ArticlePDF Available

Modeling and Analysis of Optimal Strategies for Leveraging Ride-Sourcing Services in Hurricane Evacuation

Authors:

Abstract and Figures

In many large-scale evacuations, public agencies often have limited resources to evacuate all citizens, especially vulnerable populations such as the elderly and disabled people, and the demand for additional transportation means for evacuation can be high. The recent development of ride-sourcing companies can be leveraged in evacuations as an additional and important resource in future evacuation planning. In contrast to public transit, the availability of ride-sourcing drivers is highly dependent on the price, since surge pricing will occur when the demand is high and the supply is low. The key challenge is thus to find the balance between evacuation demand and driver supply. Based on the two-sided market theory, we propose mathematical modeling and analysis strategies that can help balance demand and supply through a pricing mechanism designed for ride-sourcing services in evacuation. A subsidy is considered in the model such that lower-income and vulnerable individuals could benefit from ride-sourcing services. A hypothetical hurricane evacuation scenario in New York City in the case study showed the feasibility of the proposed method and the applicability of subsidies for ride-sourcing services in evacuation. The methodology and results given in this research can provide useful insights for modeling on-demand ride-sourcing for future evacuation planning.
Content may be subject to copyright.
Sustainability2021,13,4444.https://doi.org/10.3390/su13084444www.mdpi.com/journal/sustainability
Article
ModelingandAnalysisofOptimalStrategiesforLeveraging
RideSourcingServicesinHurricaneEvacuation
DingWang*,KaanOzbayandZilinBian
C2SMARTUniversityTransportationCenter,TandonSchoolofEngineering,NewYorkUniversity,
Brooklyn,NY11201,USA;kaan.ozbay@nyu.edu(K.O.);zb536@nyu.edu(Z.B.)
*Correspondence:dw2283@nyu.edu
Abstract:Inmanylargescaleevacuations,publicagenciesoftenhavelimitedresourcestoevacuate
allcitizens,especiallyvulnerablepopulationssuchastheelderlyanddisabledpeople,andthede
mandforadditionaltransportationmeansforevacuationcanbehigh.Therecentdevelopmentof
ridesourcingcompaniescanbeleveragedinevacuationsasanadditionalandimportantresource
infutureevacuationplanning.Incontrasttopublictransit,theavailabilityofridesourcingdrivers
ishighlydependentontheprice,sincesurgepricingwilloccurwhenthedemandishighandthe
supplyislow.Thekeychallengeisthustofindthebalancebetweenevacuationdemandanddriver
supply.Basedonthetwosidedmarkettheory,weproposemathematicalmodelingandanalysis
strategiesthatcanhelpbalancedemandandsupplythroughapricingmechanismdesignedforride
sourcingservicesinevacuation.Asubsidyisconsideredinthemodelsuchthatlowerincomeand
vulnerableindividualscouldbenefitfromridesourcingservices.Ahypotheticalhurricaneevacua
tionscenarioinNewYorkCityinthecasestudyshowedthefeasibilityoftheproposedmethodand
theapplicabilityofsubsidiesforridesourcingservicesinevacuation.Themethodologyandresults
giveninthisresearchcanprovideusefulinsightsformodelingondemandridesourcingforfuture
evacuationplanning.
Keywords:hurricane;evacuation;ridesourcing;sharedmobility;pricingstrategy;subsidy;de
mandandsupply;socialequity
1.Introduction
Privatecarsusuallyserveasthemaintransportationmodeduringevacuations;how
ever,inmetropolitancities,adensepopulationmeansthatpersonalautomobilesareoften
lacking.MorethanhalfthehouseholdsinNewYorkCity(NYC)donothavepersonal
automobiles.ThisstatisticislowestinManhattan,whereonly23%ofhouseholdsown
cars[1].Consequently,manypeopleneedtousepublictransport(suchasbuses,thesub
way,trains,etc.)toreachsaferregions.Despitetheincreasinginvolvementofpublic
transitinevacuations,manyproblemsstillexist.Limitedresourceswerethefirstobstacle,
forinstance,duringHurricaneKatrinain2005.NewOrleanshasabout500busesinreg
ularservice,butneededabout2000busestoevacuateallresidentswhowerenotusing
privatecars[2].Socialequityisanothercriticalprobleminevacuation[3].Preparationfor
peopleinspecialcategories(disabled,theelderly,infants,etc.)isinadequate,andsomeof
themcannotevenreachbusstationsinemergencyevents.Oneofthemainproblemsin
NewOrleans’2005evacuationwasthelackofplanningtoevacuatecarlessresidents,the
elderly,thedisabled,andpeoplewithotherspecialneeds[2].RecentresearchbyRenne
andMayorga[4]revealsthatonly16ofthe50largestcitiesintheUnitedStatesmention
carlessandvulnerablepopulationsinevacuationplans,andonly13planshavedetailed
informationforsuchpopulations.Newtechnologiesandresearchareneededtoensure
safeandmoreequitableevacuation,especiallyforvulnerablepopulations.
Citation:Wang,D.;Ozbay,K.;Bian,
Z.ModelingandAnalysisStrategies
forLeveragingRideSourcing
ServicesinHurricaneEvacuation.
Sustainability2021,13,4444.
https://doi.org/10.3390/su13084444
AcademicEditor:LuciaRotaris
Received:7March2021
Accepted:31March2021
Published:15April2021
Publisher’sNote:MDPIstaysneu
tralwithregardtojurisdictional
claimsinpublishedmapsandinstitu
tionalaffiliations.
Copyright:©2021bytheauthors.
LicenseeMDPI,Basel,Switzerland.
Thisarticleisanopenaccessarticle
distributedunderthetermsandcon
ditionsoftheCreativeCommonsAt
tribution(CCBY)license(http://cre
ativecommons.org/licenses/by/4.0/).
Sustainability2021,13,44442of22
Improvementsintechnologyandcommunicationhaveledtotheriseofthesharing
economyandgrowthofprivatecompaniesintransportation.Fastgrowingridesourcing
companies(e.g.,Uber,Lyft),whichprovideanopportunitytomobilizetheirresourcesto
increaseevacuationcomplianceandsupportvulnerablepopulations,areespeciallypop
ularinmetropolitancities[3,5–8].Ridesourcingserviceshavemanyadvantages,suchas
flexibilityintermsoftimeandroute,andGPSenabledtoolstoeasilyconnectriders,driv
ers,andvehicles.Inanemergencyevacuation,ridesourcingservicescanservenotonly
asacomplementarytransitmode,butalsoofferaccesstomobilityimpairedpeoplewho
aredifficulttoevacuate.RidesourcingcompaniessuchasUberandLyfthavebeenin
volvedinmanyrecentevacuationevents[5,9–14],andmanydriversarewillingtopartic
ipateinevacuations[7].Withtheparticipationofridesourcingcompanies,resourcelim
itationsandsocialequityproblemsmaybeaddressedinfutureevacuations.
