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2007 Tutorials in Operations Research OR Tools and Applications: Glimpses of Future Technologies Theodore Klastorin Tutorials Chair and Volume Editor Paul Gray, Series Editor Harvey J. Greenberg, Series Founder Presented at the INFORMS Annual Meeting, November 4–7, 2007 www.informs.org Copyright (cid:1)C 2007 by the Institute for Operations Research and the Management Sciences (INFORMS). ISBN13 978-1-877640-22-3 To order this book, contact: INFORMS 7240 Parkway Drive, Suite 310 Hanover, MD 21076 USA Phone: (800) 4-INFORMS or (443) 757-3500 Fax: (443) 757-3515 E-mail: [email protected] URL: www.informs.org INFORMS2007 (cid:1)c 2007INFORMS ISBN13978-1-877640-22-3 Table of Contents Foreword iv Preface vi Acknowledgments viii Chapter 1 Nested Partitions Optimization 1 Leyuan Shi and Sigurdur O´lafsson Chapter 2 Computational Global Optimization 23 Leon S. Lasdon and Ja´nos D. Pint´er Chapter 3 Coherent Approaches to Risk in Optimization Under Uncertainty 38 R. Tyrrell Rockafellar Chapter 4 Differential Games in Marketing Science 62 Gary M. Erickson Chapter 5 Safe Scheduling 79 Kenneth R. Baker and Dan Trietsch Chapter 6 Community-Based Operations Research 102 Michael P. Johnson and Karen Smilowitz Chapter 7 Generating Robust Project Baseline Schedules 124 Willy Herroelen Chapter 8 Trends in Operations Research and Management Science Education at the Introductory Level 145 Frederick S. Hillier and Mark S. Hillier Chapter 9 Business Engineering: A Practical Approach to Valuing High-Risk, High-Return Projects Using Real Options 157 Scott Mathews and Jim Salmon Contributing Authors 176 http://tutorials.pubs.informs.org iii INFORMS2007 (cid:1)c 2007INFORMS ISBN13978-1-877640-22-3 Foreword Tutorialsarethelifebloodofourprofessionalsociety.Theyhelpintroducepeopletofields about which they previously knew little. They stimulate people to examine problems they wouldnototherwiseconsider.Theyhelppointpeopletothestateoftheartandtoimportant unsolved problems. It is no surprise that tutorials are one of the major activities at the INFORMS annual meetings. The good news this year is that the INFORMS Board of Directors approved distributing a CD of the TutORials volume to every registrant at the Seattle meeting and at the 2008 and2009annualmeetings.AttendeesareurgedtotaketheCDbacktotheirinstitutionand make the contents available to colleagues and students. The printed TutORials book will continue to be available for a small fee. History of TutORials Each year, about 15 tutorials are presented at the INFORMS meeting. Although the attendance at tutorial sessions is among the largest of all sessions—numbers around 200 in a single session are common—until three years ago, their important content was lost to the many INFORMS members who could not attend either the tutorial sessions or the annual meeting itself. Clearly, INFORMS was underusing one of its treasures. In 2003, Harvey Greenberg of the University of Colorado at Denver, founding editor of the INFORMS Journal on Computing and well known for his many contributions to OR scholarship and professional service, was appointed the tutorials chair for the Denver NationalMeeting.Herecognizedtheproblemthattutorialswereonlyavailableforlistening oncetothosewhoattendedthem.Theresultwasalackofinstitutionalmemory.Hedecided to do something about it. He organized the TutORials in Operations Research series of books. His idea was that a selection of the tutorials offered at each annual meeting would bepreparedaschaptersinaneditedvolumewidelyavailablethroughindividualandlibrary purchase. To increase their circulation, the books would also be available at the INFORMS fall annual meetings. Harvey edited the Tutorials book for the Denver INFORMS meeting in 2004, which was published by Springer. In 2005, Frederick H. Murphy, then Vice President, Publications, of INFORMS, working closely with Harvey, convinced the INFORMS Board of Directors to bring the TutORials series under the umbrella of our society. Harvey was appointed Series Editor. He, in turn, asked J. Cole Smith of the University of Florida, Tutorials Chair of the San Francisco Annual Meeting, to serve as editor of the 2005 volume, the first to be sponsored by INFORMS. In doing so, Harvey initiated the policy that the invited Tutorials chair also serve as the volume editor. As the result of a suggestion by Richard C. Larson, 2005 President of INFORMS, a CD version of the volume was also created. In mid-2005, Harvey Greenberg, nearing retirement, asked to relinquish the series editorship. Paul Gray was appointed to replace him. Last year, the Pittsburgh meeting Chair, Michael Trick, appointed three Tutorials Co- chairs—MichaelP.JohnsonandNicolaSecomandiofCarnegieMellonUniversityandBryan Norman of the University of Pittsburgh—who served as Co-Editors of the 2006 