversion of, 795–796 with Excel, 796 Markov processes, 783–784 notation, 793 operations of, 794–796 Maximal flow, 452 Maximal flow problem, 444–448 Maximax approach to decision making, 106 Maximin approach to decision making, 107 Maximization problems, 247–251 Maximums, 557, 566 M&D Chemicals, 267–272 general notation for, 276 MeadWestvaco Corporation, 246–247 Mean absolute error (MAE), 200, 223 Mean absolute percentage error (MAPE), 201, 223 Mean squared error (MSE), 201, 223 Media selection, 360–363 Memoryless properties, 781 Merrill Lynch, 13–14 Microsoft inventory models, 653–654 Microsoft Project, 594 Mine cave-in, 28–29 Minimax approach to decision making, 107, 134 Minimax regret approach, 107–109 Minimin approach to decision making, 106 Minimization problems, 267–272 Minimums, 557, 566 Mixed-integer linear programs, 482, 484, 509 general purpose, 504 Mixed strategy games, 174–178, 179 Model development, 7–10 Models, 7, 10, 19 breakeven analysis, 16 cost, revenue and profit, 14–15 integer linear programming, 484–485 quantitative analysis, 11–12 seasonal, 221–222 0-1 variables, 505–508 Moderate risk portfolios, 549–551 Money, utility of, 164 Monte Carlo simulations, 727 Morton International, 41 Most probable times, 610 Moving averages, 204–207, 223 CB Predictor, 242–243 Excel, 233–234, 235 weighted, 207–208 Multicriteria decision problems, 4, 19 Multiple choice constraints, 506–507, 510 Multiple-server model, 682–687, 694–696 Multiple-server waiting line, 682–683, 701 Multiplication, matrix, 794–795 Multiplication law, 42, 51 Multistage inventory planning, 658 Mutual funds, 545–551 index funds, 561, 566 Mutually exclusive, 103 Mutually exclusive constraints, 506–507, 510 Mutually exclusive events, 37–38, 51 vs independent events, 42 N Naïve forecasting method, 199–203 Nash, John, 178 Nationwide Car Rental, 648–649 Neiman Marcus inventory models, 645–648 Network flow problems, 420 Network graphs, 421–422 Network models linear programming, 420, 446, 451 maximal flow problems, 444–448 shortest-route problem, 440–444 See also Assignment problems; Supply chain models Networks, 420, 421, 452 New product development simulation, 713 Nodes, 104, 134 defined, 422, 452 project network, 587, 588 transshipment, 427 Nonintuitive shadow prices, 317–319 Nonlinear business processes, 531 Nonlinear optimization problems, 531, 566 applications, 552–561 Excel solutions for, 582–584 LINGO solutions, 580–582 Nonnegativity constraints, 250, 279 Nonstationary time series, 211 Normal probability distribution, 79–87, 90 project completion probabilities, 602–603 O Objective coefficient range, 310, 331 Objective function coefficient allowable decrease, 310, 331 Objective function coefficient allowable increase, 310, 331 Objective function coefficients, 307–310 Objective functions, 8, 19 data envelopment analysis (DEA), 537 defined, 249, 279 Office product demand forecasting, 198 Operating characteristics, 701 waiting line, 673 waiting line models, 680–681 multiple-server model, 683–687, 694–696 single-server model, 678–680, 692–693 Operations management applications of linear programming, 373–393 blending problems, 389–393 make-or-buy decision, 373–377 production scheduling, 377–384 workforce assignment, 384–389 Operations research (OR), 2, 18 Operations Research Society of Eastern Africa (ORSEA), 18 Operations Research Society of South Africa (ORSSA), 18 Opportunity costs, 626 Opportunity loss, 107, 134 Optimal lot size formula, 671 907 Index Optimal order quantity, 670–671 Optimal plastic production, 320 Optimal solutions, 11, 19 linear programming, 264–265 Optimistic