Table Of ContentInternational Series in
Operations Research & Management Science
H. A. Eiselt
Vladimir Marianov E ditors
Contributions
to Location
Analysis
In Honor of Zvi Drezner’s 75th Birthday
International Series in Operations Research
& Management Science
Volume 281
SeriesEditor
CamilleC.Price
DepartmentofComputerScience,StephenF.AustinStateUniversity,
Nacogdoches,TX,USA
AssociateEditor
JoeZhu
FoisieBusinessSchool,WorcesterPolytechnicInstitute,Worcester,MA,USA
FoundingEditor
FrederickS.Hillier
StanfordUniversity,Stanford,CA,USA
Moreinformationaboutthisseriesathttp://www.springer.com/series/6161
H. A. Eiselt • Vladimir Marianov
Editors
Contributions to Location
Analysis
In Honor of Zvi Drezner’s 75th Birthday
123
Editors
H.A.Eiselt VladimirMarianov
FacultyofManagement DepartmentofElectricalEngineering
UniversityofNewBrunswick PontificiaUniversidadCatólicadeChile
Fredericton,NB,Canada ComplexEngineeringSystemsInstitute
Santiago,Chile
ISSN0884-8289 ISSN2214-7934 (electronic)
InternationalSeriesinOperationsResearch&ManagementScience
ISBN978-3-030-19110-8 ISBN978-3-030-19111-5 (eBook)
https://doi.org/10.1007/978-3-030-19111-5
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Preface
Tammy&ZviDrezner©2008H.A.Eiselt
FewresearcherscanbeconsideredasinfluentialinseveralfieldsasZviDrezner.
In his main field of contributions, location theory, he is probably one of the most
prolificauthors.Inhis75thyear,someofhiscoauthorsandfriendsconsideredhim
deserving of a book that synthesizes some of his contributions and highlight their
importance for different fields. Not less relevant is his work with colleagues and
students. He has collaborated with most researchers in the facility location field
and has taught numerous students that now follow his path. As a matter of fact,
following the nomenclature for the followers of the famous mathematician, who
obtaintheso-calledErdösnumbers,wewouldliketointroduce“Dreznernumbers.”
ADreznernumberissimplythenumberofconnectionsneededtoconnectoneself
withZvi,giventhateachconnectionisascientificpaper.Inotherwords,someone
whocoauthoredapaperwithZviwillhaveaDreznernumberof1,somebodywho
v
vi Preface
wroteapaperwithsomeonewhoisamongZvi’scoauthors,hasaDreznernumber
of 2, and so forth. The two editors of this book are both proud to have a Drezner
numberof1.Thenagain,giventhe“sixdegreesofseparation”andthefactthatZvi
isaveryprolificwriter,thismaynotbetoosurprising.
Other than Zvi’s academic achievements, which we will discuss below, the
birthday boy is also a character, something rare in this increasingly standardized
world. Some years ago, one of us was invited to his and his wife Tammy’s home.
Theywereverynicetopickusupatourhotelandgetusback.Thewaybackturned
out to be a lot longer. The reason was not the usual Los Angeles traffic, but when
theygotustoourhotel,wesatforatleastanhourinthecarenjoyingtheirrepertoire
ofJewishjokes.Thatalonemadeforawonderfulevening.WealsolearnedwhyZvi
is so prolific. As most of his work involve heuristic algorithms and computational
testing, he had five computers running in parallel on different problems, crushing
numbers,andpreparingnewpublications.Oneofthosecomputerswasinthetrunk
ofthecar,makingthedailycommutealotmoreproductivethanmostofuswillever
be.That’ssomethingtothinkabout.Wedidanotherpieceofeducationthenextday.
ZviandTammytookustoaNeiman-Marcusstore,wheretheyshowedusapurse,
suggesting this would be a great gift for my wife. I had to pass, though, as $5000
pursesarenotonmylistofthingstoget.OnlyinCalifornia,Iguess.
Backtocomputationsandheuristics.Apparently,humorisinthebloodinallof
Zvi’sfamily.IdistinctlyrecalltheEuropeanWorkingGrouponLocationmeeting
inBarcelonain2000,whenZvi’swife,Tammy,presentedaworkbybothofthem
on genetic algorithms. They had introduced different genders in their algorithm,
which apparently worked out well computationally. Tammy commented that with
thewords(atruism,Iguess)that“apparently,itmakessensetohavesex.”Thereis
nothingwecanaddtothat.
