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Frederick S Hillier Stanford University Mark S Hillier University of Washington Cases developed by Karl Schmedders University of Zurich Molly Stephens Quinn, Emanuel, Urquhart & Sullivan, LLP INTRODUCTION TO MANAGEMENT SCIENCE: A MODELING AND CASE STUDIES APPROACH WITH SPREADSHEETS, FIFTH EDITION Published by McGraw-Hill/Irwin, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY, 10020 Copyright © 2014 by The McGraw-Hill Companies, Inc All rights reserved Printed in the United States of America Previous editions © 2011, 2008, 2003 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper QVR/QVR ISBN MHID 978-0-07-802406-1 0-07-802406-4 Senior Vice President, Products & Markets: Kurt L Strand Vice President, Content Production & Technology Services: Kimberly Meriwether David Managing Director: Douglas Reiner Senior Brand Manager: Thomas Hayward Executive Director of Development: Ann Torbert Managing Developmental Editor: Christina Kouvelis Senior Developmental Editor: Wanda J Zeman Senior Marketing Manager: Heather Kazakoff Director, Content Production: Terri Schiesl Project Manager: Mary Jane Lampe Buyer: Nichole Birkenholz Cover Designer: Studio Montage, St Louis, MO Cover Image: Imagewerks/Getty Images Media Project Manager: Prashanthi Nadipalli Typeface: 10/12 Times Roman Compositor: Laserwords Private Limited Printer: Quad/Graphics All credits appearing on page or at the end of the book are considered to be an extension of the copyright page Library of Congress Cataloging-in-Publication Data Hillier, Frederick S Introduction to management science : modeling and case studies approach with spreadsheets / Frederick S Hillier, Stanford University, Mark S Hillier, University of Washington ; cases developed by Karl Schmedders, University of Zurich, Molly Stephens, Quinn, Emanuel, Urquhart, Sullivan LLP.—Fifth edition pages cm ISBN 978-0-07-802406-1 (alk paper) Management science Operations research—Data processing Electronic spreadsheets I Hillier, Mark S II Title T56.H55 2014 005.54—dc23 2012035364 The Internet addresses listed in the text were accurate at the time of publication The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill, and McGraw-Hill does not guarantee the accuracy of the information presented at these sites www.mhhe.com To the memory of Christine Phillips Hillier a beloved wife and daughter-in-law Gerald J Lieberman an admired mentor and one of the true giants of our field About the Authors Frederick S Hillier is professor emeritus of operations research at Stanford University Dr Hillier is especially known for his classic, award-winning text, Introduction to Operations Research, co-authored with the late Gerald J Lieberman, which has been translated into well over a dozen languages and is currently in its 9th edition The 6th edition won honorable mention for the 1995 Lanchester Prize (best English-language publication of any kind in the field) and Dr Hillier also was awarded the 2004 INFORMS Expository Writing Award for the 8th edition His other books include The Evaluation of Risky Interrelated Investments, Queueing Tables and Graphs, Introduction to Stochastic Models in Operations Research, and Introduction to Mathematical Programming He received his BS in industrial engineering and doctorate specializing in operations research and management science from Stanford University The winner of many awards in high school and college for writing, mathematics, debate, and music, he ranked first in his undergraduate engineering class and was awarded three national fellowships (National Science Foundation, Tau Beta Pi, and Danforth) for graduate study After receiving his PhD degree, he joined the faculty of Stanford University, where he earned tenure at the age of 28 and the rank of full professor at 32 Dr Hillier’s research has extended into a variety of areas, including integer programming, queueing theory and its application, statistical quality control, and production and operations management He also has won a major prize for research in capital budgeting Twice elected a national officer of professional societies, he has served in many important professional and editorial capacities For example, he served The Institute of Management Sciences as vice president for meetings, chairman of the publications committee, associate editor of Management Science, and co-general chairman of an international conference in Japan He also is a Fellow of the Institute for Operations Research and the Management Sciences (INFORMS) He currently is continuing to serve as the founding series editor for a prominent book series, the International Series in Operations Research and Management Science, for Springer Science 1 Business Media He has had visiting appointments at Cornell University, the Graduate School of Industrial Administration of Carnegie-Mellon University, the Technical University of Denmark, the University of Canterbury (New Zealand), and the Judge Institute of Management Studies at the University of Cambridge (England) Mark S Hillier, son of Fred Hillier, is associate professor of quantitative methods at the Michael G Foster School of Business at the University of Washington Dr Hillier received his BS in engineering (plus a concentration in computer science) from Swarthmore College He then received his MS with distinction in operations research and PhD in industrial engineering and engineering management from Stanford University As an undergraduate, he won the McCabe Award for ranking first in his engineering class, won election to Phi Beta Kappa based on his work in mathematics, set school records on the men’s swim team, and was awarded two national fellowships (National Science Foundation and Tau Beta Pi) for graduate study During that time, he also developed a comprehensive software tutorial package, OR Courseware, for the Hillier–Lieberman textbook, Introduction to Operations Research As a graduate student, he taught a PhD-level seminar in operations management at Stanford and won a national prize for work based on his PhD dissertation At the University of Washington, he currently teaches courses in management science and spreadsheet modeling He has won several MBA teaching awards for the core course in management science and his elective course in spreadsheet modeling, as well as a universitywide teaching award for his work in teaching undergraduate classes in operations management He was chosen by MBA students in 2007 as the winner of the prestigious PACCAR award for Teacher of the Year (reputed to provide the largest monetary award for MBA teaching in the nation) He also has been awarded an appointment to the Evert McCabe Endowed Faculty Fellowship His research interests include issues in component commonality, inventory, manufacturing, and the design of production systems A paper by Dr Hillier on component commonality won an award for best paper of 2000–2001 in IIE Transactions He currently is principal investigator on a grant from the Bill and Melinda Gates Foundation to lead student research projects that apply spreadsheet modeling to various issues in global health being studied by the foundation vi About the Case Writers Karl Schmedders is professor of quantitative business administration at the University of Zurich in Switzerland and a visiting associate professor at the Kellogg School of Management of Northwestern University His research interests include management science, financial economics, and computational economics and finance In 2003, a paper by Dr Schmedders received a nomination for the Smith-Breeden Prize for the best paper in the Journal of Finance He received his PhD in operations research from Stanford University, where he taught both undergraduate and graduate classes in management science, including a case studies course He received several teaching awards at Stanford, including the universitywide