approach to decision making, 106–107, 134 Optimistic times, 597, 610 Optimization applications, 531 asset allocation, 545–552 data envelopment analysis (DEA), 531–539 index fund construction, 561–565 nonlinear optimization, 552–561 portfolio models, 545–552 revenue management, 539–545 Optimizing production, inventory and distribution, 384–385 Ordering costs, 626, 628, 659 Order-quantity, reorder point model with probabilistic demand how-much-to-order decision, 651 inventory models, 650–654, 657 when-to-order decision, 652–654 Origin nodes, 427 Outcomes, experimental, 31–33, 64 P Parameters, 715, 747 Paths, 589, 609 Patient infections, 732 Payoff, 104–105, 134 Payoff tables, 104–105, 134 Perfect information, 112–113 Performance measures, 673 Periodic review inventory systems, 654, 660 Periodic review model with probabilistic demand, 654–657 PERT/CPM (performance evaluation and review technique/critical path method) activity identification, 587–588 critical path, 588–593 procedure, 594 project scheduling, 594–595 PERT (program evaluation and review technique), 586, 609 Pessimistic times, 597, 610 Pfizer, 726–727 Pharmaceutical demand levels, 726–727 Pharmaceutical product development, 102, 126 Pharmacia & Upjohn, 726–727 Planned shortages in inventory models, 637–641 Poisson probability distribution, 73–75, 90 and the exponential distribution, 89 waiting line models, 675, 678, 682, 701 Polaris missile project, 586 Portfolio models, 545–552 Portfolio selection, 366–369 Posterior probabilities, 43, 51 decision analysis, 119, 134 Postoptimality analysis, 305 See also Sensitivity analysis Preboard screening, 743 Priceline pricing with sensitivity analysis, 325 Prior probabilities, 43, 51, 118, 134 Probabilistic inputs, 713, 747 Probabilistic input values, generating simulation, 719–723 Probabilistic inventory models, 624, 629, 659 order-quantity, reorder point model with probabilistic demand, 650–654, 657 periodic review model with probabilistic demand, 654–657 single period model with probabilistic demand, 644–649 Probabilistic models, 10 Probabilities, 28, 50 Bayes’ theorem, 33, 43–47, 51 branch, 129–133 conditional, 38–41, 51 decision making, 109–113 of events, 33–34 experiments, 29–30 outcomes of, 31–33, 64 random variables, 64–65 sample space, 30, 34 Simpson’s paradox, 47–50, 51 in sports, 63 Probability density functions, 90 uniform distribution, 76–77 Probability distributions binomial, 69–73 continuous random variables, 76–78 discrete random variables, 65–67 expected values, 67–68 exponential, 87–89 normal, 79–87 Poisson, 73–75 standard deviation, 68–69 standard normal, 80–84 uniform, 76–78 variance, 68–69 Probability functions, 66, 90 Probability trees, 43 Probable times, 597, 610 Problem formulation, 103–106, 248, 279 Problem solving, 19 and decision making, 3–5 Procter & Gamble, 434 Product design and market share optimization problem, 500–504, 510 Production and inventory application, 448–451 Production scheduling, 377–384 Product sourcing heuristic, 434 Profit and volume models, 15 Profit lines, 257–258 Program evaluation and review technique (PERT), 586, 609 Project completion probabilities, 602–603 Project manager assignments, 439–440 Project network, 587–588, 609 Project scheduling, 586–622 completion time variability, 601–603 crashing activity times, 605–608 critical paths expected activity times, 588–593, 594 uncertain activity times, 599–601 expected activity times, 586–595 time-cost trade-offs, 604–609 crashing activity times, 605–608 uncertain activity times, 595–603 completion time variability, 601–603 critical path, 599–601 