Recentresearchhasidentifiedtwomajorconcernsforleveragingridesourcingser
vicesinevacuation:Driveravailabilityandserviceprice[3,5,6].Incontrasttopublic
transit,driveravailabilityforridesourcingserviceshasacloserelationshipwithpricing.
Toachievemarketequilibrium,whenthedemandofridersishighandthesupplyofdriv
ersislow,apricemultiplierwillbeapplied,whichiscalled“surgepricing”.Duringevac
uations,demandcanbemuchhigherthannormalbecausemanypeoplewanttoevacuate
fromthedangerousarea,whiletheavailabilityofdriverscanbelowerthannormalsince
somedriversneedtoevacuatetheirfamiliesandmanymaybeafraidtogetontheroad.
Uberindicatedthatincreasingthepricecanmotivatemoredriverstoparticipateinthe
evacuation[15].FollowingHurricaneSandy,Uberissuedasurgeoftwicethebaseprice
onalltrips,whichreceivedintensecriticism[15,16].Surgepricesmaygetmoredriverson
theroad,butpeopleshouldnotberequiredtopayfortheirlives.However,verylimited
researchhasaddressedthisproblem.
Duringregulartimes,theobjectiveofridesourcingcompaniesistomaximizetheir
profit,butduringevacuationsthemainobjectiveistomaximizethenumberofpeople
evacuatedwithinalimitedtime.Toputmoredriversontheroad,thegovernmentorride
sourcingcompaniescanprovidesubsidiestodriversasanincentive.UberandLyfthave
offeredfreeridesinmultipleevacuationevents[5].Generally,givingsubsidiestodrivers
whilechargingalowerpricetopassengerscanincreasethenumberofmatchedtrips.With
subsidiesprovidedbythegovernmentorridesourcingcompanies,lowerincomeand
vulnerableindividualscanbenefitsubstantiallyfromridesourcingservices.Althoughthe
costofsubsidieswillalsobecomeaburdenforgovernmentsorcompanies,maximizing
thenumberofmatchedtripsandminimizingthecostofsubsidiesisatradeoff.
Giventhepotentialforleveragingridesourcingservicesindisastersasanalternative
evacuationmode,thispaperaimstoprovideamodelthatcanhelpbalancedemandand
driversupplythroughapricingmechanismdesignedforridesourcingservicesinevacu
ations.Aweightedmultiobjectivemodelisproposedthatconsiderstwoimportantfea
tures:Spatialdifferentiationandtimedependentevacuationresponsebehavior.Thespa
tialdifferentiationallowstheplatformtohavedifferentpricesettingsindifferentregions,
sincetheirdemandandsupplycanbedifferent.Thetimedependentevacuationdemand
andsupplyfunctionsareusedtoestimatetheproportionofpeoplelikelytoevacuateand
theavailabilityofservicesprovidedbydriverswithineachtimesteptodemonstratehow
theproposedmodelcanadapttodifferenttypesofevacuationresponsebehaviors.More
importantly,theweightedmultiobjectivemodelenablesdecisionmakerstofindthebest
resultthatcanevacuatemorepeoplewithintheirbudgetbychangingtheweightparam
etersoftheobjectivefunction.
TheexperienceofHurricaneIrene(2011)showslargescalemassevacuationsunder
extremeconditionsinNYCmayoverextendthepublictransitsystem[17].With1.61mil
lioncarlesspeopleinallevacuationzones,publictransitmightsuccessfullysupportsome
rangeofevacuation,butitishardtosatisfylargenumbersofevacueesandvulnerable
populationsinseveredisasters.Inthepastfewyears,appbasedelectronicdispatchser
vices,suchasUberandLyft,havebecomeverypopularinNYCandarechangingtheway
Sustainability2021,13,44443of22
peoplegetaround.Inthecasestudysection,ahypotheticalhurricaneevacuationscenario
inNYCisusedtoevaluatetheperformanceoftheproposedmethodforridesourcing
servicesinevacuations,andtheeffectofdifferenttypesofevacuationresponsebehaviors
willbeanalyzedinthecasestudy.
Themodelisdesignedtoanalyzetheworkingoftheridesourcingmarketinevacu
ations.ThemodelcanhelpridesourcingcompanieslikeUberandLyftsetpricesaswell
ashelpthecityemergencyresponsedepartmentdevelopregulationpoliciesinevacua
tions.Theuniquecontributionsofthisstudyinclude:(1)Quantifyingtherelationshipbe
tweendemand,supply,andpriceforridesourcingservicesinevacuations;(2)analyzing
theimpactofdifferenttimedependentevacuationresponsebehaviors;(3)proposinga
mathematicalmodelingapproachtooptimizepricesettingsforridesourcingservicesin
evacuationswiththetwinobjectivesofmaximizingthenumberofmatchedtripsandmin
imizingthecostofsubsidies;and(4)evaluatingtheimpactofspatialdemandandsupply
ontheoptimalpricesettings.
Theremainderofthestudyisorganizedasfollows:Section2providesanoverview
oftherelatedresearchinevacuationandsharedmobility.Section3providestheproblem
descriptionthatwillexplaintheavailableevacuationmodesinNYC.Section4presents
themodelingapproachdesignedforridesourcingservicesinevacuations.Section5pro
videsahypotheticalevacuationscenarioinNYCtoevaluatemodelperformance.Section
6willsummarizetheresearchlimitationsandpotentialfutureresearchdirections.
2.LiteratureReview
Emergencyevacuationplansareimportanttoensurethesafestandmostefficient
evacuationwhenfacingdisasters.Withmoreavailabledataandadvancedtechnology,
researcherscanoptimizedisasterpreparationandpostdisasterrecoveryplanning[18–
27].Evacuationanalysisandplanninghavebeendevelopedthroughmathematicalmod
elsofevacuationdemand,simulations,andoptimizationmodelsofevacuationclearance
time[21,28,29].Extensiveresearchintheliteratureusesdiscretechoicemodelstostudy
evacuationchoices[30–34],evacuationtime[35–37],choiceofdestination[38,39],trans
portationmodeinevacuations[39,40],androutingproblems[39,41–43].
Traditionally,evacueeswithoutaccesstopersonalautomobilesareexpectedtouse
publictransittoreachsaferregions.Sincetransithasamuchlargercapacitythanprivate
cars,theimportanceoftransitbasedevacuationhasbeenincreasinglyrecognizedduring
thepastfewdecades[2].Manystudieshavefocusedonimprovingtransitoperationsdur
ingevacuations,suchasresourceallocationintransitbasedemergencyevacuation
[44,45],transitbasedevacuationplanningforpeoplewithspecialneeds[46–48],dynamic
busdispatchingwithstochasticdemand[49],andbusdriveravailability[50].However,
transitbasedevacuationshavemanyproblemsinpractice,suchaslimitedresourcesand
thelackofplanningtoevacuatetheelderly,disabled,andpeoplewithotherspecialneeds
[2].