Walter J Gores Teaching Award After a post-doc at the Hoover Institution, a think tank on the Stanford campus, he became assistant professor of managerial economics and decision sciences at the Kellogg School He was promoted to associate professor in 2001 and received tenure in 2005 In 2008 he joined the University of Zurich, where he currently teaches courses in management science, spreadsheet modeling, and computational economics and finance At Kellogg he received several teaching awards, including the L G Lavengood Professor of the Year Award Most recently he won the best professor award of the Kellogg School’s European EMBA program (2008, 2009, and 2011) and its Miami EMBA program (2011) Molly Stephens is a partner in the Los Angeles office of Quinn, Emanuel, Urquhart & Sullivan, LLP She graduated from Stanford with a BS in industrial engineering and an MS in operations research Ms Stephens taught public speaking in Stanford’s School of Engineering and served as a teaching assistant for a case studies course in management science As a teaching assistant, she analyzed management science problems encountered in the real world and transformed these into classroom case studies Her research was rewarded when she won an undergraduate research grant from Stanford to continue her work and was invited to speak at INFORMS to present her conclusions regarding successful classroom case studies Following graduation, Ms Stephens worked at Andersen Consulting as a systems integrator, experiencing real cases from the inside, before resuming her graduate studies to earn a JD degree with honors from the University of Texas School of Law at Austin She is a partner in the largest law firm in the United States devoted solely to business litigation, where her practice focuses on complex financial and securities litigation vii Preface We have long been concerned that traditional management science textbooks have not taken the best approach in introducing business students to this exciting field Our goal when initially developing this book during the late 1990s was to break out of the old mold and present new and innovative ways of teaching management science more effectively We have been gratified by the favorable response to our efforts Many reviewers and other users of the first four editions of the book have expressed appreciation for its various distinctive features, as well as for its clear presentation at just the right level for their business students Our goal for this fifth edition has been to build on the strengths of the first four editions Co-author Mark Hillier has won several schoolwide teaching awards for his spreadsheet modeling and management science courses at the University of Washington while using the first four editions, and this experience has led to many improvements in the current edition We also incorporated many user comments and suggestions Throughout this process, we took painstaking care to enhance the quality of the preceding edition while maintaining the distinctive orientation of the book This distinctive orientation is one that closely follows the recommendations in the 1996 report of the operating subcommittee of the INFORMS Business School Education Task Force, including the following extract There is clear evidence that there must be a major change in the character of the (introductory management science) course in this environment There is little patience with courses centered on algorithms Instead, the demand is for courses that focus on business situations, include prominent non-mathematical issues, use spreadsheets, and involve model formulation and assessment more than model structuring Such a course requires new teaching materials This book is designed to provide the teaching materials for such a course In line with the recommendations of this task force, we believe that a modern introductory management science textbook should have three key elements As summarized in the subtitle of this book, these elements are a modeling and case studies approach with spreadsheets SPREADSHEETS The modern approach to the teaching of management science clearly is to use spreadsheets as a primary medium of instruction Both business students and managers now live with spreadsheets, so they provide a comfortable and enjoyable learning environment Modern spreadsheet software, including Microsoft Excel used in this book, now can be used to real management science For student-scale models (which include many practical real-world models), spreadsheets are a much better way of implementing management science models than traditional algebraic solvers This means that the algebraic curtain that was so prevalent in traditional management science courses and textbooks now can be lifted However, with the new enthusiasm for spreadsheets, there is a danger of going overboard Spreadsheets are not the only useful tool for performing management science analyses Occasional modest use of algebraic and graphical analyses still have their place and we would be doing a disservice to the students by not developing their skills in these areas when appropriate Furthermore, the book should not be mainly a spreadsheet cookbook that focuses largely on spreadsheet mechanics Spreadsheets are a means to an end, not an end in themselves A MODELING APPROACH This brings us to the second key feature of the book, a modeling approach Model formulation lies at the heart of management science methodology Therefore, we heavily emphasize the art of model formulation, the role of a model, and the analysis of model results We primarily (but not exclusively) use a spreadsheet format rather than algebra for formulating and presenting a model viii Preface ix Some instructors have many years of experience in teaching modeling in terms of formulating algebraic models (or what the INFORMS Task Force called “model structuring”) Some of these instructors feel that students should their modeling in this way and then transfer the model to a spreadsheet simply to use the Excel Solver to solve the model We disagree with this approach Our experience (and the experience reported by many others) is that most business students find it more natural and comfortable to their modeling directly in a spreadsheet Furthermore, by using the best spreadsheet modeling techniques (as presented in this edition), formulating a spreadsheet model tends to be considerably more efficient and transparent than formulating an algebraic model Another benefit is that the spreadsheet model includes all the relationships that can be expressed in an algebraic form and we often will summarize the model in this format as well Another break from tradition in this book (and several contemporary textbooks) is to virtually ignore the algorithms that are used to solve the models We feel that there is no good reason why typical business students should learn the details of algorithms executed by computers Within the time constraints of a one-term management science course, there are far more important lessons to be learned Therefore, the focus in this book is on what we believe are these far more important lessons High on this list is the art of modeling managerial problems on a spreadsheet Formulating a spreadsheet model of a real problem typically involves much more than designing the spreadsheet and entering the data Therefore, we work through the process step by step: understand the unstructured problem, verbally develop some structure for the problem, gather the data, express the relationships in quantitative terms, and then lay out the spreadsheet model The structured approach highlights the typical components of the model (the data, the decisions to be made, the constraints, and the measure of performance) and the different types of spreadsheet cells used for each Consequently, the emphasis is on the modeling rather than spreadsheet mechanics A CASE STUDIES APPROACH