using PERT/CPM, 594–595 Project scheduling: PERT/CPM, 17 Proportionality in linear programming, 251 Pseudorandom numbers, 719 Pure strategies, 173, 179 Q Qualitative analysis, 5–6 Quality control in product testing, 41 Quantitative analysis, 7–14 data preparation, 10–11 and decision making, 5–7 implementation, 13 model development, 7–10 model solution, 11–12 report generation, 13 Quantity discounts, 642–644, 659 Queue, 673, 701 Queue discipline, 677 Queueing models, 17 voting machines, 700 Queueing theory, 673, 701 908 Index right-hand sides, 310–313 sensitivity analysis, 306–310 constraint coefficient changes, 316–317 decision variables, more than two, 320–321 right-hand sides, 310–313 shadow prices, 314 shadow prices, nonintuitive, 317–319 simultaneous changes, 315–316 shadow prices nonintuitive, 317–319 nonlinear optimization, 559–560 sensitivity analysis, 314 simultaneous changes, 315–316 unconstrained problem, 553–554 R Random numbers in simulations, 719–723 Random variables, 64–65, 90 continuous, 76–78 discrete, 64–69 Range of feasibility, 313, 331 Range of optimality, 310, 331 Reduced costs, 312, 331 Redundant constraints, 263, 280 Regression analysis, 211, 223 as forecasting method, 211–216 software for, 215 time series data used with, 216–222 Regret in decision making, 107 Relative frequency method of assigning probabilities, 32, 51 Relatively efficient, 539 Relevant costs, 314, 332 Reorder points, 630, 659 Repeated trials, 773 Replenishment levels, 624, 654, 728 Restoration capacity optimization, 448 Revenue and volume models, 15 Revenue management, 539–545 in baseball, 2–3 Right-hand sides, 310–315 allowable increases and decreases, 312–313, 331–332 Risk analysis, 113–114, 134, 715–717 defined, 715, 747 simulation, 715–727 Excel, 725–726 what-if analysis, 715–724 Risk avoiders, 161, 179 asset allocation for, 546–549 and risk takers, 165–170 Risk-neutral decision makers, 168–169, 170, 179 Risk profiles, 113, 125–128, 134 Risk takers, 179 and risk avoiders, 165–170 RMC, Inc computer solutions, 265–267 constrained problems, 554–557 constraint coefficient changes, 316–317 decision variables, more than two, 320–321 general notation for, 276 graphical solutions, 251–263 local and global optima, 557–559 maximization problem, 247–251 nonlinear optimization, 552–561 constrained problem, 554–557 local and global optima, 557–559 shadow prices, 559–560 unconstrained problem, 553–554 S Saddle point, 173, 179 Safety stocks, 653, 659 Sample information, 118–119, 134 efficiency of, 129 expected values, 128, 134 Sample points, 30, 50 Sample space, 30, 34, 50 San Francisco Giants revenue management, 2–3 SEAC (Standards Eastern Automatic Computer), 266 Seasonality, 216–222 models from monthly data, 221–222 with trend, 219–221 Excel, 240–241 without trend, 216–219 Excel, 238–240 Seasonal patterns, 194–196, 216–219, 223 time series patterns, 196–197 Seasonal time series patterns, 194–196 Seasongood & Mayer, 595 Selten, Reinhard, 178 Sensitivity analysis, 134, 305, 331 constraint coefficients, changes in, 316–317 decision analysis, 113, 114–118 decision variables, more than two, 319–325 economic order quantity (EOQ) model, 631–632 with Excel, 353–354, 355 integer linear programming, 508 limitations of, 315–319 linear programming, 305–307 decision variables, more than two, 319–325 objective function coefficients, 307–310 right-hand sides, 310–315 with LINGO, 353–354 objective function coefficients, 307–310 right-hand sides, 310–315 shadow prices, nonintuitive, 317–319 simultaneous changes, 315–316 Serpentine lines, 677 Service levels, 654, 728 Service