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two-wayservices.One-waysystemsprovidemoreflexibilitytouserssincetheycanbedropped-offatanystation.However,theirmodelinginvolvesanumberofcomplexitiesarisingfromtheneedtorelocatevehiclesaccumulatedatcertainstations.Theplanningofone-wayelectricvehicle-sharingsystemsinvolvesahostofstronglyinteractingdecisionsregardingthenumber,sizeandlocationofstations,aswellasthefleetsize.
Inthispaperwedevelopandsolveamulti-objectiveMILPmodelforplanningone-wayvehicle-sharingsystemstakingintoaccountvehiclerelocationandelectricvehiclechargingrequirements.Forrealworld
problemsthesizeoftheproblembecomesintractableduetotheextremelylargenumberofrelocationvariables.Inordertocopewiththisproblemweintroduceanaggregatemodelusingtheconceptofthevirtualhub.Thistransformationallowsthesolutionoftheproblemwithabranch-and-bound
approach.
Theproposedapproachgeneratestheefficientfrontierandallowsdecisionmakerstoexaminethetrade-offbetweenoperator’sandusers’benefits.ThecapabilitiesoftheproposedapproacharedemonstratedonalargescalerealworldproblemwithavailabledatafromNice,France.Extensivesensitivityanalysiswasperformedbyvaryingdemand,stationaccessibilitydistanceandsubsidylevels.Theresultsprovideusefulinsightsregardingtheefficientplanningofone-wayelectricvehicle-sharingsystemsandallowdecisionmakerstoquantifythetrade-offbetweenoperator’sandusers’benefits.
1.Introduction
AccordingtoFederalHighwayAdministration(FHWA)studiesa
privatevehicletravelsonaverage40kilometersperday,whichis
approximately90minutestime.Fortherestofthetimethisvehicleisidleandoccupiesaparkingspot(FHWA,2010).Analternative
iscar-sharing(alsoknownasshared-usevehicle)systems,which
haveattractedconsiderableattentionwithmultipleimplementationsworldwideduetotheirpotentialtoimprovemobilityandsustainability(Shaheen&
Cohen,2013).Thesesystemsprovidebenefitsbothtotheirusersandthesocietyasawhole.Reducedpersonaltransportationcostandmobilityenhancementhavebeencitedasthetwomostnotablebenefitstoindividualusers.Recentstudiesshowthat,car-sharingalsodecreasesaveragevehiclekilometerstraveledand,itislikelytodecreasecongestion(Crane,Ecola,Hassell,&
Natarah,2012)andemissions(Shaheen
&
Cohen,2013).Provisionofaffordablemobilitytoeconomically
disadvantagedgroupswithon-demandandpublictransportationsystemsisanothersocietalbenefit(Duncan,2011).
Theattractivenessofcar-sharingsystemsisdeterminedbythe
levelofserviceofferedandthecostassociatedwiththeuseofthe
system.Thelevelofserviceisinfluencedbytheaccessibilityof
vehiclestationsbythepotentialusers,i.e.(i)thedistancebetween
user’soriginanddestinationfrompick-upanddrop-offvehicle
stationsrespectively,and(ii)theavailabilityofvehiclesatstations.
Ontheotherhand,stationnumberandsize,aswellasfleetsize
andavailabilityofvehicles,atthe‘‘righttime’’atthe‘‘rightstation’’,influencethecostofestablishingandoperatingacar-sharing
System.Thecar-sharingsystemscanbeclassifiedintoflexible‘‘one-
way’’andthemorerestricted‘‘two-way’’types,accordingto
whethertheusersshouldreturntherentedvehicleatadifferentor
atthelocationtheypickeditup.The‘‘one-way’’systemsarealso
classifiedas‘‘free-floating’’and‘‘non-floating’’accordingtoparkingspotrestrictions.Theformerreferstoasystemwithout
restrictedparkingspots.Userscanpick-upordrop-offvehiclesin
anyparkingspotrestrictedwithinthebordersofanarea.Thelatter
isusedfordefiningsystemsinwhichpick-upanddrop-offlocationsofthevehiclesshouldbedesignatedparkingspots.‘‘free-floating’’models,reservationisnotpossiblewhereas‘‘non-floating’’modelsprovideusersboththeabilitytomakereservationandtheflexibilityofone-waytrips.Whiletwo-waysystemsallowusersforreservations,thestateofpracticeinone-waysystemsisrenting-basedonreal-timeavailabilityorwithshorttermreservations(e.g.30minutesinadvance).Arecent
studyshowedwithanagentbasedsimulationthatparkingreservationscanimprovethequalityofserviceforone-waycarsharingsystems(Kaspi,Raviv,&
Tzur,2014).