Thelimitedresourcesandtheproblemofsocialequityinevacuationsarestillun
solved[3,5].ThedevastatingeventsofHurricaneKatrinain2005demonstratedthelimi
tationsofcurrentevacuationplans,withmanyoftheselessonslearnedindicatingtheim
portanceofequitableevacuationplanningandtheneedtocreateamultimodaltranspor
tationsystemwithmoreevacuationoptions[2].DuringHurricaneKatrina,between
127,000and300,000peopledidnothaveaccesstoreliabletransportationintheNewOr
leansmetropolitanarea,andabout100,000peopledidnotevacuatebeforelandfall[51,52].
Althoughsomecitiesnowprovideemergencyplanstothecarlesspopulation,thespecial
needsofvulnerablepopulationsremainunaddressed[4].Moreresearchisneededinareas
suchashowtodefinethevulnerablepopulation[4]andhowtheymakechoicesduring
anevacuation[40].Discussionsofsocialequityproblemscanbefoundintheliterature
[4,53–58].
Recentstudiesshowtheresourcelimitationsandsocialequityproblemsmaybead
dressedbyleveragingthesharingeconomy,whichincludescarsharing,homesharing,and
Sustainability2021,13,44444of22
ridesourcingservices[3,5,6].Thesharedresourcesfromprivatecompaniesandcitizens
maysupplementpublicresourcesinevacuations,whichcanyieldseveralbenefitsthat
havebeenidentifiedintheliterature,suchasincreasingcompliancetoevacuation,im
provingevacuationefficiency,andprovidingservicesforvulnerablepopulations,butlim
itationsalsoexist(e.g.,liabilityandcost)[3,5,6].Theemergenceofthesharingeconomy
broughtnewopportunitiesforamoreequitabletransportationsystembyincreasingac
cessibility,reducingcostsofpersonalautomobiles,andallowingmoreflexibletravelpat
terns[59,60].Anoverviewofsharedmobilitycanbefoundintheliterature[61–65].Equity
anddiscriminationissuesofsharedmobilityalsoexistandhavebeendiscussedinthe
literature[59,66,67].
Ridesourcingservicesareespeciallypopularinmetropolitanregions;datashows
UberandLyftcarsoutnumberyellowcabsinNYCby4to1[68].Thefeasibilityandlim
itationofusingridesourcingservicesforevacuationhavebeenstudiedintheliterature
[3,5–8].Researchershaveprovidedextensiverecommendationsandguidelinestounder
standanddevelopmoreequitableevacuationbyleveragingthesharingeconomy.Fur
thermore,ridesourcingserviceshavebeenactiveinmanydisastersintheUnitedStates
andreceivedpositivefeedback[6].In2012,whenHurricaneSandystruckNYC,public
transportationwasverylimitedforalargenumberofcarlessresidents,andthedemand
forUberrideswasastronomicallyhigh[15,16].In2017,beforeIrmamadelandfallinFlor
ida,UberandLyftofferedfreeridestoandfromsheltersnearTampa[9,10].Inthecaseof
HurricaneHarvey,alsoin2017,Uberprovidedfreeridestoorfromsheltersinmultiple
cities[11].In2018,UberandLyftalsoprovidedfreeridestoandfromsheltersasHurri
caneFlorenceapproached[12,13].Figure1summarizestheactionsofUberandLyftdur
inghurricaneevacuationsintheUnitedStates[5,9–14].
Althoughondemandridesourcinghasmanyadvantagesinevacuations,inappro
priateplanningmayleadtonegativeimpacts.Theridesourcingplatformsconsistofa
typicaltwosidedmarket,andmanyinfluentialworksontheeconomicsoftwosidedmar
ketshavebeenstudiedintheliterature[69–74].Thedynamicpricingstrategywhichhelps
tobalancevaryingdemandandsupplyiscrucialforridesourcingplatforms.Cachonet
al.[75]studiedtheperformanceofthefixedprice/wageandtheoptimaldynamicpricing
contract,withresultsshowingthatthelattercansubstantiallyincreaseplatforms’profit.
Castilloetal.[76]proposedadynamicpricingmethodtoavoidhighpriceswhendemand
ishigh.Theroleofoptimalpricesandtheintermediary’sshareofrevenuewasstudiedby
Bikhchandani[73].Thespatialdifferentiationandnetworkexternalityindynamicpricing
hasbeenexploredbyWuetal.[74].Zhaetal.[77]studiedthespatialdifferencebetween
eachregionandproposedanoptimizationmethodforgeometricmatchingandpricing
forridesourcingmarkets.
Manystudieshaveexploredtheneedtoimprovetheoperationofondemandride
sourcingduringregulartimes.However,verylimitedresearchhasbeenconductedon
emergencyevacuations.Therecentresearchfoundintheliteratureconsistsofsurveyre
latedstudiestoaddressquestionssuchaswhetherdriverswouldbewillingtoprovide
ridesinevacuationsandthepreferencetouseridesourcingplatformsduringevacuations
[6–8].Lietal.[7]investigatedtheuseofridesourcingservicesfornonoticeevacuations
inChina;thestudyshowsthatamajorityofdriversarewillingtoparticipateinevacua
tions.Mostmaledrivers(52outof59)arewillingtoprovideservicewhentheirfamily
membersareinthesafearea,andsingle,young,maledriversshowstrongwillingness:10
ofthe11indicatedwillingnesstoprovideservicesinevacuation.ThestudyinWongand
Shaheen[6]shows59%to72%ofdriversarewillingtosharepersonaltransportationdur
inganevacuation.BorowskiandStathopoulos[8]exploredevacuationdemandfromsur
veydatacollectedinthethreepopularmetropolitanareasintheUnitedStates.Theresult
showsridesourcingwasselectedasapreferredevacuationmode17.6%ofthetime,while
drivingwasselected49.5%ofthetime,transit34.2%,andbike/walking12.9%.Thefeasi
bilityofleveragingthesharingeconomyinevacuationswasstudiedintheliterature
[3,5,6],whichpointedoutthatdriveravailabilityandpricearethebiggestconcernswhen
Sustainability2021,13,44445of22
usingridesourcingservices.However,tothebestofourknowledge,nostudyhasyet
paidsubstantialattentiontothemodelingofthisprobleminthecontextofevacuation
operations.
Figure1.Participationofridesourcingservicesinhurricaneevacuations.
3.ProblemDescriptionandMethodologyOverview
NYCEmergencyManagement(NYCEM)isresponsibleforemergencyplanningand
preparation.Figure2showsthe2016hurricaneevacuationzonemapprovidedbyNY
CEM;thezonesarecolorcodedandlabeledasrepresentedonthemap.Therearesixhur
ricaneevacuationzones,rankedbytheriskofstormsurgeimpact,withZone1beingthe
mostlikelytoflood.Duringanevacuation,thecitywillorderresidentstoevacuatede
pendingonthehurricane’strackandtheprojectedstormsurge.
