Do not distribute or copy - UC Davis Graduate School of ...Unitrans of peak demand periods...
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Do not distribute or copy Public Transit Ridership Analysis of The Unitrans Transit System for Resource Optimization
Transcript of Do not distribute or copy - UC Davis Graduate School of ...Unitrans of peak demand periods...
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Public Transit Ridership
Analysis of The Unitrans TransitSystem for Resource Optimization
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TableofContents
ExecutiveSummary................................................................................................................1
1.Introduction.......................................................................................................................1
2.DataCharacteristics............................................................................................................22.1DataBackground........................................................................................................................22.2WeatherandPrecipitation..........................................................................................................32.3DataReduction...........................................................................................................................32.4CompilingData...........................................................................................................................32.5ObservationsofBusLines...........................................................................................................32.6DataCorrelation.........................................................................................................................4
3.ModelAnalysis...................................................................................................................43.1ModelSelection..........................................................................................................................4
3.1.1WintersModel............................................................................................................................53.1.2MultipleRegressionModel.........................................................................................................53.1.3ModelComparison.....................................................................................................................6
3.2ModelInterpretation..................................................................................................................63.3ModelDiagnostics......................................................................................................................73.4Forecast......................................................................................................................................7
4.SummaryandRecommendations.......................................................................................7
Appendix...............................................................................................................................10AppendixA-SupplementalinformationforModelStructureandDiagnostics.................................10AppendixB–SupportinginformationforModelandForecast.......................................................11
References.............................................................................................................................15
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ExecutiveSummary
TheUCDavisUnitranstransitsystemisfacingaconvergenceofseveralproblemsthatcandramaticallyaffectitsoperations.Unitranscontinuestoseeexcessiveridershipduringinclementweatherleadingtoincreasinglydissatisfiedcustomers.Second,alegislativelymandatedminimumwageincreaseinCaliforniawilleffectivelyincreasetheirlaborcostby$800,000annuallystartingin2021.Finally,theUnitransfleetischangingwiththeadditionofthreedoubledeckerbusesthatneedtobescheduledeffectively.UnitransneedsaplantoaddresstheseissuesandhasaskedHATConsultingtomakeananalyticalevaluationandmakerecommendationsforoperationalchange.
AstatisticalanalysisofUnitransoperationsperformedbyHATConsultinghasdevelopedforecastmodelsthatinformUnitransofkeyfactorsthatinfluenceoperationaldecisions.ThesekeyinsightscaninformUnitransofpeakdemandperiodsthroughouttheyear,andpassengerdemandvariationsbasedonprevailingweatherpatterns.Unitranscanutilizethisinformationforvariousoperationalchangessuchasdecreasingtheservicelevelsduringperiodsoflowdemandandresultinasavingsofover$33,000inoperationalcosts.Alternatively,Unitranscanincreasehiringby6%toaccommodatepeakdemandperiodsalongwithdoublingbuslinecapacitybyshiftingbusresources.WithHATConsultingrecommendations,Unitranscanfullyoptimizeitsresourcesandbudgetarydecisions.
1.Introduction
Foundedin1968,withtwovintagedoubledeckerbusesfromLondon,UnitransisthepublicbussystemfortheUniversityofCaliforniaDavis(UCDavis)andtheCityofDavis.With48busesand18routes,Unitranscarriesover4millionpassengersperyear1.Over22,000passengersusethebussystemonanormalday.Thedrivers,supervisors,andmuchofthesupportstaffforUnitransareUCDavisstudentsprovidingtransportationtostudents,andcommunitymembersastheytraveltodowntownDavis,schools,hospitals,shoppingcenters,theatresandmanyotherdestinations.
Unitransreceivesitsrevenuefromvarioussources.ThebulkoftherevenuecomesfromtheAssociatedStudentsofUCDavisintheformofaTransitFee.Forfiscalyear2016-2017,thefeeprovided$2,574,746.Othersourcesincluded$710,000fromtheCityofDavis,$20,000fromYoloCounty,$1,300,000fromFederalfunding,$265,000fromFares(estimated),$31,000fromadvertisingand$170,000frommiscellaneoussources2.SincefundingfromridershipfaresaccountforsuchasmallpartofUnitrans’revenues,itdoesnotneedtoheavilyrelyonittofunditsoperations.
Despitehavingfairlystablesourcesofrevenue,Unitransisfacinganumberofissues.Thetransitsystemisfacingagrowingannualdeficitcomingfromtheiroperationallaborcosts.LegislationthatincrementallyraisestheCaliforniaminimumwageto$15perhourby2021isthebiggestdriverofthisdeficit.Unitransestimatesa$200,0003annualincreaseinlaborcoststhrough2021.Additionally,Unitranscontinuestoexperienceovercapacityridershipduringpeakdemandperiodscoincidingwithinclementweather.Thishasledtocrowdedbusesandunhappypassengers.Unitransusestwo“Tripper4”busestohelpalleviatethecrowding,butitisstillinsufficient.Lastly,Unitransplanstoreplace
1http://unitrans.ucdavis.edu/about/2Palmere,A.pp.5-6.3Palmere,A.pp.6.4A“Tripper”busisasparebusintheUnitransfleetthatisdeployedtocrowdedbuslinesasneededtoincreasecapacity.Unitranscurrentlykeep2singledeckbusesinreservetofillthisrole.