Theproblemofensuringvehicleavailabilityandfulfillingreser-
vationbecomesmoreprominentwhenthevehiclescanberented
andusedonaone-waybasisinnon-floatingsystems.Theone-wayoperationofthevehiclescoupledwiththeimbalanceofdemandforvehicles,bothattheoriginofthetrip(pick-upstation)andatthedestination(drop-offstation),mayresulttoasituationwherevehiclesareaccumulatedtostationswheretheyarenotneeded,whileatthesametimethereisvehicleshortageatthestationswheremorevehiclesareneeded(Barth,Todd,&
Xue,2004).
Vehiclerelocation,i.e.transferofvehiclesfromstationswith
highvehicleaccumulationtostationswhereshortageisexperienced,isatechniquethathasbeenproposedtoimprovetheperformanceofone-waycar-sharingsystems(e.g.Cucu,Ion-Boussier,Ducq,&
Boussier,2009;
Jorge,Correia,&
Barnhart,2014;
Kek,Cheu,&
Chor,2006).Thelackofefficientvehiclerelocationcoupledwiththeneedtoguaranteeagivenlevelofvehicleavailabilitymayleadtoanunnecessaryincreaseofthefleetsizeandvehicleunderutilization.Theefficientandcost-effectivestrategicplanning,andtheoperationofone-waycar-sharingsystemsrequiremodelsthatwilloptimallydeterminethenumberandlocationoftheservicestations,thefleetsize,andthedynamicallocationofvehiclestostations.Thesemodelsshouldassistdecisionmakerstostrikeanoptimumbalancebetweenthelevelofserviceofferedandthetotalcost(includingvehiclerelocationcosts)forimplementingandoperatingthecar-sharingsystem.
However,theliteraturecurrentlylacksamodelthatcan
considersimultaneouslydecisionsrelatedtothedeterminationof
stationlocation,sizeandnumber,andfleetsize,whiletakinginto
accountthedynamicsofvehiclerelocationandbalancingforasystemwithreservations.Existingmodels(Correia&
Antunes,2012;
Lin&
Yang,2011)eitherlookatstationlocationswithoutdueconsiderationtovehiclerelocationdecisions(Lin&
Yang,2011),orconsiderstationlocationsassumingthatonlythedemandinthecatchmentareaofopenedstationsneedstobeserved(Correia&
Antunes,2012).Inthecasewherevehiclerelocationismodeled(Correia&
Antunes,2012),therelocationofthevehiclesandtheassociatedcostsareconsideredonlyattheendoftheoperatingperiod(usuallyaday),andthereforetheyareinfluencingthefleetsize.
Theobjectiveofthispaperistwofold:
(i)todevelopandsolvea
mathematicalmodelfordeterminingtheoptimumfleetsize,and
thenumberandlocationoftherequiredstationsofone-way
non-floatingreservation-based,forbothpick-upanddrop-off,
car-sharingsystemsbytakingintoaccountthedynamicrepositioning(relocation)ofvehicles,and(ii)toapplytheproposedmodelforplanningandoperatingaone-wayelectricalcar-sharingsysteminthecityofNice,France.
Theremainderofthispaperisorganizedasfollows.Section2
providesanoverviewofpreviousrelatedworkandfurtherelaboratesontheargumentsjustifyingtheneedfortheproposedmodel,Section3presentstheformulationandthesolutionapproachoftheproposedmodel,Section4describestheapplicationoftheproposedmodelforplanningandoperatingaone-wayelectricalcar-sharingsysteminNice,France,Section5highlightspracticalconsiderationswhileSection6discussestheresearchconclusionsandprovidesrecommendationsforfuture
Research.
2.Previousrelatedresearch
Modelsrelatedtotheplanningandoperationofcar-sharing
systemscanbeclassifiedintothefollowingtwobroadcategories:
(i)modelsaddressingstrategicplanningdecisionsand(ii)models
supportingoperationaldecisions.
2.1.Modelsforstrategicplanningdecisions
Strategicplanningdecisionsseektodeterminethenumber,size
andlocationofstations,andthenumberofthevehiclesthatshould
beassignedtoeachstation,inordertooptimizeameasureoracombinationofmeasuresforsystemperformance.Stationlocationmodelshavebeendevelopedtolocatebicyclestations(Lin&
Yang,2011)andcarstations(Correia&
Antunes,2012).Althoughthefocusofourworkisonelectricalcar-sharingsystems,wealsoreviewmodelsthataddressthestationlocationofshared-usebicycles,givensomesimilaritiesofthetwosystems.
Theproblemoflocatingstationsforshared-usebicycleshas
beenstudiedrecently(Lin&
Yang,2011).Thispaperpresentsa
modelfordeterminingthenumberandlocationofbicyclestations
andthestructureofthenetworkofbicyclepathsthatshouldbe
developedtoconnectthebicyclestations.Theproblemisformulatedasanon-linearintegermodel.Theobjectivefunctionusedexpressesthetotalyearlycostencounteredbytheoperatorandtheusers.Asmallscaleexamplewasusedtoillustratethe