Figure2.HurricaneevacuationzonesinNYC(Source:NYCEM).
Sustainability2021,13,44446of22
3.1.AvailableTrafficModesinEvacuation
AccordingtoAmericanCommunitySurvey[1],carownershipinNYCandManhat
tanis46%and23%,respectively.Assumingallmembersofahouseholdwillusethe
householdcartoevacuate,46%ofpeopleinNYCwillevacuatebythemselves,and54%
ofhouseholdswithoutaccesstopersonalcarswillneedtofindotherwaystoevacuate.
Traditionally,transitisthemaintransportationmode.TheexperienceofHurricaneSandy
indicatedhowmuchNYCdependsonthemasstransitsystem,especiallybusesbecause
railisoftennotavailableintheouterboroughs.However,largescalemassevacuation
mayoverextendthepublictransitsystemunderextremeconditions[78].Forexample,
duringHurricaneIrene(2011),thesubwaysysteminNYChaltedservice,andstations
weredamagedasaresultofrainandflooding[17].Inaddition,with0.2millioncarless
peopleinZone1and1.61millioncarlesspeopleinallevacuationzones,busesmightbe
abletosupportsomerangeofevacuation,buttheycannotservealargenumberofevac
ueesinseveredisasters,nottomentionmembersofthemobilitydisabledpopulation.
Taxisalsoplayedanimportantroleduringpastevacuationevents.Comparedto
busesandsubways,taxiscanbeflexibleintermsoftimeandlocation,andtheycansuc
cessfullyevacuateasmallpopulation.However,formassevacuation,thenumberofex
istingtaxiswouldfallfarshortofsatisfyingthedemand(NYChasabout17,000taxicabs).
Additionally,taxicompanies’ratesaresetbylocalgovernmentsandcannotrisebecause
ofevacuation,butwithoutextracompensation,manytaxidriversmaynotbewillingto
workduringextremeweatherconditions.
Micromobilitycanbeanotheralternativetrafficmodeduringemergencyevacua
tions.Bicyclesandescootersareconvenientvehiclesforshortdistancetravel,especially
inverydenselypopulatedurbanareassuchasNYC.ThearticlebyMartin[79])statesthat
peoplewhousedbicyclesduringHurricaneKatrinawereabletoevacuatefasterthancar
usersbecausetheycouldavoidsittingintraffic.ThesurveyconductedbyBorowskiand
Stathopoulos[8]showsthatbiking/walkingwasselectedasapreferredevacuationmode
12.9%ofthetime.Inthecontextofmassevacuation,however,theuseofmicromobility
requirescarefulplanning.Thestreetsmayneedtoberedesignedwithdedicatedmicro
mobilitylanes,andphysicalbarrierssuchasbollardsorcurbsshouldbetakenintocon
siderationforsafetyissues.
NYChasthelowestrateofprivatecarownershipinthenationandthehighestnum
berofridesourcingvehicles.Inthepastfewyears,therapidgrowthofappbasedelec
tronicdispatchservices,suchasUberandLyft,haschangedthewaypeoplegetaround.
Asof2018,therewereabout130,000forhirevehicles(FHVs),mainlyridesourcingvehi
cles,inNYC[80].Generally,ridesourcingcompaniesrelyonmobilephonesandinternet
toprovideservices.Thismayraisetheconcernthatnoteveryonehasaccesstomobile
phonesandinternet.ResearchbyPewResearchCenter[81]foundthat19%ofAmericans
donothaveasmartphone,and4%ofAmericansdonothaveanykindofcellphone.Vul
nerablepeoplewithoutaccesstomobilephonesmayrequireassistanceduringevacua
tions,perhapsintheformofpublicagenciesworkingwithridesourcingcompaniesto
planthesetripsinadvance.Formostotherpeople,theuseofsmartphonesandrealtime
GPSlocationenablesridesourcingservicestoconnectriders,drivers,andvehiclesmore
quicklyandeffectivelyinthecaseofnaturaldisasterssuchashurricanes,whereevacuees
havearelativelylongertimetoreacttoevacuationordersbytheauthorities.Moreover,
servicedisruptionsthatmakeitdifficulttousecellphonesduringnonoticeevents,such
asearthquakesandhumanmadedisasters,arenotexpectedtooccurinthecaseofhurri
caneevacuations.However,itisimportanttoconsiderpossiblelossofwirelessservices
incertaincaseswhenplanningtouseridesourcingservicesthatdependoncellphones
[82].
AlthoughpublictransitisdominantinNYC,ridesourcingservicescansometimes
bemorepreferredthanthetransitsystem.ManyNewYorkersuseUberorLyftbecause
theyarecomfortable,private,andeasytoaccess.AccordingtoMetropolitanTransporta
tionAuthority(MTA)ridershipreports[83]andTaxi&LimousineCommission(TLC)trip
Sustainability2021,13,44447of22
data[80],thepercentageofannualridershipofFHVsandtaxisin2017was18%.The
modalsplitbetweentaxisandFHVswasestimatedbytheiraveragedailytripsin2019—
27%oftripswerecompletedbytaxis,while73%oftripswerecompletedbyFHVs[84].
Withpositivefeedbackreceivedforservicesprovidedduringpreviousdisasters,ride
sourcingserviceshavethepotentialtobeanimportanttrafficmodeinevacuations.
3.2.TheRoleofRideSourcingServicesinEvacuationManagement
RussoandRindone[85]classifiedemergencymanagementactionsintofourcatego
ries:Prevention/mitigation,preparedness,response,andrecovery.Prevention/mitiga
tionscompriseactivitiescarriedoutinadvancetoreducetheimpactofthedisaster,in
cludinglandmanagementandplanning,publicinformationcampaigns,andeducational
programs.Preparednessensurescommunities,resources,andservicescanrespondtothe
impactandincludesactivitiessuchasevacuationplanning,exercising,andtraining.Re
sponseactivities,whichcontrolormodifytheemergency,includeimplementationof
emergencyplansandmobilizationofresources.Thelastcategory,recovery,includesac
tivitiesandservicestosupportcommunityreconstructionafteremergencysituations.Suc
cessfulevacuationiscloselyrelatedtotiming.Whensufficienttimeisavailable,apredes
ignatedevacuationplancaneffectivelymovepeopletosafeareas.However,itishardto
moveallthepeoplewhenevacuationtimeislimited.Inthiscase,awelldesignedemer
gencyplanforshortnoticeeventscanhelpreduceriskandmovemorepeople.Inmany
cities,therearealsoshelterinplaceplansforpeoplewhocannotevacuate[86].