However, all this still would be quite sterile if we simply presented a long series of brief examples with their spreadsheet formulations This leads to the third key feature of this book—a case studies approach In addition to examples, nearly every chapter includes one or two case studies patterned after actual applications to convey the whole process of applying management science In a few instances, the entire chapter revolves around a case study By drawing the student into the story, we have designed each case study to bring that chapter’s technique to life in a context that vividly illustrates the relevance of the technique for aiding managerial decision making This storytelling, case-centered approach should make the material more enjoyable and stimulating while also conveying the practical considerations that are key factors in applying management science We have been pleased to have several reviewers of the first four editions express particular appreciation for our case study approach Even though this approach has received little use in other management science textbooks, we feel that it is a real key to preparing students for the practical application of management science in all its aspects Some of the reviewers have highlighted the effectiveness of the dialogue/scenario enactment approach used in some of the case studies Although unconventional, this approach provides a way of demonstrating the process of managerial decision making with the help of management science It also enables previewing some key concepts in the language of management Every chapter also contains full-fledged cases following the problems at the end of the chapter These cases usually continue to employ a stimulating storytelling approach, so they can be assigned as interesting and challenging projects Most of these cases were developed jointly by two talented case writers, Karl Schmedders (a faculty member at the University of Zurich in Switzerland) and Molly Stephens (formerly a management science consultant with Andersen Consulting) The authors also have added some cases, including several shorter ones In addition, the University of Western Ontario Ivey School of Business (the second-largest producer of teaching cases in the world) has specially selected cases from their case collection that match the chapters in this textbook These cases are available on 604 Appendix A Tips for Using Microsoft Excel for Modeling FIGURE A.3 The Format Cells dialog box right justified, printed vertically or horizontally, etc.), the font, the borders, the patterns, and the protection If a cell displays ####, this means that the column width is not wide enough to show the contents of the cell To change column widths or row heights, click and drag the vertical or horizontal lines between the column or row labels Double-clicking on the vertical line between column labels will make the column just wide enough to show the entire contents of every cell in the column Appendix B Partial Answers to Selected Problems CHAPTER 2.6 d Fraction of 1st 5 0.667, fraction of 2nd 5 0.667. Profit 5 $6,000 2.13 b x1 5 13, x2 5 5. Profit 5 $31 CHAPTER 3.3 3.6 3.12 3.17 c d d b 3.333 of Activity 1, 3.333 of Activity Profit 5 $166.67 26 of Product 1, 54.76 of Product 2, 20 of Product Profit 5 $2,904.76 1.14 kg of corn, 2.43 kg of alfalfa Cost 5 $2.42 Cost 5 $410,000 Shipment Quantities Customer Customer Customer 300 0 200 100 300 Factory Factory 3.19 c $60,000 in Investment A (year 1), $84,000 in Investment A (year 3), $117,600 in Investment D (year 5) Total accumulation in year 6 5 $152,880 3.22 a Profit 5 $13,330 Cargo Placement Front Center Back Cargo Cargo Cargo Cargo 7.333 4.667 4.167 8.333 10 0 CHAPTER 4.2 d end tables, 40 coffee tables, 30 dining room tables Profit 5 $10,600 4.4 e 19% participation in Project A, 0% participation in Project B, and 100% participation in Project C Ending Balance 5 $59.5 million 605 606 Appendix B Partial Answers to Selected Problems 4.9 d FT (8am–4pm), FT (12pm–8pm), FT (4pm–midnight), PT (8am–12pm), PT (12pm–4pm), PT (4pm–8pm), PT (8pm–midnight) Total cost per day 5 $1,728 CHAPTER 5.1 e Allowable range for unit profit from producing toys: $2.50 to $5.00 Allowable range for unit profit from producing subassemblies: 2$3.00 to 2$1.50 5.4 f (Part a) Optimal solution does not change (within allowable increase of $10) (Part b) Optimal solution does change (outside of allowable decrease of $5) (Part c) By the 100% rule for simultaneous changes in the objective function, the optimal solution may or may not change C8AM: $160 S $165 % of allowable increase 100 a 165 160 b 50% 10 C4PM: $180 S $170 % of allowable decrease 100 a 180 170 b 200% Sum 250% 5.11 a Produce 2,000 toys and 1,000 sets of subassemblies Profit 5 $3,500 b The shadow price for subassembly A is $0.50, which is the maximum premium that the company should be willing to pay 5.15 a The total expected number of exposures could be increased by 3,000 for each additional $1,000 added to the advertising budget b This remains valid for increases of up to $250,000 e By the 100% rule for simultaneous changes in right-hand sides, the shadow prices are still valid Using units of thousands of dollars, CA: $4,000 S $4,100 % of allowable increase 100 a 4,100 4,000 b 40% 250 CP: $1,000 S $1,100 % of allowable increase 100 a 1,100 1,000 b 22% 450 Sum 62% CHAPTER 6.2 6.5 6.9 6.15 b S1-D1, 10 S1-D2, 30 S1-D3, 30 S2-D1, 30 S2-D2, S2-D3 Total cost 5 $580 c $2,187,000 Maximum flow 5 15 b Replace after year Total cost 5 $29,000 CHAPTER 7.3 b Marketing and dishwashing by Eve, cooking and laundry by Steven Total time 5 18.4 hours 7.8 Optimal path 5 OADT Total distance 5 10 miles Appendix B Partial Answers to Selected Problems 607 CHAPTER 8.7 c Invest $46,667 in Stock and $3,333 in Stock for $13,000 expected profit Invest $33,333 in Stock and $16,667 in Stock for $15,000 expected profit 8.11 d Dorwyn should produce window and door CHAPTER 9.4 a d 9.7 b c 9.12 a b 9.16 c 9.21 c f 9.22 a c 9.23 9.26 9.30 9.35 Speculative investment Counter-cyclical investment A3 A2 A1 $18 EVPI 5 $3,000 The credit-rating organization should not be used Choose to build computers (expected payoff is $27 million) They should build when p ≤ 0.722 and sell when p > 0.722 EVPI 5 $7.5 million P(Sell 10,000 | Predict Sell 10,000) 5 0.667 P(Sell 100,000 | Predict Sell 100,000) 5 0.667 a The optimal policy is to no market research and build the computers c $800,000 f, g Leland University should hire William If he predicts a winning season, then they should hold the campaign If he predicts a losing season, then they should not hold the campaign a Choose to introduce the new product (expected payoff is $12.5 million) b $7.5 million c The optimal policy is not to test but to introduce the new product g Both charts indicate that the expected profit is sensitive to both parameters, but is somewhat more sensitive to changes in the profit if successful than to changes in the loss if unsuccessful a Choose not to buy insurance (expected payoff is $249,840) b Choose to buy insurance (expected utility is 499.82) CHAPTER 10 10.1 10.3 10.9 10.13 10.17 10.19 10.29 10.35 a 39 b 26 c 36 MAD 5 15 2,091 When a 5 0.1, forecast 5 2,072 552 b MAD 5 5.18 c MAD 5 3 d MAD 5 3.93 62 percent b y 5 410 1 17.6x d 604 608 Appendix B Partial Answers to Selected Problems CHAPTER 11 11.3 11.8 11.12 11.15 11.18 11.23 11.28 11.31 11.35 a True b False c True a L 5 2 b Lq 5 0.375 c W 5 30 minutes, Wq 5 5.625 minutes a 96.9% of the time b L 5 0.333 g Two members Lq is unchanged and Wq is reduced by half a L 5 3 d TC (status quo) 5 $85/hour TC (proposal) 5 $73/hour a 0.211 hours c Approximately 3.43 minutes c 0.4 d 7.2 hours Jim should operate cash registers Expected cost per hour 5 $80.59 CHAPTER 12 12.1 12.5 b Let the numbers 0.0000 to 0.5999 correspond to strikes and the numbers 0.6000 to 0.9999 correspond to balls The random observations for pitches are 0.3039 5 strike,  0.7914 5 ball, 0.8543 5 ball, 0.6902 5 ball, 0.3004 5 strike, 0.0383 5 strike a Here is a sample replication Summary of Results: Win? (1 Yes, No) Number of Tosses Simulated Tosses Toss Results Die Die Sum 2 2 4 6 7 8 Win? 0 NA NA NA NA Lose? Continue? 