AnotheramazingfactisZvi’sabilitytopull“well-known”factsfromgeometry,
trigonometry,andotherfieldsoutofahat,wheneverneeded.IremembertellingZvi
about one of the problems I was working on. He listened, and when I was done,
hesaidsomethinglike“oh,that!”Thisremindedmeofthewell-publicizedepisode
of young G. B. Dantzig, who told John von Neumann about his results on linear
programmingduality,whichapparentlysparkedthesameresponse.
ItwouldbeexceedinglydifficulttopinpointZvi’smajorcontribution;also,this
is a highly personal assessment. To us, his 1982 paper in Regional Science and
UrbanEconomics,probablythefirststeptowardcompetitivelocationmodelsbyan
operationsresearcher,willcertainlybeveryclosetothetopofthelist.Themerging
process for the quadratic assignment problem in his 2003 paper in INFORMS
Journal on Computing was a breakthrough in developing heuristics for quadratic
assignmentandotherlocationproblems.The2004paperonthe“BigTriangleSmall
Triangle”methodcoauthoredwithAtsuoSuzukiinOperationsResearchhadmany
follow-ups.
It would be impossible to include all Zvi’s work or the impact he has had on
otherresearchersinasinglebook.
WeknowthatZviisknowledgeableinmanyfields,butwethoughtitwouldbe
an excellent idea if we let him write about the topic he must know most about:
Preface vii
his own achievements. He has summarized them in the first chapter of this book.
Starting with the story of how he received his degree, we learn about his first
paper in 1962 (many of those who have followed in his footsteps and are now
active in the field were not even born then!) in the Astronomer’s Bulletin, a story
vaguelyreminiscentofVarignonandhisgnomonics.ThisisfollowedbyZvi’sreally
impressive curriculum vitae and some inspiring thoughts regarding teaching the
subject.
RichardL.ChurchhasafreshlookattheWeberproblem.Hedoesawaywiththe
usualviewofWeber’scontribution,whichlooksnotsomuchasWeber’sbookbut
asGeorgPick’smathematicalappendix,basedonLaunhard’swork.Itturnsoutthat
whileWeberdescribesaverysimpleprototypeofalocationproblemthatgoeslittle
beyondtheusualFermatandTorricellimodels,hisactualdiscussionisaboutmuch
morecomplexproblems,anumberofwhichsometimesarereferredtobysomeof
hislatter-daysuccessorsas“generalizationsofthestandardWeberproblem,”even
thoughtheywerealreadydescribedbyWeber.
Jack Brimberg and Said Salhi investigate p-median problems in continuous
space.BasedonCooper’soriginallocation—allocationmethod—theyfirstreviewa
number of heuristic algorithms based on Cooper’s contribution, followed by the
introduction of a number of refinements. New algorithms, such as a depth-first
search method and a decomposition technique, are described, and computational
resultsareoffered.
AtsuoSuzuki’smaininterestconcernsWeberproblems,andhiscontributionin
this book is a Weber problem with a new twist. In particular, the piece discusses
a Weber problem on the sphere. The applications of such problems are found on
locations on a global scale. The formulation of this problem turns out to have a
nonconvexobjective.Asaresult,theusualWeiszfeldalgorithmwillnotnecessarily
find an optimal solution. He employs a version of the big triangle-small triangle
method,developedbyZviDreznerandtheauthor.
Anita Schoebel’s work is on well-known continuous locations but with the
additional twist that the single new facility has to have integer coordinates. The
applications of this problem are found in robust decision-making. Her paper
delineatesfinitedominatingsetsforproblemswith(cid:2)1,(cid:2)2,and(cid:2)∞distances.
The chapter by George Wesolowsky also looks at the Weber problem with
particular focus on the many papers he and Zvi have written together on the
subject. This includes the usual minisum problem, continuous location problems
with minimax and maximin objectives (the latter in case of undesirable facilities),
coveringmodels,hubproblems,aswellasdifferentsolutionapproaches,including
trajectorymethodsandaDemjanov-stylealgorithm.