Ridesourcingservicescanplayapromisingroleineachpartoftheemergencyman
agementprocess.Intheprevention/mitigationstage,ridesourcingcompaniescanpartner
withgovernmentstoplantripsforindividualswithspecialneedsinadvance,provide
resourceinformation,andhelpincreaseemergencyeducationtoimprovepeople’swill
ingnesstoshare.Inthepreparednessstage,ridesourcingcompaniescanpartnerwith
governmentstoplantripsforindividualswithspecialneedsinadvance.Trainingactivi
tiesareimportantinriskreductionandcanimproveevacuationplanning[87].Special
trainingandexercisescanbeprovidedtointeresteddrivers,whocanthenassistallpeople
inemergencies[3,8].Intheresponseandrecoverystages,ridesourcingcanhelpdistribute
resourceinformation,transferevacueeswithspecialneeds,andprovidetravelservices
duringtheevacuationandintherecoveryperiodthatfollows.Themethodologypro
posedinthispapercanprovideinsightsforpublicofficialsandridesourcingcompanies
touseintheiremergencymanagementprocesses.
3.3.MethodologyOverview
Weproposeamathematicalmodeldesignedtobalancethedemandandsupplyfor
ridesourcingservicesinevacuations.Thespatialcharacteristicofthemodelcanprovide
differentpricesettingsinsafeareasandevacuationareas.Thetemporalcharacteristicwill
quantifytheproportionofpeoplelikelytoevacuateindifferenttimeperiods.Themeth
odologyframeworkisplottedinFigure3.Thebidirectionalarrowsindicatethatelements
interactwitheachother.Forexample,thepricesettingsinthestrategyboxwillaffectde
mandandsupply,whichinturnwillaffectprices.
Sustainability2021,13,44448of22
Figure3.Thelogicalframeworkofthemethodology.
4.ModelingApproach
4.1.Notation
ThelistofvariablesusedinthissectionissummarizedinTable1.
Table1.Listofvariables.
NotationDescriptionVariables
𝑝Pricetopassengersinregion𝑖
𝑤Wagetodriversinregion𝑖
𝑣Passengers’utilityfortakingridesourcingservices
𝑐Drivers’costforprovidingservicesinregion𝑖
𝐹Thecumulativedistributionofpassengerutility𝑣withdensityfunction
𝑓
𝐹Thecumulativedistributionofdrivers’costwithdensityfunction
𝑓
𝑣Passengers’utilityforchoosingotheroutsideoptions,suchastransit
𝑣Drivers’utilityforchoosingnottoparticipate
𝐷Demandofridesourcingservicesinregion𝑖
𝑆Supplyofridesourcingservicesinregion𝑖
𝜇Thenumberofdemandsinregion𝑖
,
thenumberofsuppliesisone,𝜇canbeviewedasthenum
berofdemands
p
erunitnumberofsu
pp
lies
𝜃Marketti
g
htnessinre
g
ion𝑖
,
e
q
ualto𝜃𝑆/𝐷
𝑀𝐷,𝑆Thematchin
g
functionofdemandandsu
pp
l
y
,indicatin
g
thenumberofmatchedtri
p
sinre
g
ion𝑖
𝑚𝜃Matchin
g
p
robabilit
y
of
p
assen
g
ersinre
g
ion𝑖
𝑚𝜃Matchingprobabilityofdriversinregion𝑖
𝛼,𝛽Weightparameters
4.2.Demand,Supply,andDynamicPricing
Theridesourcingservicesconsistofatypicaltwosidedmarket,wherepriceaffects
bothdemandandsupply.Usually,wecallthefarechargedtopassengersthepriceand
remunerationspaidtodriversthewage.Therearetwotypesofuncertaintyduringevac
uation.Thefirstisthedrivers’costtoprovideservicesinevacuations.Forexample,since
somedriversmustalsoevacuatetheirfamilies,participationcanbecostlyforthem,while
Sustainability2021,13,44449of22
theservicesofdriverswhoareavailableandwillingtohelptheevacueescanbelesscostly.
Thesecondtypeofuncertaintyoccursatthedemandlevel.Onregulardays,thedemand
forridesourcingservicescanbehigherduringpeakhoursorloweratoffpeakhours.In
evacuations,however,thedemandcanbeconstantlymuchhigherwhilethenumberof
availabledriverscanbemuchlowerthanregulardays.
Tobespecific,weconsiderasystemwithtworegions:Thedisasterimpactedregion,
whereevacuationordersareissued,andthesafe/normalregion.Inthissystem,passen
gerscanuseeitherridesourcingservicesorotheroutsideoptions(e.g.,passengerscan
travelbypublictransitifthepriceofridesourcingserviceistoohighforthem).Following
thepreviousstudiesonthetwosidedmarket[73,74,77],weassumeeachpassengerwill
haveautility𝑣fortakingridesourcingservices,whichisanindependentdrawfromthe
cumulativedistributionfunction𝐹withdensityfunction𝑓,andeachpassengeralso
hastheutility𝑣forchoosingotheroutsideoptions.Onthesupplyside,driverswillhave
differentcostsforprovidingservicesindifferentregions.Weassumethepairofcost
𝑐,𝑐∈0, 𝛾,whichisindependentlydistributedacrossdriverswithcumulativedis
tributionfunction𝐹anddensityfunction𝑓.Eachdriveralsohastheutility𝑣for
choosingnottoparticipate.
Theridesourcingcompaniesknowthenumberofpassengersandthenumberof
driversinregion𝑖,aswellasthedistributionsofagents’types𝐹,𝐹.However,eachpas
sengers’valueordrivers’costisnotknown,sointhispaperweonlyfocusonaggregate
levelanalysisanddonotdoperfectpricediscrimination.Thetransactioncostandother
fixedcostsareignoredsincetheydonothaveamajorimpactonthepricingstrategy.Let
𝑖1representtheregionwithevacuationorderand𝑖2representthesaferegion.The
ridesourcingcompanieswillselectapairofprices𝑝,𝑝forpassengersandapairof
wages𝑤,𝑤fordriversindifferentregions.Forexample,anypassengersinregion𝑖
withvaluesgreaterthan𝑝arewillingtousetheridesourcingservice,andanydriverin
region𝑖withcostlessthan𝑤arewillingtoprovideservices.Atregulartimes,𝑤𝛿𝑝,
where𝛿isafixedcommissionratethatenablesthemarkettofunctionandtheplatform
toearnprofits.AswearemodelingthepriceinevacuationsandUberindicatedthey
wouldwaiveallservicefees,thefixedcommissionrateisnotconsideredinthispaper.