0 NA NA NA NA Yes Yes No No No No No 12.10 a Let the numbers 0.0000 to 0.3999 correspond to a minor repair and 0.4000 to 0.9999 correspond to a major repair The average repair time is then (1.224 1 0.9 50 1 1.610)/3 5 1.26 hours 12.17 b The average waiting time should be approximately day c The average waiting time should be approximately 0.33 days CHAPTER 13 a Min Extreme distribution (Mode 5 170.3, Scale 5 50.9, Shift 5 320.0) a The mean project completion time should be approximately 33 months c Activities B and J have the greatest impact on the variability in the project completion time 13.15 a Mean profit should be around $107, with about a 96.5% chance of making at least $0 13.3 13.7 Index A Abbink, E., 247 Absolute references, 28, 139, 603 Action Adventures (case study), 596–597 Advertising-mix problems campaign planning in, 47 cost–benefit–trade-off problems and, 82–83 management considerations in, 88–90 mathematical model in spreadsheet in, 50–51 as mixed problem, 88–90 problem analysis for, 66–71 problem identification in, 65–66 Profit & Gambit Co., 46–51 resource allocation and, 71–72 Solver applied to, 49–50 spreadsheet formulation in, 91–93 spreadsheet model formulation for, 47–49 Super Grain Corp., 65–71 Aiding Allies (case study), 224–227 Airline scheduling (case study), 229–230 Alden, H., 162 Alden, J M., 449 Algebraic formulation, in product-mix problem, 31–32 Algebraic models, 32–33 Algorithms genetic, 299 for network optimization problems, 194 for Nonlinear Solver, 276 for quadratic programming, 280 special-purpose, 202 Allen, S J., 136 Allowable range for objective function coefficient, 158–159, 174 for the right-hand side, 172 sensitivity report to find, 9–161 Altschuler, S., 553 Analytics, Andrews, B H., 388 Angelis, D P., 162 Animation, of computer simulations, 516, 517 Application-oriented simulators, 516 Application vignettes Bank Hapoalim Group, 284 Canadian Pacific Railway, 210 Compañia Sud Americana de Vapores (CSAV), 419 ConocoPhillips, 363 Continental Airlines, 252 Deutsche Post DHL, 298 Federal Aviation Administration, 504 Federal Express, 12 function of, 16 Gassco, 206 General Motors Corporation, 449 Hewlett-Packard, 197 KeyCorp, 459 list of, 13, 14 L.L Bean, 388 Merrill Lynch, 553 Midwest Independent Transmission Operator, Inc., 241 Netherlands Railways, 247 Pacific Lumber Company, 162 Proctor & Gamble, 97 Samsung Electronics, 50 Sasol, 515 Swift & Company, 24 Taco Bell Corporation, 398 United Airlines, 83 Waste Management, Inc., 234 Welch’s, Inc., 136 Westinghouse Science and Technology Center, 346 Workers’ Compensation Board of British Columbia, 331 Arcs, 197, 210 Argüello, M., 252 Arrivals, in queueing system, 436 Assigning Art (case study), 261–263 Assigning Students to Schools (case study), 119–120, 193, 266 Assignment problems characteristics of, 100, 102 example of, 99–100 explanation of, 99 fixed requirements and, 88 as minimum-cost flow problems, 194, 201 spreadsheet model for, 100, 101 Assignments, 99 Auditing tools (Excel), 143 Automobile assembly (case study), 60 Averaging forecasting method explanation of, 385, 386, 412 formula for, 421 use of, 396–398, 410 Avriel, M., 284 B Bank Hapoalim Group, 284 Barnum, M P., 459 Bayes’ decision rule explanation of, 328–330 views of, 326 Bayes’ theorem, 343 Benefit constraints advertising-mix problems and, 82 cost–benefit–trade-off problems and, 82, 86 explanation of, 88 Bennett, J., 553 Berkey, B G., 346 Bernoulli distribution, 567–568, 587 Bidding for construction project See Reliable Construction Co (case study) Big M Company example, 95–99 Binary decision variables, 232 Binary integer programming (BIP) case study of, 233–239 for crew scheduling, 246–250 explanation of, 232–233 mixed, 232, 241, 250–254 for project selection, 239–342 pure, 232, 250 for setup costs for initiating production, 250–254 for site selection, 241–245 Binary integer programming (BIP) model, 236–237 Binary variables explanation of, 232, 587 formulation with, 240–241, 243–244, 247–248, 251–252 Binomial distribution, 558, 560, 568 BIP See Binary integer programming (BIP) BIP model, 236–237 BMZ Company (case study), 202–204, 206–207 Bottom-up forecasting approach, 418 Bowen, D A., 459 Brainy Business (case study), 380–381 609 610 Index Branches, 330 Break-even analysis complete mathematical model of problem in, 9–10 expressing problem mathematically in, incorporating break-even point into spreadsheet model in, 10–11 problem analysis and, 8–9 spreadsheet model in, 6–8 what-if analysis of mathematical model in, 10 Break-even point explanation of, incorporated into spreadsheet model, 10–11 Brennan, M., 504 Broadcasting the Olympic Games (case study), 230–231, 266 Burns, L D., 449 Business analytics, Byrne, J E., 83 C Caliente City problem, 243–245 California Manufacturing Co problem, 233–239 Call center case study See Computer Club Warehouse (case study) Canadian Pacific Railway (CPR), 210 Capacity, 197 Capacity Concerns (case study), 115–116 Capital budgeting, resource-allocation problem, 75–80 Carlson, B., 241 Carlson, W., 12 Case, R., 210 Case studies lists, 14–15 value of, 16 Cash flow management problem See Everglades Golden Years Company Cash Flow Problem (case study) Causal forecasting in case study, 417–418 examples of, 413 explanation of, 413 linear regression and, 414–416 in spreadsheets, 414 use of, 413, 416–417 Cells (Excel) entering data, text and formulas into, 601–602 explanation of, 599 filling, 602–603 formulation of, 603–604 moving or copying, 602 range names for, 603 relative and absolute references to, 603 results, 529, 539, 544, 588 selection of, 601 statistic, 529–531, 539, 544 uncertain variable cells, 528, 529, 538, 539, 542–543, 550 Central-tendency distributions, 563, 564 Changing cells, 26 Coefficient in the objective function See Objective function coefficient Coin-flipping game, 490–494 See also Computer simulation Commercial service systems, 440–441 Compañia Sud Americana de Vapores (CSAV), 419 Computer Club Warehouse (case study), 386–409, 417 See also Forecasting methods Computer simulation accuracy of, 534 animation for, 516 coin-flipping game as example of, 490–494 corrective maintenance vs preventive maintenance decision as example of, 494–500 explanation of, 489 for financial risk analysis, 552–556 generating random observations from probability distribution and, 498, 501, 503–504 optimizing with RSPE’s Solver and, 583–590 overview of, 488 performance measures estimation and, 507 process of, 505–507 role of, 489–490 software selection for, 516 use of, 489–490 Computer simulation (case study) analysis of, 508–514 assumptions in, 511–512 background information for, 501 building blocks of simulation model for stochastic system in, 504–505 data collection for, 503 decision factors in, 501–502 financial factors in, 508 generating random observations from probability distributions in, 503–504 performance measurement estimation in, 507 process used in, 505–508 simulation model validity in, 510–512 Computer simulation models discrete-event, 516 explanation of, 504 for stochastic system, 504–505 testing accuracy of, 516 testing validity of, 510–512, 516–517 Computer simulation process data collection simulation model formulation as step in, 515 plan simulations to be performed as step in, 517 problem formulation and study plan as step in, 515 recommendations presentation following, 517 simulation model accuracy check as step in, 516 simulation model validity test as step in, 516–517 simulation runs and results analysis as step in, 517 software selection and computer program construction as step in, 516 Computer simulation with RSPE