volume. Thisyear’svolumeeditorisTheodoreKlastorin,distinguishedprofessorattheUniversityof Washington, who is the tutorials chair for the Seattle meeting. He assembled nine tutorials iv Foreword TutorialsinOperationsResearch,(cid:1)c 2007INFORMS v for this volume that, as in previous years, cover a broad range of fields within OR. These tutorials include • Nested participation optimization • Computational global optimization • Risk in optimization under uncertainty • Differential games in marketing science • Safe scheduling • Community-based operations research • Project management • Using options theory to assess projects • Trends in OR and MS education at the introductory level The authors come from major universities and a world-known company. They include (alphabetically) The Boeing Company, Carnegie Mellon University, Dartmouth College, CatholicUniversityofLeuven(Belgium),NorthwesternUniversity,StanfordUniversity,Uni- versity of Texas, University of Washington, and University of Wisconsin. On behalf of the INFORMS membership. I thank the volume editor for creating this year’s exciting tutorial series and doing the enormous amount of work required to create this volume. INFORMS is also indebted to the authors who contributed the nine chapters. The tutorial series also benefits from the work of its Advisory Committee, consisting of Harvey J. Greenberg (University of Colorado at Denver and Health Sciences Center), FrederickS.Hillier(StanfordUniversity),MichaelP.Johnson(CarnegieMellonUniversity), J.ColeSmith(UniversityofFlorida),andDavidWoodruff(UniversityofCalifornia,Davis). Finally,animportantthankyoutoMirandaWalker,KateLawless,PatriciaShaffer(Director of Publications), and the members of the publications staff at the INFORMS office for the physical preparation of this volume and its publication in a timely manner. Paul Gray Claremont Graduate University Claremont, California INFORMS2007 (cid:1)c 2007INFORMS ISBN13978-1-877640-22-3 Preface Welcome to the TutORials in Operations Research 2007, subtitled “OR Tools and Appli- cations: Glimpses of Future Technologies”; this is the fourth published volume in the series that was started by Harvey J. Greenberg in 2004. Like its predecessors, the tutorials in this book, as well as eight others, will be presented at the 2007 INFORMS annual meeting in Seattle, Washington. They all represent both the breadth and depth of methodologies and applications that define operations research’s (OR) varied and significant contribu- tions. This year, we are fortunate to have a group of tutorials presented by mostly senior INFORMS members who have extensive experience in advancing their respective topics as well as applying and presenting their material. OR has been applied to numerous problems in the nonprofit sector with considerable success.Forexample,thepotentialandchallengesofworkinthisareaareillustratedbythe tutorial by Michael P. Johnson (“Community-Based Operations Research”). In his chapter (co-authored with Karen Smilowitz), Johnson argues that political and social forces cause public sector problems to be “messier” and more complex than problems in the private sector. Johnson and Smilowitz illustrate their points with case studies in the areas of food security and affordable housing. In other presentations, Kenneth R. Baker presents a tutorial on “safe scheduling”. In his chapter (co-authored with Dan Trietsch), Baker presents a review of scheduling theory and describes how results from deterministic scheduling theory can be extended to stochastic problems to accommodate safety times explicitly. In a related tutorial, Willy Herroelen dis- cussestheissueofgeneratingprojectplanningschedulesthatareprotectedfromrandomdis- ruptiveeventsandunanticipateddelays(“GeneratingRobustProjectBaselineSchedules”). Extending the topic of planning under the threat of possible disruptive events, R. Tyrrell Rockafellar’stutorial(“CoherentApproachestoRiskinOptimizationUnderUncertainty”), explores various strategies for optimizing stochastic planning problems and the mathemat- ical implications of these strategies, as well as recently developed methodologies that avoid some of the problems (e.g., nonconvexity) inherent in previously used approaches. Extendingoptimizationrelatedtopics,LeonS.Lasdonpresentsatutorialonsolvingglobal optimizationproblems(“ComputationalGlobalOptimization”).Inhischapter(co-authored with Ja´nos D. Pint´er), Lasdon discusses various strategies that have proven effective for findingglobaloptimainnonlinearmodelsthathavemultiplelocalandglobaloptima.Lasdon and Pint´er review previously suggested solution approaches and present current problem areas and research opportunities. In a related tutorial, “Nested Partitions Optimization,” Leyuan Shi, presents the nested partitions (NP) method for solving large-scale discrete optimization problems. In her chapter (co-authored