Facility location models for distribution system design

Facilitylocationmodelsfordistributionsystemdesign

AndreasKlosea,b,*,AndreasDrexlc

aUniversit€atSt.Gallen,9000St.Gallen,SwitzerlandbInstitutf€urOperationsResearch,Universit€atZ€urich,8015Z€urich,SwitzerlandcChristian-Albrechts-Universit€atzuKiel,Olshausenstr.40,24118Kiel,Germany

Received1October2001;accepted14October2003Availableonline15January2004

Abstract

Thedesignofthedistributionsystemisastrategicissueforalmosteverycompany.Theproblemoflocatingfacilitiesandallocatingcustomerscoversthecoretopicsofdistributionsystemdesign.Modelformulationsandsolutionalgorithmswhichaddresstheissuevarywidelyintermsoffundamentalassumptions,mathematicalcomplexityandcomputationalperformance.Thispaperreviewssomeofthecontributionstothecurrentstate-of-the-art.Inparticular,continuouslocationmodels,networklocationmodels,mixed-integerprogrammingmodels,andapplicationsaresummarized.Ó2003ElsevierB.V.Allrightsreserved.

Keywords:Strategicplanning;Distributionsystemdesign;Facilitylocation;Mixed-integerprogrammingmodels

1.Introduction

Decisionsaboutthedistributionsystemareastrategicissueforalmosteverycompany.Theproblemof

locatingfacilitiesandallocatingcustomerscoversthecorecomponentsofdistributionsystemdesign.

Industrialfirmsmustlocatefabricationandassemblyplantsaswellaswarehouses.Storeshavetobelo-

catedbyretailoutlets.Theabilitytomanufactureandmarketitsproductsisdependentinpartonthe

locationofthefacilities.Similarly,governmentagencieshavetodecideaboutthelocationofoffices,

schools,hospitals,firestations,etc.Ineverycase,thequalityoftheservicesdependsonthelocationofthe

facilitiesinrelationtootherfacilities.

Theproblemoflocatingfacilitiesisnotnewtotheoperationsresearchcommunity;thechallengeof

wheretobestsitefacilitieshasinspiredarich,colorfulandevergrowingbodyofliterature.Tocopewith

themultitudeofapplicationsencounteredinthebusinessworldandinthepublicsector,aneverexpanding

familyofmodelshasemerged.Location-allocationmodelscoverformulationswhichrangeincomplex-

ityfromsimplelinear,single-stage,single-product,uncapacitated,deterministicmodelstonon-linear

*Correspondingauthor.Address:Institutf€urOperationsResearch,Universit€atZ€urich,8015Z€urich,Switzerland.E-mailaddresses:andreas.klose@unisg.ch(A.Klose),drexl@bwl.uni-kiel.de(A.Drexl).

0377-2217/$-seefrontmatterÓ2003ElsevierB.V.Allrightsreserved.

doi:10.1016/j.ejor.2003.10.031EuropeanJournalofOperationalResearch162(2005)4–29

www.elsevier.com/locate/dswprobabilisticmodels.Algorithmsinclude,amongothers,localsearchandmathematicalprogramming-

basedapproaches.

Itisthepurposeofthispapertoreviewsomeoftheworkwhichhascontributedtothecurrentstate-

of-the-art.Thefocusisonthefundamentalassumptions,mathematicalmodelsandspecificreferencesto

solutionapproaches.Forthesakeofbrevity,workwhichhasbeendoneusingsimulationisneglected(see,

forinstance,Connersetal.,1972).

Theoutlineoftheworkisasfollows:InSection2typesofmodelsareclassified.Section3reviews

continuouslocationmodels.Then,Section4isdedicatedtonetworklocationmodels,whileSection5

providesmixed-integerprogrammingmodels.Finally,Section6coversavarietyofapplications.

2.Typesofmodels

Facilitylocationmodelscanbebroadlyclassifiedasfollows:

1.Theshapeortopographyofthesetofpotentialplantsyieldsmodelsintheplane,networklocationmod-

els,anddiscretelocationormixed-integerprogrammingmodels,respectively.Foreachofthesubclasses

distancesarecalculatedusingsomemetric.

2.Objectivesmaybeeitheroftheminsumortheminmaxtype.Minsummodelsaredesignedtominimize

averagedistanceswhileminmaxmodelshavetominimizemaximumdistances.Predominantly,minsum

modelsembracelocationproblemsofprivatecompanieswhileminmaxmodelsfocusonlocationprob-

lemsarisinginthepublicsector.

3.Modelswithoutcapacityconstraintsdonotrestrictdemandallocation.Ifcapacityconstraintsforthe

potentialsiteshavetobeobeyeddemandhastobeallocatedcarefully.Inthelattercasewehaveto

examinewhethersingle-sourcingormultiple-sourcingisessential.

4.Single-stagemodelsfocusondistributionsystemscoveringonlyonestageexplicitly.Inmulti-stagemod-

elstheflowofgoodscomprisingseveralhierarchicalstageshastobeexamined.

5.Single-productmodelsarecharacterizedbythefactthatdemand,costandcapacityforseveralprod-

uctscanbeaggregatedtoasinglehomogeneousproduct.Ifproductsareinhomogeneoustheir

effectonthedesignofthedistributionsystemhastobeanalyzed,viz.multi-productmodelshaveto

bestudied.

6.Frequently,locationmodelsbaseontheassumptionthatdemandisinelastic,thatis,demandisindepen-

dentofspatialdecisions.Ifdemandiselastictherelationshipbetween,e.g.,distanceanddemandhasto

betakenintoaccountexplicitly.Inthelattercasecostminimizationhastobereplacedthrough,for

example,revenuemaximization.

7.Staticmodelstrytooptimizesystemperformanceforonerepresentativeperiod.Bycontrastdynamic

modelsreflectdata(cost,demand,capacities,etc.)varyingovertimewithinagivenplanninghorizon.

8.Inpracticemodelinputisusuallynotknownwithcertainty.Dataarebasedonforecastsand,hence,are

likelytobeuncertain.Asaconsequence,wehaveeitherdeterministicmodelsifinputis(assumedtobe)

knownwithcertaintyorprobabilisticmodelsifinputissubjecttouncertainty.

9.Inclassicalmodelsthequalityofdemandallocationismeasuredonisolationforeachpairofsupplyand

demandpoints.Unfortunately,ifdemandissatisfiedthroughdeliverytoursthen,forinstance,delivery

costcannotbecalculatedforeachpairofsupplyanddemandpointsseparately.Combinedlocation/

routingmodelselaborateonthisinterrelationship.

Additionalattributessuchassingle-vs.multiple-objectivemodelsordesirablevs.undesirablefacilities

maybedistinguished(see,forinstance,Aikens,1985;BrandeauandChiu,1989;Daskin,1995;ReVelleand

Laporte,1996;HamacherandNickel,1998).A.Klose,A.Drexl/EuropeanJournalofOperationalResearch162(2005)4–295