applications for, 535 bidding for construction project using, 536–540 case study of, 526–536 cash flow management using, 546–551 choosing correct distribution for, 562–575 decision making with parameter analysis reports and trend charts using, 575–583 financial risk analysis using, 552–556 optimizing with, 583–590 overview of, 525 project management using, 540–546 revenue management using, 557–562 Conditional probability, 341 Confidence intervals, 509, 517, 534 ConocoPhillips, 363 Conservation of flow, 197 Constant service times, 439 Constraint boundary equation, 35 Constraint boundary line, 35 Constraints in advertising-mix problems, 68 benefit, 82, 86, 88 cost–benefit–trade-off problems and, 82, 86 Index effect of simultaneous changes in, 175–178 effect of single changes in, 169–174 explanation of, 9–10, 30 fixed-requirement, 88, 90, 95, 99 functional, 32, 88, 169 nonnegativity, 32, 99 resource, 80, 88 Consumer market survey, 418 Continental Airlines, 252 Contingent decisions, 236 See also Yes-or-no decisions Continuation of the Super Grain (case study), 317–318 Continuous distribution, 498, 501, 562, 572–575 Controlling Air Pollution (case study), 189–191 Copeland, D., 12 Corrective maintenance vs preventive maintenance example, 494–498 Cost–benefit–trade-off problems advertising mix and, 82–83 explanation of, 81–82 formulation procedure for, 87 nonlinear version of, 283 personnel scheduling and, 83–87 Cost graphs, use of, 271–272 Costy, T., 449 Crew scheduling problem, binary integer programming for, 246–250 Cunningham, S M., 388 Curve fitting method (Excel), 273 Custom distributions, 570–572 Customers See also Queueing models in queueing system, 434, 450 in system, 450 Cutting Cafeteria Costs (case study), 61 D Data for computer simulation studies, 503, 515 consolidation of, 333–334 for cost–benefit–trade-off problems, 82 organizing and identifying, 136–137 separated from formulas, 138 for spreadsheet models, 135–138 Data cells, 26, 137–138 Data tables, 335–338, 353–354 Decision analysis applications for, 365–366 case study of, 323–325 decision criteria and, 325–330 decision trees for, 330–338, 344–350 function of, 323 information needs and, 338–340 overview of, 322–323 probability updates and, 340–344 for problems with sequence of decisions, 344–354 sensitivity analysis and, 333–338, 351–354 utilities to reflect value of payoffs and, 354–365 Decision conferencing, 365–366 Decision criteria background of, 325–326 Bayes’ decision rule and, 328–330 maximax, 326 maximin, 326–327 maximum likelihood, 327 Decision making with parameter analysis reports and trend charts, 575–583 with probabilities, 328–330 risk tolerance and, 362 role of management science in, without probabilities, 326–327 Decision nodes, 330, 345 Decisions analyzing problems with sequence of, 344–354 contingent, 236 interrelationships between, 235–236 role of management science in, Decision-support system, Decision trees to analyze problem with sequence of decisions, 344–350 to analyze utility problems, 360–362 construction of, 345–346 explanation of, 330, 345 RSPE, 350, 601 sensitivity analysis with, 333–338 spreadsheet software for, 330–333 Decision variables, 8, 32 Decreasing marginal returns explanation of, 270–272 nonlinear programming with, 277–286 separable programming for, 287 Decreasing marginal utility for money, 355 Delphi method, 418 Demand nodes, 197, 200 Dependent variables, 413 Descriptive analytics, Destination dummy, 216 explanation of, 212, 213 Deutsche Post DHL, 298 Discontinuities, 271 611 Discrete distribution, 562–563 Discrete-event simulation modeling, 516 Distributions See also Probability distributions Bernoulli, 567–568, 587 binomial, 558, 560, 568 central tendency, 563, 564 characteristics of available, 562–563 continuous, 498, 501, 562, 572–575 custom, 570–572 discrete, 562–563 exponential, 436–437, 449, 450, 454, 565 frequency, 552 geometric, 568–570 integer uniform, 528–529, 565 lognormal, 564, 565 negative binomial, 568–570 normal, 501, 553, 557, 558, 563, 564, 586, 587 Poisson, 566, 567 time-series forecasting methods and, 410–411 triangular, 537, 544, 563–565 uniform, 553, 565, 566 Distributions menu, 528 Distribution Unlimited Co problem, 195–196 See also Minimum-cost flow problems D/M/s model, 439 Downs, B., 24 Dummy destination, 216 Dupit Corp Problem (case study), 445–448, 467–468 Dyer, J S., 363 Dynamic problems, 126 E Economic analysis, of number of servers to provide, 473–476 Eidesen, B H., 206 Epstein, R., 419 Equivalent lottery method, 356, 359 Estimated trend, 404 Estimated trend formula, 421 Etzenhouser, M J., 162 Event nodes, 330, 345 Event-scheduling approach, 516 Everglades Golden Years Company Cash Flow Problem (case study) background of, 125–126, 547 computer simulation and, 546–551 debugging and, 141–144 modeling with spreadsheets and, 126–135, 140–141 612 Index Evolutionary Solver advantages and disadvantages of, 305–306 applied to traveling salesman problem, 302–305 explanation of, 268, 299 for portfolio selection, 300–302 Excel (Microsoft) auditing tools on, 143 cells, 601–604 curve fitting method on, 273 Evolutionary Solver, 298 generating random numbers with, 491–493 guidelines for use of, 17 LN() function on, 504 for minimum-cost flow problems, 198–199 Nonlinear Solver, 268, 274–276, 297, 298 RAND() function on, 490, 495 ROUND function, 558 SUMPRODUCT function, 30, 31, 70, 100, 138, 267, 273 toggle function on, 141, 142 VLOOKUP function on, 495–496 window, 599 workbooks, 599–600 worksheets, 599–601 Expected monetary value (EMV) criterion, 329 Expected number of customers, 450 Expected payoff (EP) Bayes’ decision rule and, 354, 355 explanation of, 328, 347–348 Expected utilities, 360 Expected value of perfect information, 337–339 performance measures and, 442–443 of sample information, 348–350 Exponential distribution explanation of, 436, 565 for interarrival times, 436–437, 449, 450, 454 Exponential smoothing forecasting method explanation of, 385, 400, 412 formula for, 421 with trend, 385, 402–408, 412, 421 use of, 400–402, 404 Exponential utility function explanation of, 362 used with RSPE, 362–365 F Fabrics and Fall Fashions (case study), 116–118 Fallis, J., 210 Farm Management (case study), 191–193 Fattedad, S O., 331 Feasible solution explanation of, 32 for linear programming problems, 33, 35 Feasible solutions property, 198 Federal Aviation Administration (FAA), 504 Federal Express, 12 Finagling the Forecasts (case study), 429–432 Finance case studies, 15 Financial risk analysis explanation of, 552 spreadsheet model to apply computer simulation to, 553–556 Think-Big Development Co case, 552–553 Finite queue, 437 Fioole, P.-J., 247 Fischer, M., 298 Fischetti, M., 247 Fixed-requirement constraints advertising-mix problems and, 90 explanation of, 88 transportation problems and, 95, 99 Fixed-requirements problems, 88 Fletcher, L R., 162 Fodstad, B H., 206 Forecasting error, 389 Forecasting errors, 386 Forecasting methods applications for, 384 averaging, 385, 412 case study of, 386–409 causal, 413–417 comparison of, 411–412 exponential smoothing, 385, 412 exponential smoothing with trend, 385, 412 goal of, 410 judgmental, 384, 418 last-value, 385, 412 linear regression, 385–386 moving-average, 385, 412 overview of, 385–386 recommendations for, 412–413 statistical, 384, 418 time-series, 391–412 Formulas absolute or relative reference, 28 forecasting, 421 for M/G/1 model, 455 for M/M/1 model, 450–451 nonlinear, 267, 268, 273–294 separating data from, 138 in spreadsheets, 267, 268 use of relative and absolute references for related, 139 Freddie the Newsboy’s Problem (case study) computer simulation and Solver applied to, 584–586 conclusions regarding, 534–535 description of, 526 parameter analysis report for, 576–580 RSPE applied to, 527–534 simulation results accuracy in, 534 spreadsheet model for, 526–527 Frequency distribution, 552 Freundt, T., 298 Frontline Systems, 