with Sigurdur O´lafsson), she discusses how to implement the NP method, how it relates to other exact and heuristic methods, and illustrates the applicability of the NP method to various problems in supply chain management, health case delivery, and data mining. In the years since the first OR application was published by A. Charnes in 1956, the profession has matured in both the development and application of OR methodologies and tools.Inhistutorial,FrederickS.Hillier(withco-authorMarkS.Hillier)discussthetrendsin OR and management science education over the past forty years. Hillier’s tutorial discusses changes that have occurred and explore what changes might be expected in the future. Exploring the interface between OR methodologies and related areas, Gary M. Erickson willpresentatutorialon“DifferentialGamesinMarketingScience”.Inhischapter,Erickson vi Preface TutorialsinOperationsResearch,(cid:1)c 2007INFORMS vii presents an overview of differential games as applied in marketing science and advertising. Erickson’s tutorial should be of interest to Operations Management researchers, among others, who are interested in expanding their work to include marketing issues. Erickson explores the challenges of using differential games and will discuss a number of applications and numerical examples. Inthefinalchapter,ScottMathews(withJimSalmon)ofTheBoeingCompanydiscusses animportantapplicationofOR/financemethodologiestotheproblemofplanningandeval- uating risky proposed projects. Their approach (termed “business engineering”) combines concepts from real options with Monte Carlo simulation and demonstrates how their multi- disciplinary methodology can provide firms with a tool that can help them evaluate and structure high-benefit projects while minimizing risks. These 2007 TutORials’ chapters illustrate the contributions that derive from an inter- disciplinary field that lies at the intersection of economics, engineering, computer science, mathematics,probabilityandstatistics,andpsychology.ThetutorialsdemonstratehowOR can bring synergy, insights, and solutions to complex problems. It is the goal of the 2007 INFORMS tutorials committee to represent a breadth and width of current problem areas and tools that define our profession. We hope that all the tutorials presented will stimulate additional interest, research, and application in the many areas where OR has much to contribute. Ted Klastorin University of Washington Seattle, Washington INFORMS2007 (cid:1)c 2007INFORMS ISBN13978-1-877640-22-3 Acknowledgments Many people have assisted with the substantial effort to organize the 2007 Tutorials in Operations Research. My great thanks to Paul Gray who serves as the series editor but has provided much more ... serving as a mentor, advisor, reviewer, and project planner. INFORMS staff members Miranda Walker, Patricia Shaffer, and Kate Lawless have worked tirelessly to prepare this volume in a timely manner despite my (unintentional) efforts to derailtheirefforts.ThanksalsotoSeattleINFORMSChairZeldaZabinskywhocontinually offered her constant support and optimism even when conditions dictated otherwise. My deepest gratitude to the anonymous reviewers who assisted with the review and editing of thesepapersunderverytightdeadlines;Iammostgratefulfortheircounselandhardwork. And,lastbutcertainlynotleast,Ithankmycolleagueswhohavecontributedtothisvolume as well as everyone who has agreed to present a tutorial at the 2007 INFORMS meeting in Seattle. Ted Klastorin University of Washington Seattle, Washington viii INFORMS2007 (cid:1)c 2007INFORMS|isbn13 978-1-877640-22-3 doi10.1287/educ.1073.0033 Nested Partitions Optimization Leyuan Shi Industrial and Systems Engineering Department, University of Wisconsin–Madison, Madison, Wisconsin 53706, [email protected] Sigurdur O´lafsson Industrial and Manufacturing Systems Engineering Department, Iowa State University, Ames, Iowa 50011, olaff[email protected] Abstract Weintroducethenestedpartitions(NP)methodforsolvinglarge-scalediscreteopti- mizationproblems.Assuchproblemsarecommoninmanypracticalapplicationsthe NPmethodhasbeenfoundusefulindiverseapplicationareas.Ithasforexamplebeen appliedtoclassiccombinatorialoptimizationproblems,suchasthetraveling-salesman problem and production-scheduling problems, as well as more recent applications in data mining and radiation therapy. The tutorial discusses the basic idea of the NP method, shows in some detail how it should be implemented, presents the basic con- vergence properties of the method, and discusses several successful implementations in diverse application areas. Keywords discreteoptimization;metaheuristics;combinatorialoptimization;mixedintegerpro- gramming 1. Introduction This tutorial introduces the nested partitions (NP) method. The NP method is a powerful optimizationmethodthathasbeenfoundtobeveryeffectiveforsolvinglarge-scalediscrete