If𝜇representsthenumberofdemandsinregion𝑖andthenumberofsupplyis
one,𝜇canbeviewedasthenumberofdemandsperunitnumberofsupply.Weassume
thenumberofmatchedtripsinregion𝑖isamatchingfunctionofdemandandsupply
𝑀𝐷,𝑆.Thematchingfunctiongivesthemaximalnumberofmatchedtripsandhasthe
followingproperty:
𝑀𝜌𝐷,𝜌𝑆 𝜌𝑀𝐷,𝑆forany𝜌0(1)
Let𝜃representthemarkettightnessinregion𝑖,whichisequalto𝜃𝑆/𝐷.Based
onthepropertyofthematchingfunction,thematchingprobabilityofpassengerinregion
𝑖is:
𝑚𝜃𝑀1, 𝜃(2)
Thematchingprobabilityofdriversinregion𝑖is:
𝑚𝜃𝑀1/𝜃,1(3)
Wecanfindthat𝑚𝜃isstrictlyincreasingfor𝜃∈0,1and𝑚𝜃isstrictlyde
creasingfor𝜃1.Inthispaper,weassumethetotalnumberofmatchedtripsisequal
totheminimalnumberofdemandandsupply,whichisequalto:
𝑀𝐷,𝑆 𝑚𝑖𝑛𝐷,𝑆(4)
Toestimatethedemandforridesourcingservices,weassumepassengerswillaccept
theserviceonlyifthenetpayoffislargerthantheiroutsideoptions:
Sustainability2021,13,444410of22
𝑚𝜃𝑣𝑝𝑣(5)
Thedemandinregion𝑖underprice𝑝willbe:
𝐷 𝜇1𝐹𝑝𝑣/𝑚𝜃 (6)
Similarly,driverswhochoosetoprovideserviceswithdifferentwagesindifferent
regionswillbewillingtoprovideserviceinregion𝑖onlyiftheearninginregion𝑖is
higherthaninanotherregionandhigherthantheutilityofnotparticipating(𝑖 means
notinregion𝑖):
𝑚𝜃𝑤 𝑐𝑚𝑎𝑥𝑣,𝑚𝜃𝑤 𝑐(7)
Equation(7)canbetransferredto:
𝑚𝜃𝑤 𝑐𝑣𝑐𝑤𝑣/𝑚𝜃(8)
𝑚𝜃𝑤 𝑐𝑚𝜃𝑤 𝑐𝑐𝑤
𝑤 𝑐(9)
Withdrivers’cost𝑐,theunitsofserviceprovidedinregion𝑖willbeequalto:
𝛺𝑐,𝑐0, 𝛾|𝑐𝑤𝑣/𝑚𝜃,𝑐𝑤
𝑤 𝑐 (10)
4.3.TheOptimizationModelforPricingStrategyinEvacuation
Weproposeamodeltooptimizetheridesourcingmarketinevacuations.Wedivide
thestudyareaintotworegions:𝑖1representstheregionwithanevacuationorder,
while𝑖2representsthesaferegion.Theridesourcingcompaniesorgovernmentcan
determinethepricesforpassengersandwagesfordriversintworegions𝑝,𝑝,𝑤,𝑤.
Atregulartimes,ridesourcingcompaniessetpricesandwagestomaximizetheirprofit,
whilethemainobjectiveinevacuationmodelingistomaximizethenumberofevacuated
peoplewithinalimitedtime.
Toincreasethesupplyofdriverswhilechargingalowerpricetopassengersduring
anevacuation,subsidiescanbeprovidedbyprivatecompaniesorthegovernmentasan
incentivefordriverstoparticipate.Thesimultaneousoptimizationofthesystemconsid
eringincreasingmatchedtripsanddecreasingsubsidycostsrequiresadesignedtrade
off.Generally,givingahigherwagetodriverswhilechargingalowerpricetopassengers
canincreasethetotalnumberofmatchedtrips,butsubsidycostswillbecomeaburden
fortheridesourcingcompaniesorgovernment.Weproposetomodeltheproblemby
optimizingtheconflictingobjectiveofmaximizingthenumberofmatchedtripsinthe
evacuationregionwhileminimizingthecostofsubsidies.Tosolvethemultiobjective
problem,aweightedapproachwaschosensothatthesumoftwoconflictingobjectives
willbemaximized.Insteadofhavingasingleoptimalsolution,themodelcanprovidea
setofsolutionsbychangingtheweightparameters(𝛼,𝛽.
Aswehavementioned,theservicefee(commissionrate)isnotconsideredinevacu
ation,soallthepriceschargedtopassengerswillgotodrivers.Additionally,thesubsidy
willonlybeprovidedfordriversintheevacuationregion,so𝑤𝑝while𝑤𝑝.This
canbemodifiedinfuturepractices,suchasaddingthecommissionrateinthesaferegion
so𝑤𝛿𝑝,where𝛿isafixedcommissionrate.Thecostofsubsidiesforeachtripequals
𝑤𝑝,whichisthedifferencebetweenthewagepaidtodriversandthepricechargedto
passengers.ThenonlinearlyconstrainedoptimizationproblemisformulatedinModel1.
Model1
𝑚𝑎𝑥
,,, 𝛼𝑀𝐷,𝑆 𝛽𝑀𝐷,𝑆𝑤𝑝
(11)
Sustainability2021,13,444411of22
s.t.𝐷𝑆𝜇1𝐹𝑝𝑣/𝑚𝜃
𝑓
𝑥,𝑦𝑑𝑥𝑑𝑦 (12)
𝑤𝑝 𝑎𝑛𝑑 𝑤𝑝(13)
𝑝,𝑝,𝑤,𝑤∈ℜ
(14)
where𝛼∈0,1,𝛽∈0,1,and𝛼𝛽1.Generally,theoptimalsolutionishardtoob
tainfromModel1.However,withsomeappropriateassumptionsforthedistributionof
𝐹(.)and𝐹(.),wecanfindtheexistenceoftheoptimalsolution.
Assumption1.Thecumulativepassengervaluedistribution𝐹(.)isstrictlyconcave.Thecu
mulativecostdistribution𝐹(.)isstrictlyconcave,sothejointdistributionofsupplyfunction
𝑓𝑥,𝑦𝑑𝑥𝑑𝑦isstrictlyconcave.
Assumption1requiresthatthedensityfunction𝑓isadecreasingfunction.Many
commonlyuseddistributionssatisfythisassumption(e.g.,uniform,exponential,Pareto).
Thejointstrictconcavityof𝑓𝑥,𝑦𝑑𝑥𝑑𝑦alsohasasimilarproperty.Thisshowsthata
higherpassengerutilitywillleadtofewerpassengers,whilemoreservicewillbeprovided
withhigherwages.Tosimplifyouranalysishere,intheremainderofthepaperweassume
that𝐹and𝐹areuniformlydistributedon0,1and0,1,respectively.Similaras
sumptionsforridesourcingservicesatregulartimescanbefoundinBikhchandani[73]
andWuetal.[74].Sinceweonlyfocusontheapplicationofridesourcingservices,to
simplifythemodel,theoutsideoptionsareassumedtobe0(𝑣𝑣0).Then,wehave
thedemandfunctioninregion𝑖:
𝐷 𝜇1𝐹𝑝(15)
FromEquation(10),theprovidedservicesforthetworegionsare:
𝛺𝑐,𝑐0,1|𝑐𝑤, 𝑐𝑤𝑤 𝑐(16)
Proposition1.BasedonAssumption1,auniquetupleofoptimalprices𝑝
,𝑝
,𝑤
,𝑤
forthe
objectivefunctioninEquation(11)canbeobtained.