16, 42 Functional constraints, 32, 88 Fundamental property of utility functions, 356 G Gassco, 206 General Motors Corporation (GM), 449 General-purpose simulation language, 516 Generation, 299 Genetic algorithms, 299 Geometric distribution, 568–570 Giehl, W., 298 GI/M/s model, 439 Global maximum, 275–277 Goferbroke Company (case study), 323–325 Graphical Linear Programming and Sensitivity Analysis, 160 Graphical method explanation of, 33 to solve two-variable problems, 33–37 summary of, 37 uses for, 37, 38 Grass-roots forecasting approach, 418 Group decision support systems, 365–366 H Hellemo, L., 206 Herr Cutter’s Barber Shop (case study) See Computer simulation (case study) Hewlett-Packard (HP), 197 Holloran, T J., 83 Holman, S P., 162 Howard, K., 504 Index How-much decisions, 232 Hueter, J., 398 Huisman, D., 247 Hutton, R D., 449 I Identifying features in cost–benefit–trade-off problems, 87 explanation of, 64 Increasing marginal utility for money, 355 Independent variables, 413 Infeasible solution, 32 Infinite queue, 437, 438 Influence diagram, 365 Information technology (IT), Institute for Operational Research and the Management Sciences (INFORMS), 12, 13 Integer programming problems, 75 Integer programming model, 30 Integer solutions property, 198 Integer uniform distribution, 528–529, 565 Interactive Management Science Modules, 17, 37, 160, 409 Interarrival times in computer simulation model, 503, 513 exponential distribution for, 436–437, 449, 450, 454 in preemptive priorities queueing model, 464 symbols for, 439 Interfaces, 3, 12, 13 Internal service systems, 441 International Federation of Operational Research Societies (IFORS), 12 International Investments (case study), 319–321 Inverse transformation method, 498 Ireland, P., 210 J Jackson, C A., 449 Joint probabilities, 341 Judgmental forecasting methods, 384, 418 Jury of executive opinion, 418 K Kang, J., 50 Keeping Time (case study), 20–21 KeyCorp, 459 Kim, B.-I., 234 Kim, D S., 449 Kim, S., 234 613 Local maximum, 275 Lognormal distribution, 564, 565 King, P V., 346 Kohls, K A., 449 Kotha, S K., 459 Krass, B., 234 Kroon, L., 247 Kuehn, J., 210 M L L.L Bean, Inc., 388 Labe, R., 553 Lack-of-memory property, 437 Last-value forecasting method explanation of, 385, 394–396, 412 formula for, 421 Latest trend formula, 421 Leachman, R C., 50 Lehky, M., 504 Length, 212 Liao, B., 553 Lin, Y., 50 Linear formulas, 267, 268 Linear models, 267 Linear programming applications for, 46–47, 51–52, 64, 84 assumptions of, 70 function of, 150 nonlinear vs., 269 overview of, 22 proportionality assumption of, 30, 269–270 Linear programming models analysis of, 102–103 characteristics on spreadsheets, 29–30 development of, 25–31 enrichment of, 103 formulation of, 26–31, 102 for product-mix problem, 25–31 separable programing model as, 289 terminology for, 32 for transportation problems, 96–97 validation of, 102 Linear regression application of, 417 explanation of, 414–416 forecasting with, 385–386 Linear regression line, 414, 421 Linear Solver, 306–307 Links, 210 Little, John D C., 443 Little’s formula, 443–444, 450 Littletown Fire Department Problem, 209–212 MAD See Mean absolute deviation (MAD) Maintenance problem See Computer simulation Management information systems, Management science applications for, 12–14 break-even analysis to illustration, 6–11 as decision making aid, as discipline, 2–3 explanation of, impact of, 12–17 overview of, 1–2 professional journals for, 3, 12 quantitative factors considered in, scientific approach of, 3–5 Management Science, Management science teams, Managerial decision making See Decision making Manager’s opinion method, 418 Marginal returns, decreasing, 270–287 Marketing case studies, 15 Marketing costs, nonlinear, 292–296 Maróti, G., 247 Mason, R O., 12 Mathematical models for advertising-mix problem, 50–51 application of, for break-even analysis, 9–10 function of, 4–5 in spreadsheet, 31–33 tests for, what-if analysis of, 10 Maxima global, 275–277 local, 275 Maximax criterion, 326 Maximin criterion, 326–327 Maximum flow problems applications for, 207 assumptions of, 205–206 case study of, 202–204, 206–207 as minimum-cost flow problems, 201 multiple supply and demand points and, 206–207 solving very large, 208–209 Maximum likelihood criterion, 327 McAllister, W J., 346 McGowan, S M., 252 McKenney, J L., 12 614 Index M/D/s model, 439, 462 Mean absolute deviation (MAD) explanation of, 386, 389–390 exponential smoothing forecasting and, 402, 407 formula for, 421 Mean arrival rate, 436 Mean service rate, 438, 461, 465 Mean square error (MSE) explanation of, 386, 390 formula for, 421 minimum value of, 415 time-series forecasting and, 407 Meiri, R., 284 Meketon, M., 210 Merrill Lynch, 553 Method of least squares, 415 Meyer, M., 515 M/G/1 model applications of, 456–457, 510, 511 assumptions of, 454 explanation of, 439, 510 formulas for, 455 insights provided by, 455–456 Microsoft Excel See Excel (Microsoft) Midwest Independent Transmission Operator, Inc., 241 Minimizing total cost, 212–214 Minimizing total time, 214–217 Minimum acceptable level of benefits, 82 Minimum-cost flow problems applications for, 200–201 assumptions of, 197–198 example of, 195–196 Excel to formulate and solve, 198–199 feasible solutions property and, 198 general characteristics of, 197–198 integer solutions property and, 198 method solve large, 199–200 network simplex method for, 200 types of, 194, 201–202 Mixed BIP application of, 241 explanation of, 232 for setup costs for initiating production, 250–254 Mixed problems advertising-mix problem, 88–90 explanation of, 88 spreadsheet formulation for, 91–95 M/M/1 model applications of, 451–454 assumptions of, 450, 464 explanation of, 439, 449 formulas for, 450–451 software for, 451 M/M/2 model, 439 M/M/s model, 439, 458, 459 Model enrichment, 103 Modeling, use of Excel for, 599–604 Models, 4, 15 See also Mathematical models Model validation, 102 Money See Utility function for money Money in Motion (case study), 227–229 Morahan, G T., 363 Moving-average forecasting method explanation of, 385, 398, 412 formula for, 421 use of, 398–400 MS Courseware, 16 MSE See Mean square error (MSE) Multiple-server queueing models application of, 459–461 assumptions of, 458 explanation of, 438, 457–458, 472 Multiple-server system, 438 Mutation, 299 Mutually exclusive alternatives, 235–236 N Naive method, 396 Natural logarithms, 504 Negative binomial distribution, 568–570 Netherlands Railways, 247 Network models for maximum flow problem, 204 for minimum-cost flow problems, 196 Network optimization problems maximum flow problems as, 202–209 minimum-cost flow problems as, 195–202 overview of, 194 shortest path problems as, 209–218 Networks, 194, 197 Network simplex method, 200, 202 New Frontiers (case study), 118–119 Newsvendor problem, 526 See also Freddie the Newsboy’s Problem (case study) Next-event time-advance procedure, 505, 516 Nigam, R., 553 Nodes, 197, 330 Nonlinear formulas construction of, 273–274 in spreadsheets, 267, 268 Nonlinear marketing costs, 292–296 Nonlinear programming application of, 269 challenges of, 269–277 with decreasing marginal returns, 277–286 difficult problems related to, 297–298 evolutionary solver and genetic algorithms and, 299–306 linear vs., 269 portfolio selection with, 283–286 quadratic programming as, 280, 285 separable programming and, 287–296 spreadsheet models for, 280–283 use of, 268 use of RSPE for, 306–310 Nonlinear programming models constructing nonlinear formulas for, 273–274 explanation of, 268 methods to solve, 274–277 nonproportional relationships in, 269–272 Nonlinear Solver explanation of, 268, 274–275 for nonlinear programming problems, 297, 298 Nonnegativity constraints, 32, 99 Nonpreemptive priorities, 463 Nonpreemptive priorities queueing model application of, 464–478 explanation of, 464 Nonproportional relationships explanation of, 270 nonlinear programming and, 