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Solve problem 12 of Chapter 7(Page 259. 7-12)  need solver !!! Rev. Confirming Pages Introduction to Management Science A Modeling and Case Studies Approach with Spreadsheets hil24064_fm_i-xx.indd ihil24064_fm_i-xx.indd i 05/12/12 2:18 PM05/12/12 2:18 PM Rev. Confirming Pages The McGraw-Hill/Irwin Series Operations and Decision Sciences OPERATIONS MANAGEMENT Beckman and Rosenfield, Operations, Strategy: Competing in the 21st Century, First Edition Benton, Purchasing and Supply Chain Management, Second Edition Bowersox, Closs, Cooper, and Bowersox Supply Chain Logistics Management, Fourth Edition Brown and Hyer, Managing Projects: A Team-Based Approach, First Edition Burt, Petcavage, and Pinkerton, Supply Management, Eighth Edition Cachon and Terwiesch, Matching Supply with Demand: An Intro- duction to Operations Management, Third Edition Cooper and Schindler, Business Research Methods, Eleventh Edition Finch, Interactive Models for Operations and Supply Chain Management, First Edition Fitzsimmons and Fitzsimmons, Service Management: Operations, Strategy, Information Technology, Seventh Edition Gehrlein, Operations Management Cases, First Edition Harrison and Samson, Technology Management, First Edition Hayen, SAP R/3 Enterprise Software: An Introduction, First Edition Hill, Manufacturing Strategy: Text & Cases, Third Edition Hopp, Supply Chain Science, First Edition Hopp and Spearman, Factory Physics, Third Edition Jacobs, Berry, Whybark, and Vollmann, Manufacturing Planning & Control for Supply Chain Management, Sixth Edition Jacobs and Chase, Operations and Supply Management: The Core, Third Edition Jacobs and Chase, Operations and Supply Management, Fourteenth Edition Jacobs and Whybark, Why ERP?, First Edition Larson and Gray, Project Management: The Managerial Process, Fifth Edition Leenders, Johnson, Flynn, and Fearon, Purchasing and Supply Management, Thirteenth Edition Nahmias, Production and Operations Analysis, Sixth Edition Olson, Introduction to Information Systems Proj- ect Management, Second Edition Schroeder, Goldstein, and Rungtusanatham, Operations Management: Contemporary Concepts and Cases, Sixth Edition Seppanen, Kumar, and Chandra, Process Analysis and Improvement, First Edition Simchi-Levi, Kaminsky, and Simchi-Levi, Designing and Managing the Supply Chain: Concepts, Strategies, Case Studies, Third Edition Sterman, Business Dynamics: Systems Thinking and Modeling for Complex World, First Edition Stevenson, Operations Management, Eleventh Edition Swink, Melnyk, Cooper, and Hartley, Managing Operations Across the Supply Chain, Second Edition Thomke, Managing Product and Service Development: Text and Cases, First Edition Ulrich and Eppinger, Product Design and Development, Fourth Edition Zipkin, Foundations of Inventory Management, First Edition QUANTITATIVE METHODS AND MANAGEMENT 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 Spreadsheets, First Edition hil24064_fm_i-xx.indd iihil24064_fm_i-xx.indd ii 05/12/12 2:18 PM05/12/12 2:18 PM Rev. Confirming Pages Introduction to Management Science A Modeling and Case Studies Approach with Spreadsheets Fifth Edition 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 hil24064_fm_i-xx.indd iiihil24064_fm_i-xx.indd iii 05/12/12 2:18 PM05/12/12 2:18 PM Rev. Confirming Pages 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. 1 2 3 4 5 6 7 8 9 0 QVR/QVR 0 9 8 7 6 5 4 3 ISBN 978-0-07-802406-1 MHID 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) 1. Management science. 2. Operations research—Data processing. 3. 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 hil24064_fm_i-xx.indd ivhil24064_fm_i-xx.indd iv 06/12/12 2:28 PM06/12/12 2:28 PM Rev. Confirming Pages 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 hil24064_fm_i-xx.indd vhil24064_fm_i-xx.indd v 05/12/12 2:18 PM05/12/12 2:18 PM Rev. Confirming Pages vi 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 men- tion 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 Introduc- tion 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 fel- lowships (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 interna- tional 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 Man- agement Science, for Springer Science  1  Business Media. He has had visiting appointments at Cornell University, the Graduate School of Industrial Administration of Carnegie-Mellon Uni- versity, 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 engi- neering 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 gradu- ate 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 Wash- ington, 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. hil24064_fm_i-xx.indd vihil24064_fm_i-xx.indd vi 05/12/12 2:18 PM05/12/12 2:18 PM Rev. Confirming Pages vii 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 Man- agement 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 Jour- nal 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 university- wide 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 Euro- pean 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 Engineer- ing 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. Follow- ing graduation, Ms. Stephens worked at Andersen Consulting as a systems integrator, expe- riencing 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. hil24064_fm_i-xx.indd viihil24064_fm_i-xx.indd vii 05/12/12 2:18 PM05/12/12 2:18 PM Rev. Confirming Pages viii 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 ini- tially 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 mod- eling 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 distinc- tive 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 do 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 over- board. Spreadsheets are not the only useful tool for performing management science analy- ses. 