Proof.Withthemarketequilibriumrequirement,𝑆𝐷,theobjectivefunctioncan
bewrittenas:
𝑚𝑎𝑥
,,,Π 𝛼𝑆 𝛽𝑆
𝑤𝑝(17)
BasedonEquation(15)and𝐷𝑆,thepassengerpriceisequalto:
𝑝𝐹
1𝑆
𝜇(18)
Theobjectivefunctioncanbewrittenas:
𝑚𝑎𝑥
,,, Π 𝛼𝑆 𝛽𝑆
𝑤 𝐹
1𝑆
𝜇(19)
Assumption1impliesthat𝐹
isconvexandstrictlyincreasing;thejointsupply
function𝑓𝑥,𝑦𝑑𝑥𝑑𝑦isalsoastrictlyconcavefunction.Theassumptiononthedistri
butionfunctionsshowsthatthesecondaryderivativeofthefunctionΠisnegativeandΠ
isstrictlyconcave,whichguaranteestheoptimalityanduniquenessofthesolutionin
Model1.
Rememberwesettworegions:𝑖1representstheregionwiththeevacuationor
der,while𝑖2representsthesaferegion.Wecandivideanystudyareaintothesetwo
Sustainability2021,13,444412of22
regions.ThesupplyfunctionscanbeobtainedwithEquation(16)and𝑆
𝑓𝑥,𝑦𝑑𝑥𝑑𝑦undertwoconditions:
1. IfthewageinRegion2ishigherthanRegion1𝑤𝑤:
𝑆
𝑤𝑤𝑤𝑤,𝑆
𝑤𝑤(20)
2. IfthewageinRegion1ishigherthanRegion2𝑤𝑤:
𝑆 
𝑤 𝑤,𝑆
𝑤𝑤𝑤𝑤(21)
Withtheequilibriumcondition,thepriceforpassengerscanbeobtainedbyhaving
demandfunctionequalsupplyfunction𝐷𝑆.UsingEquation(15),thepriceswillbe:
𝑝 1 𝑆/𝜇(22)
Equations(20)and(21)showthatthewageinregion𝑖willdirectlyaffectthenumber
ofservicessuppliedinthatregion:Ahigher𝑤willincreasethesupply𝑆inregion𝑖
whiledecreasingthesupplyinanotherregion𝑆.Thepriceequation𝑝 1 𝑆/𝜇
showsthatthewagewillaffectthepassengerprice.Thisisbecausethespatialdifference
ofwagewillchangethesupplydistributionindifferentregions,andthesupplywillin
turnaffectthedemandinthesameregion.WithAssumption1,Model1canbetransferred
toModel2below.
Model2
𝑚𝑎𝑥
,,, 𝛼𝑆 𝛽𝑆
𝑤𝑆/𝜇1(23)
s.t.𝐷𝑆𝜇1𝐹𝑝
𝑓
𝑥,𝑦𝑑𝑥𝑑𝑦(24)
𝑤𝑝 𝑎𝑛𝑑 𝑤𝑝(25)
𝑝,𝑝,𝑤,𝑤∈ℜ
(26)
Thesequentialquadraticprogramming(SQP)algorithmbuildinPython,whichisan
iterativemethodforconstrainednonlinearoptimization,isusedtosolvetheproblem.
4.4.TimeDependentDemandandSupplyofRideSourcingServicesinEvacuation
Inevacuations,thedemandcannotbeevenlydistributedineachhour,somodeling
timedependentevacuationdemanddeterminesthenumberofpeopleevacuatingand
spreadsthemtemporally[26,88,89].Thisistypicallydonebyusingademandresponse
curve,whichestimatestheproportionofpeoplebeginningtoevacuatewithineachtime
interval.TheU.S.ArmyCorpsofEngineers(USACE)proposedthreetypesofresponse
curves—slow,median,andfast—basedonbehavioralanalysisofpaststorms[90].Lietal.
[20]estimatedtheevacuationresponsecurveduringHurricaneIreneinCapeMay
County,NewJersey.AsthecalibratedScurvesobtainedusinglogitfunctionsareob
servedtofittheempiricaldatabetter,thiswillbeusedasthedemandresponsefunction
inthispaper.
Similarly,weassumetheavailabilityofridesourcingdriversduringanevacuation
istimedependent.Moredriversarewillingtoofferservicesatthebeginningoftheevac
uation,butastimegoesbyitbecomesmoredangerousfordriverstoprovideservices.As
aresult,thesupplyofdriversshouldbeatimedependentdecreasingcurve.Sincethe
dataandrelatedstudiesarelimitedforestimatingthesupplyresponsebehaviorofride
Sustainability2021,13,444413of22
sourcingservicesinpastevacuations,weassumethesupplyisadecreasingScurvesim
ilartothedemandmodel,butcontinuouslydecreasingwithtimet.Thecumulativede
mandandpercentsupplyfunctionsareequalto:
𝑃
,
1/1𝑒𝑥𝑝𝑎
𝑡𝐻
(27)
𝑃
,
1/1𝑒𝑥𝑝𝑎
𝑡𝐻
(28)
where𝑃
,
isthecumulativedemandpercentageofevacueesattimet,𝑃
,
isthepercent
ageofsupplyattimet,and𝑎
,𝑎
,𝐻
,𝐻
areshapeparameters.𝑎
givestheslopeofthe
cumulativedemandloadingcurve,and𝐻
isthehalfloadingtime,whenhalfoftheevac
ueesinthesystemhavedeparted.𝑎
givestheslopeofthetrafficsupplycurve,and𝐻
indicatesthetimewhenhalfoftheservicescanbeprovided.Theparametersshouldbe
calibratedusingrealdatainthefutureifavailable.
Figure4showsexamplesofevacuationdemandandsupplyresponsecurves.Figure
4ashowsthecumulativeevacuationdemand,Figure4b,cshowthepercentpopulation
evacuatedandpercentservicesuppliedineachtimestep(Tisthetotalevacuationtime),
respectively.Tostudytheimpactofdifferentevacuationresponsebehaviorsonthetotal
matchedtripsandcostofsubsidiesinanevacuation,wecandividetheentireevacuation
intomultipletimeperiods.Foreachtimeperiod,wecanuseModel2tooptimizetheprice
settings,thensumthematchedtripsandcostovertheentireevacuation.
(a)
(b)(c)
Figure4.Examplesofevacuationresponsecurvesbythelogitmodel;(a)cumulativeevacuationcurves;(b)percentevac
uatedateachhour;(c)percentsupplyateachhour.