rates, 676, 701 Service times, 676 Setup costs, 634–635, 659 Shadow prices, 311–312, 331 financial planning, 373 interpretation of, 314 nonintuitive, 317–319 nonlinear optimization, 559–560 portfolio selection, 369 Shortages, 637, 659 Shortest route, 452 Shortest-route problem, 440–444 Simon, Herbert A., Simple linear regression, 212–215 Simpson, Edward, 49 Simpson’s paradox, 47–50, 51 Simulation experiment, 713, 747 Simulations, 17, 713–715, 747 advantages of, 745 computer implementation, 744 with Crystal Ball, 727, 744, 761–767 customer arrival times, 733–734 customer service times, 734–735 disadvantages of, 745–746 inventory, 727–732 Excel solutions for, 730–731 random numbers, 719–723 risk analysis, 715–727 Excel, 725–726 what-if analysis, 715–724 verification and validation, 745 waiting line, 733–744 customer arrival times, 733–734 customer service times, 734–735 Excel, 738–739, 742 what-if analysis, 715–724 Simultaneous changes, 315–316 Single-criterion decision problems, 4, 19 Single lines in models, 687 Single period inventory model, 659 Single period model with probabilistic demand, 644–649 Single server waiting line, 674, 701 model of, 678–682, 691–693 Slack, 593, 610 Slack variables, 262–263, 280 Smoothing constant, 208, 223 Software See Excel; LINGO Solar energy investment decisions, 370 Sports probabilities, 63 909 Index Spreadsheet simulation add-ins, 727, 744 Standard deviations, 68–69, 90 Standard form, 263, 280 Standard normal probability distribution, 80–84, 90 Standards Eastern Automatic Computer (SEAC), 266 State of the system, 774, 787 State probabilities, 776, 787 States of nature, 103, 134 Static simulation models, 733, 747 Stationary time series, 190–191, 223 Steady-state operation, 677, 701, 787 Steady-state probabilities, 779 Stochastic models, 10, 19 Stock-outs, 637, 659 Subjective method of assigning probabilities, 32–33, 51 Subjective probabilities, 29 Success of a trial, 69 Sunk costs, 314, 332 Supply chain design, 493–498 Supply chain design problem, 496, 509 Supply chain models, 420–434 freight car assignment optimization, 427 transportation problem, 420–423 freight car assignment optimization, 427 variations on, 423–426 transshipment problem, 427–433 variations on, 433 Supply chains, 420, 452 Surplus variables, 270–271, 280 T Tabular approach to Bayes’ theorem, 46–47 Taylor, Frederic W., Tea production and distribution, 331 Timber harvesting linear programming, 246–247 Time-cost trade-offs, 604–609 Time series, 190, 222 Time series method, 189 Time series patterns, 190–198 cyclical pattern, 197 horizontal pattern, 190–192 seasonal pattern, 194–196, 216–219 and trend patterns, 196–197, 219–221 selecting, for forecasting, 197–198 trend patterns, 192–194 and seasonal patterns, 196–197, 219–221 See also Forecasting Time series plot, 190, 222 Tornado diagrams, 118 Total cost models, 635–637 Traffic flow simulations, 714 Transient periods, 677, 701 Transition probabilities, 774–775, 787 Transportation problems, 420–423, 452 assignment problem, 435–440 Excel solutions for, 474–475 feasible solutions, 423 freight car assignment optimization, 427 linear programming model, 426 transshipment problem, 427–433 variations on, 423–426 Transposition, matrix, 794 Transshipment nodes, 427 Transshipment problems, 427–433, 452 Excel solutions for, 475–478 linear programming model, 433 production and inventory application, 448–451 variations on, 433 TreePlan for decision analysis, 150–156 Trend patterns, 192–194, 223 and seasonal patterns, 196–197, 219–221 Trend projections, 235–238, 239, 240 Trend time series pattern, 192–194 