269–272 Normal distribution, 501, 553, 557, 558, 564, 586, 587 Number of customers in queue, 443 Number of customers in system, 443 O Objective cell, 28 Objective function, 10, 32 Objective function coefficients allowable range for, 158–159 effect of changes in one, 155–161 effect of simultaneous changes in, 161–168 Objective function line, 36–37 Oh, J., 553 Oiesen, R., 504 100 percent rule for changes in right-hand side, 178 for simultaneous changes in objective function coefficient, 168 Operations Research, Operations research (OR), See also Management science Optimal solutions explanation of, 32, 35, 150 with graphical method, 33, 37 Index parameter analysis and trend charts and, 575, 583–584 what-if analysis and, 152 Origin, 212, 213 Output cells, 27–28 Overtime costs, 287–295 Owen, J H., 449 P Pacfic Lumber Company (PALCO), 162 Parameter analysis reports decision making with, 575–583 to determine effect of making changes to parameter in constraint, 171–172, 175–178 sensitivity analysis using, 156–159 two-way, 162–165 Parameter cells defining decision variable as, 576–578 explanation of, 157, 158 Parameters explanation of, 10, 32 of model, 151 sensitivity, 151 Payoff decision criteria and, 328, 347–348 explanation of, 325 Payoff table, 325 Pedersen, B., 206 Perdue, R K., 346 Peretz, A., 284 Perfect information, expected value of, 337–339 Performance measures for advertising-mix problems, 68–69 for computer simulation problem, 507 for cost–benefit–trade-off problem, 86 of probabilities as, 444–445 for queueing systems, 442–445 Personnel scheduling cost–benefit–trade-off analysis and, 83–87 United Airlines and, 83 PERT three-estimates approach, 541, 542 Piecewise linear, 271 Planning Planers (case study), 523–524 Point estimates, 509, 517 Point of indifference, 358, 359 Poisson distribution, 566, 567 Popov, A., Jr., 234 Population, 299 Portfolio selection to beat market, 299–301 Evolutionary Solver for, 300–302 nonlinear program for, 283–286 Posterior probabilities, 340–345 Predictive analytics, Preemptive priorities, 463 Preemptive priorities queueing model, 463–464 Prescriptive analytics, Preventive maintenance vs corrective maintenance example, 494–498 Pricing under Pressure (case study), 597–598 Priority classes, 463 Priority queueing models application of, 464–468 explanation of, 463 nonpreemptive, 463–464 preemptive, 463–464 Prior probabilities Bayes’ decision rule and, 328 explanation of, 325, 326, 345 Pri-Zan, H., 284 Probabilities conditional, 341 decision making with, 327–330 decision making without, 326–327 joint, 341 as measures of performance, 444–445 posterior, 340–345 prior, 325, 326, 328, 345 unconditional, 341 Probability density function, 563 Probability distributions in coin-flipping game, 492–493 in computer simulation, 498, 501, 503–504, 507 in corrective vs preventive maintenance study, 494 problems caused by shifting, 410–411 random observations from, 498, 501 steady-state, 444–445 triangular, 537, 544 Probability tree diagram, 341, 342 Procter & Gamble (P & G), 97 Production rates, 26, 28–29 Product-mix problems See also Wyndor Glass Co Product Mix Problem (case study) background of, 23 formulated on spreadsheet, 25–32 graphical method and, 33–37 management discussion and issues for, 23–24 management science team work on, 24–25 overtime costs and, 287–295 resource allocation and, 72–73 on Risk Solver Platform for Education, 42–46 615 separable programming and, 287–296 use of Solver for, 38–42 what-if analysis and, 151–155 Professional journals, 3, 12 Profit & Gambit Co advertising-mix problem, 46–51, 82–83 See also Advertising-mix problems Profit graphs, use of, 271–272 Programming, 22 Project Pickings (case study), 121–123 Project selection problem, binary integer programming for, 239–241 Proportionality assumption, of linear programming, 30 Proportional relationships, 269 Prudent Provisions for Pensions (case study), 148–149 Pure BIP, 232, 250 Puterman, M L., 331 Q Quadratic programming explanation of, 280 for portfolio selection, 285 Queue capacity, 437 Queue discipline, 438 Queueing models arrivals and, 436 assumptions of, 440 basic queueing system and, 434–435 example of, 435–436 exponential distribution of interarrival times and, 436–437 labels for, 439 multiple-server, 457–461, 472 nonpreemptive priorities, 464–478 overview of, 433–434 preemptive priorities, 463–464 priority, 463–468 single-server, 448–457 Queueing Quandary (case study), 485–486 Queueing simulator, 509, 510, 513 Queueing systems case study of, 445–448 commercial services, 440–441 design of, 469–473 examples of, 440–442 explanation of, 434–435 internal service, 441 measures of performance for, 442–445 server decisions for, 473–476 service and, 438 service-time distributions and, 438–439 transportation service, 441–442 616 Index Queueing theory, 433, 448 Queues explanation of, 433, 434 finite, 437 infinite, 437, 438 nature of, 437–438 R Random arrivals, 436, 454 Random numbers explanation of, 490 generation of, 491–492 Random observations, from probability distribution, 498, 501 Random variables, 410, 445 Range names for Excel cells, 603 explanation of, 6, 26, 138–139 Reclaiming Solid Wastes (case study), 120–121 Reducing In-Process Inventory (case study), 486–487, 524 References, relative and absolute, 28, 139, 603 Regression equation, 415 Relative references, 28, 139, 603 Reliable Construction Co (case study) background of, 536–537 computer simulation for, 540, 542–545 parameter analysis report for, 580–581 project management issues in, 540–542 sensitivity charts and, 545–546 spreadsheet model for applying computer simulation to, 537–539 Resource-allocation problem advertising mix and, 71–72 capital budgeting as, 75–80 characteristics of, 72 explanation of, 71 formulation procedure for, 80–81 product mix and, 72–73 TBA Airlines problem and, 73–75 Resource constraints, 80, 88 Results cell, 529, 539, 544, 588 Revenue management explanation of, 557 overbooking problem and, 557–562 Risk, determining attitude toward, 357–359 Risk analysis, 552 See also Financial risk analysis Risk averse, 355 Risk neutral, 355, 360 Risk profile, 552 Risk seekers, 355 Risk Solver Platform for Education (RSPE) See also Computer simulation with RSPE; Solver to analyze decision trees, 330–333, 360–362 to analyze models and choose solving method, 306–310 decision tree tool, 350, 601 Excel worksheets with, 601 explanation of, 16, 42 to generate random values from probability distributions, 504 optimizing with computer simulation and, 583–590 parameter analysis report generated by, 157 product-mix problem on, 42–46 Solver tool and, 583–590 use of, 162–165, 171–172 Rømo, F., 206 RSPE See Computer simulation with RSPE; Risk Solver Platform for Education (RSPE) RSPE Solver, 583–590 S Sahoo, S., 234 Salesforce composite method, 418 Sample average, 410, 534 Samsung Electronics, 50 Sasol, 515 Savvy Stock Selection (case study), 318–319 Schrijver, A., 247 Schuster, E W., 136 Scientific method explanation of, 3–5 steps in, 4–5 Seasonal factor explanation of, 391–392 formula for, 421 Seasonally adjusted time series explanation of, 392–394 formula for, 421 use of, 413 Self, M., 24 Selling Soap (case study), 188–189 Sellmore Company problem, 99–102 Sensitive parameters, 151 Sensitivity analysis See also What-if analysis binary integer programming and, 238 Data Table use for, 353–354 with decision trees, 333–338 explanation of, 152 to find allowable range, 159–161 parameter analysis report for, 156–159 for problems with sequence of decisions, 351–354 spreadsheets for, 155–156 Sensitivity chart, 545–546 Sensitivity reports to find allowable range, 159–161 gleaning additional information from, 165–167, 176–178 Separable programming explanation of, 287 nonlinear marketing costs and, 292–295 overtime costs and, 287–295 smooth profit graphs and, 291–292 Servers, queueing systems and, 434 Service cost, 473 Service times constant, 439 