Tutorials in operations research

186 Pages·2007·3 MB·english

by  Klastorin T. (ed.)

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:
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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
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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
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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
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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
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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
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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
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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