Trial-and-error solution approach, 11–12 Trials, 69 Trials of the process, 774, 787 Two-person, zero sum games, 170–171, 179 market share, competing for, 171–173 mixed strategy games, 174–178 pure strategy, identifying, 173 solving, 178 Type-I service level, 654 U Unbounded solutions, 274–276, 280 Uncertain activity times, 595–603 Uncontrollable inputs, 9–10, 19 Unemployment rates, 49–50 Uniform probability distribution, 76–78, 90 Union of events, 35, 51 Union Pacific, 427 U.S Air Force project scheduling, 603 U.S Government Accountability Office (GAO), 773 U.S Navy, fuel conservation by the, 279 U.S presidential election voting machines, 700 Utility, 158–160, 179 and decision making, 160–165 of money, 164 risk avoiders and risk takers, 165–170 Utility function for money, 167–168, 179 Utilization factor, 679 V Validation, 745, 748 Valley Metal Container, 484–485 Vancouver International Airport, 743 Variable annuities, 552 Variable costs, 14, 19 Variance, 68–69, 90 activity times, 597 binomial probability distribution, 73 Venn diagrams, 34, 51 Verifications, 745, 748 Volunteer scheduling, 505 Voting machines, 700 W Waiting line models, 17, 673–674 arrivals, distribution of, 674–676 constant service time, 693 economic analysis of, 689–690 Excel solutions for, 681–682, 699 with finite calling populations, 696–699 Excel solutions for, 699 general relationships for, 687–688 Kendall notation for, 691 manager’s use of, 680 multiple-server model, 682–687, 694–696 operating characteristics, 683–687, 694–696 and single lines, 687 operating characteristics improvements, 680–681 multiple-server model, 683–687, 694–696 single-server model, 678–680, 692–693 queue discipline, 677 service times, distribution of, 676 single lines, 687 single-server model, 678–682, 691–693 constant service time, 693 manager’s use of, 680 operating characteristic improvement, 680–681 operating characteristics, 678–680, 692–693 single server waiting line, 674 steady-state operation, 677 structure of, 674–677 Waiting lines in governmental agencies, 690 Waiting lines simulations, 714 Warehouse order-picking efficiency, 746–747 Weighted moving averages, 207–208, 223 910 Index What-if analysis, 715–724, 747 When-to-order decision, 630–631, 652–654 Whole Foods, 677 Worker disability claims, 111 Workforce assignments, 384–389 World load, 305 Worst-case scenarios, 716, 747 Z 0-1 integer linear programs, 482, 484, 509 aluminum can production, 484–485 0-1 variables capital budgeting, 490–491 customer order allocation model, 507–508 fixed cost, 491–493 location problem, 498–500 modeling flexibility, 505–508 product design and market share optimization problem, 500–504 supply chain design, 493–498 volunteer scheduling, 505 Quantitative Methods for Business 12e WEBfiles Chapter Excel Files Nowlin.xlsx Chapter Excel Files Bicycle.xlsx Carlson Sales.xlsx Cholesterol.xlsx CountySales.xlsx ExchangeRate.xlsx Gasoline Revised.xlsx Masters.xlsx Pollution.xlsx SouthShore.xlsx TVSales.xlsx Umbrella.xlsx Vintage.xlsx Chapter LINGO Files Bluegrass.lng Electronic.lng ModifiedRMC.lng RMC.lng Chapter Excel Files Bollinger.xlsx Grand.xlsx Hewlitt.xlsx Janders.xlsx Market.xlsx McCormick.xlsx McCormickMod.xlsx Relax.xlsx Welte.xlsx LINGO Files Cincinnati.lng Contois.lng Foster.lng Fowle.lng Gorman.lng ModifiedRyan.lng Ryan.lng Excel Files Eastborne.xlsx Ice-Cold.xlsx Martin-Beck.xlsx Ohio-Trust.xlsx RMC-Setup.xlsx Salem.xlsx LINGO Files RMC.lng M&D.lng Excel Files Bluegrass.xlsx Electronic.xlsx ModifiedRMC.xlsx RMC.xlsx Excel Files Cincinnati.xlsx Contois.xlsx 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