distributions for, 438–439, 455 exponential distribution for, 450, 464 M/G/1 model and, 454 in queueing systems, 438 symbols for, 439 Set covering constraint, 244 Set covering problem, 244 Setup costs, mixed BIP and, 250–254 Shadow price, 172 Shipping Wood to Market (case study), 114–115 Shortest path problems applications for, 212 assumptions of, 212 example of, 209–212 minimizing total cost in, 212–214 minimizing total time in, 214–217 Simplex method, 199 Simulation, 489 See also Computer simulation Simulation clock, 505 Simulation models, 504 See also Computer simulation models Single-server queueing models explanation of, 448–449 M/M/1, 449–454 Single-server system, 438 Sink, 205 Site selection, binary integer programming for, 241–245 Smart Steering Support (case study), 382–383 Smoothing constant, 400 Smooth profit graphs, 291–292 Index Solutions, for linear programming models, 32 Solver See also Excel (Microsoft); Risk Solver Platform for Education (RSPE) for advertising-mix problem, 49–50 applications for, 38, 42, 306 for assignment problems, 100, 102 for BIP programming, 237 computer simulation and, 583–590 Evolutionary, 268, 299–306 explanation of, 16 gaining access to, 38 guidelines for use of, 139–140 linear, 306–307 nonlinear, 268, 274–275, 297, 298 nonlinear programming models and, 295, 296 product-mix problem on, 38–42 for transportation problems, 98 worksheets used with, 600–601 Song, C., 252 Source, 205 Southwestern Airways problem, 246–250 Special-purpose algorithms, 202 Spreadsheet analysis, illustration of, 6–11 Spreadsheet modeling procedure analysis as element of, 132–135 expanding and testing full-scale model of, 131–132 explanation of, 126–127 hand calculations as step in, 128–129 sketching out spreadsheet as element of, 129–130 starting with small version of spreadsheet as element of, 130, 131 testing small version as element of, 131 visualizing where you want to finish as, 127–128 Spreadsheet models for advertising-mix problems, 47–49, 67, 69 for assignment problems, 100, 101 binary integer programming, 237, 242, 245, 249, 253 for break-even analysis, 6–8 for cash flow problems, 125–135 for computer simulations, 491, 496, 499, 500, 506, 510, 511, 513 for computer simulations with RSPE, 526–527, 535, 538, 543, 548, 549, 554, 559, 573, 587 for cost–benefit–trade-off problems, 85 example of poor formulation of, 140–141 explanation of, guidelines for producing good, 135–141 incorporating break-even point into, 10–11 linear programming, 29–30 for maximum flow problems, 208 M/G/1 model, 456, 471 for minimum-cost flow problems, 199 for mixed problems, 91–95 M/M/1 model, 452 M/M/s model, 460, 461, 470 for nonlinear programming, 280–283 for nonpreemptive priorities, 466 overview of, 124–125 for portfolio selection, 300, 301, 303–305 procedure to debug, 141–144 process for, 126–135 for product-mix problems, 25–31 for sensitivity analysis, 351–352 sensitivity analysis using, 155–156 for shortest path problems, 211, 215, 217 for transportation problems, 97–99 for what-if analysis, 169–171 Spreadsheet software See also Excel; Solver applications for, 1–2 for computer simulation studies, 516 for decision trees, 330–333 Stable time series, 411 Staffing a Call Center (case study), 62 State of the system, 505 Statistical forecasting methods See also Forecasting methods explanation of, 384 judgmental methods vs., 384, 418 Statistic cell explanation of, 529–530 procedure to define, 530–531 in simulation model, 539, 544 Statistics table, 531–532, 540, 545 Steady-state condition, 443 Steady-state probability distribution, 444–445 Steenbeck, A., 247 Stochastic system explanation of, 489 simulation model for, 504–505 Stocking Sets (case study), 263–265 Sud, V P., 504 SUMPRODUCT function, 30, 31, 70, 100, 138, 267, 273, 290, 328 617 Super Grain Corp advertising-mix (case study), 65–71, 88–93 Supply nodes, 197 Swart, W., 398 Swift & Company, 24 T Taco Bell Corporation, 398 Tanino, M., 504 Tazer Corp problem, 239–241, 586–590 Tech reps, 445, 448 Think-Big Development Co., 552–556 Time series explanation of, 390 stable, 411 unstable, 411–412 Time-series forecasting methods averaging, 396–398 comparison of, 411–413 explanation of, 390, 393–394 exponential smoothing, 400–402 exponential smoothing with trend, 402–408 goal of, 410 last-value, 394–396 moving-average, 398–400 seasonal effects and, 391–392 seasonally adjusted, 392–394 shifting distributions and, 410–411 software for, 409 Toggle function (Excel), 141, 142 Tomasgard, A., 206 Total cost minimization, 212–214 Total profit, 26, 28, 42 Total time minimization, 214–217 Transcontinental Airlines problem overbooking and, 557–562 parameter analysis report and trend chart for, 582–583 Transportation problems explanation of, 95 fixed requirements and, 88 formulated in linear programming terms, 96–97 as minimum-cost flow problems, 194, 201 Procter & Gamble and, 97 spreadsheet model of, 97–99 Transportation service systems, 441–442 Transshipment nodes, 197 Transshipment problems, as minimumcost flow problems, 201 Traveling salesman problem applying Evolutionary Solver to, 302–305 explanation of, 302 618 Index Trend estimated, 404 explanation of, 402 exponential smoothing with, 402–408 formulas for, 421 Trend charts application of, 579–583 explanation of, 575, 578 Trend line, 402, 404 Trend smoothing constant, 405 Trials, 526, 560 Triangular distribution, 537, 544, 563–565 Turnquist, M A., 449 25 percent rule, 388 Two-way parameter analysis report, 162–165 Utility functions decision trees and, 360–362 explanation of, 357 exponential, 362–365 fundamental property of, 356 Utilization factor multiple-server queueing models and, 457 for preemptive priorities queueing model, 464 single-server queueing models and, 448–449 V Validity, of simulation models, 516–517 Vander Veen, D J., 449 Van Dyke, C., 210 W U Uncertain variable cells, 528, 529, 538, 539, 542–543, 550 Unconditional probabilities, 341 Undirected arc, 210n Uniform distribution, 553, 565, 566 United Airlines, 83 University Toys and the Business Professor Action Figures (case study), 379–380 Unstable time series, 411–412 Urbanovich, E., 331 Utility function for money construction of, 359–360 explanation of, 355–357 Waiting cost, 473, 474 Waiting time in queue, 443, 447, 451 Waiting time in system, 443, 450 Walls, M R., 363 Ward, J., 197 Waste Management, Inc., 234 Welch’s, Inc., 136 Westinghouse Science and Technology Center, 346 Wetherly, J., 504 What-if analysis See also Sensitivity analysis benefits of, 151–152 change in one objective function coefficient and, 155–161 explanation of, 10, 150 of mathematical models, 10 for product-mix problem, 153–155 simultaneous change in constraints and, 175–178 simultaneous change in objective function coefficients and, 161–169 single change in constraints and, 169–174 What-if questions, 150 White, A., 252 Who Wants to Be a Millionaire? (case study), 379 Workbook (Excel), 599–600 Workers’ Compensation Board (WCB) of British Columbia, 331 Worksheets (Excel) explanation of, 599 use of, 600–601 Wyndor Glass Co Product Mix Problem (case study), 23–46, 72–73, 136, 137, 151–156, 162–165, 250–254, 278–283, 287–296 See also Product-mix problems Y Ybema, R., 247 Yes-or-no decisions binary decision variables for, 235 as contingent decisions, 236 explanation of, 232 for site selection, 242 Young, E E., 331 Yu, G., 252 ... Dramatic advances in computerized data capture, processing power, data transmission, and storage capabilities are enabling organizations to integrate their various databases into massive data... SCIENCE Hillier and Hillier, Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets, Fifth Edition Stevenson and Ozgur, Introduction to Management Science with. . .Introduction to Management Science A Modeling and Case Studies Approach with Spreadsheets The McGraw-Hill/Irwin Series Operations and Decision Sciences OPERATIONS MANAGEMENT Beckman and Rosenfield,