Sustainability2021,13,444414of22
5.NumericalStudy
Ridesourcingservicesmayhelpaddressthelimitedresourcesandsocialequity
problems[3].Weproposedamathematicalmodelthatcanhelpbalancedemandand
driversupplythrougharealisticpricingmechanismforridesourcingservicesinevacua
tions.Subsidiesareconsideredanincentivetohelpincreasethesupplyofdriversinevac
uations.Themainobjectiveofevacuationrelatedmodelingistomaximizethenumberof
evacuatedpeoplewithinalimitedtime.Aweightedmultiobjectivemodelisusedtomax
imizethetotalnumberofmatchedtripsintheevacuationregionwhileminimizingthe
costofsubsidies.Infuturepractice,ridesourcingcompaniescanusethemodeltodeter
mineprices,andgovernmentcandevelopregulationpoliciesbasedonthemodelandre
sults.
Theproposedpricingstrategyistestedusingahypotheticalhurricaneevacuation
scenarioinNYC.TaxiandFHVtripdataarereleasedbyNYCTLC[80].Thetaxidataset
isavailablefrom2010,whileFHVdataisavailablefrom2015.Themostrecentevacuation
orderwasHurricaneSandyin2012.NYCofficialsissuedmandatoryevacuationorders
forEvacuationZone1,whichhadabout370,000residents,onSunday,28October2012.
WeusetaxidataduringHurricaneSandytoestimatethedemandandsupplyofride
sourcingservicesbecausethisisthesafestwaytoevaluatethemodelperformancewith
realisticdatafrompreviousevacuationevents.Thiscanbeimprovedinthefuturewith
reliabledataorsurveyresultsfordemandandsupplyestimationofridesouringservices
inevacuations.Figure5showsthenumberoftaxitripsbypickuplocationsintheevacu
ationzone.WecomparedthetaxitripsonSunday,28October2012(evacuationorder
issuedinHurricaneSandy)andSunday,14October2012,whichistwoweeksbefore
Sandywithnormalweathercondition.Thecolorsinouterboroughsarelighterduringthe
evacuationperiodcomparedtonormaltimeperiods,whichindicatesalowernumberof
taxitripsintheareaaftertheevacuationorderisissuedbeforethelandfallofHurricane
Sandy.
(a)HurricaneSandy(28October2012)(b)Normaltime(14October2012)
Figure5.Thenumberoftaxitripsbypickuplocationintheevacuationzones;(a)themandatoryevacuationorderedon
28October2012duringHurricaneSandy;(b)normaltimetwoweeksbeforeSandyon14October2012.(Thehighlighted
areaisthecasestudyarealocatedinManhattanfrom60thStreetsouth).(Datasource:NYCTLCdata).
ThecasestudyareaislocatedinManhattanfrom60thStreetsouth,whichishigh
lightedinFigure5.TheFHVtriprecordsareonlyavailablefrom2015,butthedemand
andsupplyofFHVtripsinfutureevacuationeventsshouldhavesimilartrendsastaxi
dataduringHurricaneSandy.Thenumberoftaxipickuptripsandthecorresponding
Sustainability2021,13,444415of22
ridershipineachzoneareshowninTable2.Ridershipisestimatedbycountingthenum
berofpassengersfromthetaxitripdata.Thetotalridershipwillbeusedasanapproxi
mateFHVdemand.TheaveragedailytripsinZone1duringSandyevacuationis81%of
theregulartime,whichcanbeanindicationofdecreasedsupplyduringtheevacuation
beforethelandfallofHurricaneSandy.Weassumethepercentdecreasedsupplyinthe
casestudywillbesimilarineachzoneasduringSandy.InOctober2019,theaveragedaily
tripsofhighvolumeFHVsandtaxiswas682,635tripsand243,641trips,respectively.We
assumethetotalsupplyofFHVsinthiscasestudywillbe2.8timesthenumberoftaxi
tripsduringSandy.Theaveragepassengerineachtripis1.7personspervehicle,accord
ingtotaxidatafromtheSandyevacuation,soweassumeeachsupplycanserve1.7de
mands.
Table2.TaxidataduringandbeforeHurricaneSandyinthecasestudyarea.
EvacuationZoneSandyEvacuationBeforeSandy
TaxiTripsTaxiRidershipTaxiTripsTaxiRidership
Zone123,48241,66628,95450,878
Zone215,08927,03116,66629,385
Zone317,86131,62220,82537,022
Zone424,11242,66926,73347,252
Zone540,17170,01143,47276,030
Zone633,63258,96734,21559,373
Table3showsalistofmajorinputparametersforthemodel.Threetypesofdemand
supplyresponsebehaviorswithdifferentshapeparametersaretested:Slowresponse,me
dianresponse,andfastresponse.Theslowresponsecanrepresentmoreproactiveevacu
ationplanningoralessdangerouseventinwhichpeoplewillinitiallyevacuateslowly
andcontinuetoincreaselater.Inafastresponse,manypeoplemayreacttoevacuation
quicklyandbegintoevacuateatanearliertime,sothesupplywillbemainlyneededdur
ingearlyperiods.Whenmoreevacuationtripdataisavailableinthefuture,theshape
parametersofthedemandandsupplyresponsecurvecanbecalibratedwithrealdata.
Table3.Inputparameters.
ParameterSymbolUnitValue
1. Evacuationtime
T
Hour24
2. Passengervaluedistribution𝐹0,
$0,1
3. Drivercostdistribution𝐹 0,
$0,1
4. Demandandsupplycurveparameters
- Slowresponse𝑎,𝐻,𝑎,𝐻‐ 0.2,14,0.2,14
- Medianresponse𝑎,𝐻,𝑎,𝐻‐ 0.3,12,0.3,12
- Fastresponse𝑎,𝐻,𝑎,𝐻‐ 0.4,10,0.4,10
5.1.ComparisonbetweenDifferentPricingStrategies
AssumeahypotheticalevacuationisorderedinZone1.Let𝑖1representtrips
withinZone1and𝑖2representtripsinthestudyareaoutsideofZone1.Tostudythe
impactofevacuationbehaviorsonthetotalmatchedtripsandcostofsubsidies,𝜇ateach
timestepwillbeestimatedfromEquations(27)and(28).Theparametersofdemandand
supplycurveareshowninTable3;𝜇isassumedtobe1.Otherinputparametersare
giveninTable3.Wecomparethreepricingstrategieshere.TheobjectiveofFHVplatforms
istomaximizetheirprofitatregulartimes.Thus,Method1istousethepricingstrategy
atregulartimes,allowingthepassengerpricetobehigherorlowerthanthedrivers’wage
inbothregionsbysettingtheobjectivefunctiontobeequalto:
Sustainability2021,13,444416of22
𝑚𝑎𝑥
,,,𝑆
𝑝𝑤(29)
Then,wetestthemodelperformancewithdifferentweightparametersintheobjec
tivefunction.Weselecttwoextremeconditionswhere𝛼0, 𝛽1and𝛼1, 𝛽0as
Method2andMethod3.Thethreemethodsarebrieflydescribedbelow:
Method1:PricingstrategyatregulartimeswiththeobjectiveinEquation(29).