MozartMenezes’sworkdealwithvotingmethods,“wisdomofthecrowd,”and
Condorcet points. In location and voting problems, he explores relations between
WebersolutionsandCondorcetpointsandconductsnumericalexperimentsregard-
ing the computation of Condorcet points for problems with Euclidean distances.
He uses the notion of a “benevolent dictator” to examine the relative efficiency of
Condorcetsolutions.
viii Preface
TalyDrezner,ascientistinbiogeography,discussesheuristicsinherpaperwitha
focusongeneticalgorithms.Herpieceonbiologicalprinciplesingeneticalgorithms
withmaleandfemalesubsetsisanoriginalwork.Shesubsequentlydescribessome
statisticaltestsdevelopedtoverifycomputationalresults.
Inherpaper,SibelAlumurreviewsavarietyofhublocationandrelatedproblems
under special consideration of Zvi Drezner’s contributions to the individual field.
Besideshublocationproblems,sheincludesroundtriplocationproblems,transfer
point location problems, and collection depot location problems. Each of the
problems is formulated, and the impact of Zvi’s work on the specific field is
highlighted.
Tammy Drezner, best known for her work on attraction functions, presents
thoughts and results in her contribution to this book. Defining the concept of
attractiveness, she first addresses distance decay and different attraction func-
tions. She then explores different extensions, e.g., budget constraints, lost demand
(nonessential goods), and solution concepts (e.g.,von Stackelberg’s famed leader-
followermodel)alongwithproperties,suchastheconsistencyofrules.Someresults
concerningsolutiontechniquesfinishherchapter.
Pawel Kalczynski’s contribution concerns competitive location models in the
planethatarebasedontheconceptofcovering.Hedelineatesspheresofinfluence,
defines purchasing power, and formulates a competitive model based on covering
ideas.Leader-followeralgorithmsandheuristicsareofferedalongsidewithbounds
andcomputationalexperience.
XinandWangexaminealocationproblemwithamedianobjective,inwhichthe
weights,representingthecustomers,arerandom.Theauthorsconsiderproblems,in
which a “value-at-risk” constraint has been added. They develop an algorithm for
theproblem,whichtheyillustratebymeansofanumericalexample.
ThelastchapterinthisbookbyDawitZeromisdifferentfromtheothers,inthat
itdealswithanewstatisticaldistribution,viz.,thebivariateexponentialdistribution
anditsproperties,whichheandZvidevelopedtogether.Wearegladtoincludethis
work, as it is one of the many examples in which Zvi has gone beyond location
modelsandshownthatheis,indeed,atrueRenaissanceman.
Last,butcertainlynotleast,wewouldliketoexpressourthankstotheSpringer
staff,whoweregreatasusual:CamillePriceforsnuckeringusintoputtingtogether
another book; Matthew Amboy, Neil Levine, and Faith Su for supporting us all
the way and facilitating the process; as well as Aparajita Srivastava and Christine
Criglerinproduction.AllthatisleftforustodoistowavetoZvi(and,ofcourse,
Tammy)andwishthemmanyhappyreturnsandmanymorepapers.
Professor Marianov acknowledges the support by grant FONDECYT 1160025
and by the Complex Engineering Systems Institute through grant CONICYT PIA
FB0816.
Fredericton,NB,Canada H.A.Eiselt
Santiago,Chile VladimirMarianov
February2019
Contents
1 MyCareerandContributions............................................. 1
ZviDrezner
2 UnderstandingtheWeberLocationParadigm.......................... 69
RichardL.Church
3 A General Framework for Local Search Applied
totheContinuousp-MedianProblem.................................... 89
J.BrimbergandS.Salhi
4 Big Triangle Small Triangle Method for the Weber
ProblemontheSphere..................................................... 109
AtsuoSuzuki
5 IntegerLocationProblems ................................................ 125
AnitaSchöbel
6 ContinuousLocationProblems ........................................... 147
GeorgeO.Wesolowsky
7 VotingforLocatingFacilities:TheWisdomofVoters.................. 169
MozartB.C.Menezes
8 Neighbourhood Reduction in Global and Combinatorial
Optimization:TheCaseofthep-CentreProblem ...................... 195
SaidSalhiandJackBrimberg
9 InnovationsinStatisticalAnalysisandGeneticAlgorithms........... 221
TalyDawnDrezner
10 HubLocationandRelatedModels ....................................... 237
SibelA.Alumur
ix