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 formula- tion 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 pri- marily (but not exclusively) use a spreadsheet format rather than algebra for formulating and presenting a model. hil24064_fm_i-xx.indd viiihil24064_fm_i-xx.indd viii 05/12/12 2:18 PM05/12/12 2:18 PM Rev. Confirming Pages Preface ix Some instructors have many years of experience in teaching modeling in terms of for- mulating algebraic models (or what the INFORMS Task Force called “model structuring”). Some of these instructors feel that students should do their modeling in this way and then transfer the model to a spreadsheet simply to use the Excel Solver to solve the model. We dis- agree with this approach. Our experience (and the experience reported by many others) is that most business students find it more natural and comfortable to do 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 mod- eling 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 mate- rial 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 hil24064_fm_i-xx.indd ixhil24064_fm_i-xx.indd ix 05/12/12 2:18 PM05/12/12 2:18 PM Rev. Confirming Pages x Preface the Ivey website, cases.ivey.uwo.ca/cases , in the segment of the CaseMate area designated for this book. This website address is provided at the end of each chapter as well. We are, of course, not the first to incorporate any of these key features into a management science textbook. However, we believe that the book currently is unique in the way that it fully incorporates all three key features together. OTHER SPECIAL FEATURES We also should mention some additional special features of the book that are continued from the fourth edition. • Diverse examples, problems, and cases convey the pervasive relevance of management science. • A strong managerial perspective. • Learning objectives at the beginning of each chapter. • Numerous margin notes that clarify and highlight key points. • Excel tips interspersed among the margin notes. • Review questions at the end of each section. • A glossary at the end of each chapter. • Partial answers to selected problems in the back of the book. • Supplementary text material on the CD-ROM (as identified in the table of contents). • An Excel-based software package (MS Courseware) on the CD-ROM and website that includes many add-ins, templates, and files (described below). • Other helpful supplements on the CD-ROM and website (described later). A NEW SOFTWARE PACKAGE This edition continues to integrate Excel 2010 and its Solver (a product of Frontline Systems) throughout the book. However, we are excited to also add to this edition an impressive more recent product of Frontline Systems called Risk Solver Platform for Education (or RSPE for short). RSPE also is an Excel add-in and its Solver shares some of the features of the Excel Solver. However, in addition to providing all the key capabilities of the Excel Solver, RSPE adds some major new functionalities as outlined below: • A more interactive user interface, with the model parameters always visible alongside the main spreadsheet, rather than only in the Solver dialog box. • Parameter analysis reports that provide an easy way to see the effect of varying data in a model in a systematic way. • A model analysis tool that reveals the characteristics of a model (e.g., whether it is linear or nonlinear, smooth or nonsmooth). • Tools to build and solve decision trees within a spreadsheet. • The ability to build and run sophisticated Monte Carlo simulation models. • An interactive simulation mode that allows simulation results to be shown instantly when- ever a change is made to a simulation model. • The RSPE Solver can be used in combination with computer simulation to perform simu- lation optimization. A CONTINUING FOCUS ON EXCEL AND ITS SOLVER As with all the preceding editions, this edition continues to focus on spreadsheet modeling in an Excel format. Although it lacks some of the functionalities of RSPE, the Excel Solver continues to provide a completely satisfactory way of solving most of the spreadsheet models encountered in this book. This edition continues to feature this use of the Excel Solver when- ever either it or the RSPE Solver could be used. Many instructors prefer this focus because it avoids introducing other complications that might confuse their students. We agree. hil24064_fm_i-xx.indd xhil24064_fm_i-xx.indd x 05/12/12 2:18 PM05/12/12 2:18 PM Rev. Confirming Pages Preface xi However, the key advantage of introducing RSPE in this edition is that it provides an all-in- one complement to the Excel Solver. There are some important topics in the book (including decision analysis and computer simulation) where the Excel Solver lacks the functionalities needed to deal with these kinds of problems. Multiple Excel add-ins—Solver Table, Tree- Plan, SensIt, RiskSim, Crystal Ball, and OptQuest (a module of Crystal Ball)—were intro- duced in previous editions to provide the needed functionalities. RSPE alone now replaces all of these add-ins. OTHER SOFTWARE Each edition of this book has provided a comprehensive Excel-based software package called MS Courseware on the CD-ROM and website. RSPE replaces various Excel add-ins in this package. Otherwise, the remainder of this package is being provided again with the current edition. This package includes Excel files that provide the live spreadsheets for all the various examples and case studies throughout the book. In addition to further investigating the exam- ples and case studies, these spreadsheets can be used by either the student or instructor as tem- plates to formulate and solve similar problems. The package also includes dozens of Excel templates for solving various models in the book. MS Courseware includes additional software as well. • Interactive Management Science Modules for interactively exploring certain manage- ment science techniques in depth (including techniques presented in Chapters 1, 2, 5, 10, 11, 12, and 18). • Queueing Simulator for performing computer simulations of queueing systems (used in Chapter 12). NEW FEATURES IN THIS EDITION We have made some important enhancements to the fifth edition. • A Substantial Revision of Chapter 1. In addition to some updates and a new end-of- chapter case, the example at the heart of the chapter has been modernized to better attract the interest of the students. The example now deals with iWatches instead of grandfather clocks. • A New Section Introduces …