optimization problems. Such problems are common in many practical applications and the NPmethodishenceusefulindiverseapplicationareas.Itcanbeappliedtobothoperational and planning problems and has been demonstrated to effectively solve complex problems in both manufacturing and service industries. The NP method was first introduced by Shi and O´lafsson (1997) and its basic properties for discrete optimization were established in Shi and O´lafsson [6]. It has been successfully appliedtomanyclassiccombinatorialoptimizationproblems,suchasthetraveling-salesman problem (Shi et al. [8]), and production-scheduling problems (O´lafsson and Shi [6]), as well as more recent applications in data mining (O´lafsson and Yang [4]) and radiation therapy (D’Souza et al. [1]). For a complete treatment of the NP method, we refer the reader to Shi and O´lafsson [7]. The tutorial discusses the basic idea of the NP method, shows in some detail how it should be implemented, presents the basic convergence properties of the method, and dis- cusses several successful implementations in diverse application areas. We start by defining the domain for which the NP method is the most applicable, namely large-scale discrete optimization problems. 2. Discrete Optimization The NP method is particularly well suited for complex large-scale discrete optimization problemswheretraditionalmethodsexperiencedifficulty.Itis,however,verybroadlyappli- 1 ShiandO´lafsson: NestedPartitionsOptimization 2 TutorialsinOperationsResearch,(cid:1)c 2007INFORMS cableandcanbeusedtosolveanyoptimizationproblemthatcanbestatedmathematically in the following generic form: minf(x), (1) x∈X where the solution space or feasible region X is either a discrete or bounded set of feasible solutions. An important special case of problem that can be effectively addressed using the NP methodaremixedintegerprograms(MIP).Forsuchproblemstheremaybeonesetofdiscrete variables and one set of continues variables and the objective function and constraints are both linear. A general MIP can be stated as follows (Wolsey [9]): z = min c1x+c2y, (2) MIP x,y∈X where X={x∈Zn,y∈Rn: A1x+A2y≤b} and we use z to denote any linear objective + MIP function,thatis,z =f(x)=cx.Althoughsomelarge-scaleMIPscanbesolvedefficiently MIP using exact mathematical programming methods, complex applications often give rise to MIPs where exact solutions can only be found for relatively small problems. When dealing with such complex large-scale problems the NP method provides an attractive alternative. However, even in such cases it may be possible to take advantage of exact mathematical programmingmethodsbyincorporatingthemintotheNPframework.TheNPmethodthere- fore provides a framework for combining the complimentary benefits of two optimization approaches that have traditionally been studied separately, namely mathematical program- ming and metaheuristics. Another important class of problems are combinatorial optimization problems (COP) where the feasible region is finite but its size typically grows exponentially in the input parameters of the problem. A general COP can be stated as follows: minf(x), (3) x∈X where |X|<∞, but the objective function f: X→R may be a complex nonlinear function. Sometimesitmayhavenoanalyticexpressionandmustbeevaluatedthroughamodel,such as a simulation model, a data-mining model, or other application-dependent models. One important advantage of the NP method is that it is effective for optimization when f is known analytically (deterministic optimization), when it is noisy (stochastic optimization), or even when it must be evaluated using an external process. 3. Methodology The NP method is best viewed as a metaheuristic framework, and it has similarities to branchingmethodsinthatitcreatespartitionsofthefeasibleregionlikebranch-and-bound does. However, it also has some unique features that make it well suited for very hard large-scale optimization problems. Metaheuristics have emerged as the most widely used approach for solving difficult large- scalecombinatorialoptimizationproblems(GendreauandPotvin[2]).Ametaheuristicpro- vides a framework to guide application-specific heuristics, such as a greedy local search, by restricting which solution or set of solutions should or can be visited next. For example, thetabusearchmetaheuristicdisallowscertainmovesthatmightotherwisebeappealingby forbidding(i.e.,makingtabu)thereverseofrecentmoves.Atthesametimeitalwaysforces the search to take the best nontabu move, which enables the search to escape local optima. Similar to tabu search, most metaheuristics guide the search from solution to solution or possibly from a set of solutions to another set of solutions. In contrast, the NP method guides the search by determining where to concentrate the search effort. Any optimization

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