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threeoftheirregularbuseswithdoubledeckerbuseswithacapacityof100passengerseach.Unitransneedsawaytoefficientlyutilizetheirresourcesandplanforfutureoperationstoincreasecustomersatisfaction.
HATConsultingvolunteeredtoanalyzeUnitrans’ridershipdatatodeterminepredictiveforecastmodelsandprescriberecommendationstooptimizethetransitsystem’soperations.HATConsultingconcentratedondeterminingpeakridershipperiodsandvariationsinridershipduetoexternalfactors.Fromtheanalysis,HATConsultinghasdeterminedthatthroughouttheyear,Unitransexperiencesseveralperiodsofpeakridershipofover26%thatarecausedbyconditionssuchrainresultinginmorepassengerstoridethebusorperiodsoftheacademicyearsuchasthebeginningandendofquartersthatalsoincreaseridership.Duringtheseweeks,Unitransshouldshifttheirdoubledeckerbusestohighuselines,effectivelyincreasingcapacityfrom60passengersupto200passengersperrun.HATConsultinghasfoundthatUnitransfacesthreeclimatescenarios:ElNino,normalyears,anddroughtyearswhichaffectstheiroverallridership.Withthis,Unitranscanplantoincreasetheirbudgetsby6%foroperationallaborinsupportofincreasepassengersinhighdemandyearsortheycanreduceservicelevelsby2.5%inlowdemandyearsresultinginsavingsofover$33,000andreducingwearandtearonthebusfleet.
TheremainderofthisreportdescribesthemethodsofanalysisthatHATConsultingperformedforUnitransandisbrokeninto4sections;first,istheexaminationoftherawdataprovidedbyUnitranstoobservepossibletrendsandanyfactorsthatmayaffectthetransportationsystem’sridership.Second,aforecastmodelusingdecompositionmethodsisdeterminedandtested.Third,regressiontechniquesareusedtocreateaforecastmodelforUnitransridership.Finally,recommendationsandactionstepsforUnitransbasedonthefindingsandpredictionsofthemodelsareprovidedtoUnitransbyHATConsulting.
2.DataCharacteristicsInthissection,thedatausedfortheanalysiswillbediscussed.Informationonthedatawillbestatedforeachvariableconsidered,thereductionofthedata,thecompilingofthedata,dataobservationsandcorrelations.2.1DataBackground
Figure1:UnitransRouteMap
HATConsultingreceivedrawdatafromUnitransfromthetimeperiodbetweenJanuary,2014andMay,2017.Atotalofforty-fiveExcelfileswerereceivedandeachincludeddataon:dateofservice,timeof
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service,busidentificationnumber,busstoplocation,busstopidentification,triprouteandidentificationnumber,andthenumberofboardingandde-boardingpassengersforeachstoplocation.Thisaccountedforatotalofthreemilliondatapointstobeevaluated.ToillustratehowsomuchdataiscollectedconsiderFigure1whichshowsthebusroutesforweekdayservices,andtheovalsectionswhichhighlighttheareasthatwillbethefocusoftheanalysis.ThehighlightedregioncontainstheG-,J-,andW-linetriprouteswhichwerethetopthreeroutesinregardtothetotalnumberofpassengers.Theserouteshavethelargestridershipbecausealongtheirpaththeyhaveahighnumberofrentalapartmentswheremostofthetenantsarestudents.Anoteonthedataprovided;therewereperiodsofzeroridershipduringschoolbreakssuchasspringbreak,andholidaybreak.Thezeroridershipvariesyear-to-year,andismainlyattributedtotheUnitransmanagementwhodecideifbuseswillrunduringthosetimes.Tocompensateforthezeroridership,historicalaveragesreplacedthosedatapoints.
2.2WeatherandPrecipitationInadditiontobusroutesdata,thedailytemperatureandprecipitation wasaddedtothemodel.WeatherdatafortheyearsevaluatedwerecollectedfromtheCaliforniaIrrigationManagementInformationSystem(CIMIS)5.
2.3DataReductionInreducingthebuslines,onlythedateofserviceandthenumberofpassengerboardingwasconsidered.Sinceweonlyfocusontotalridership,informationregardingspecificstops,bususedandde-boarding(whichdirectlycorrelatestoboarding’s)wereunnecessarytoourevaluation.Thepassengerswerethenclustered,andsummed,intogroupsofsevendaystocaptureridershipbyweek.Eachweekwasuniquelyidentifiedwithanindextoaccountforallfifty-twoweeksinayear.Similarly,theweatherdatawasgroupedintoweeklyclusters.Thedailytemperaturedatawasaveragedforeachweek,andtheweeklyrainwassummedup.Thisdatawasusedforallthreebuslinesintheanalysis.
2.4CompilingDataWiththedatareductioncomplete,threedatasetswerecreatedforeachofthebuslinesinconsideration.Insummary,thefinaldatawasformattedthesameandincluded:startingweekofservicenumberofpassengerboardingforeachbusline(G-,J-,orW-line),averagetemperature,weeklytotalrainfall,weeknumericalvaluetotrackweekofobservation,andweeklyindicator.
2.5ObservationsofBusLinesWithourfocusonthreebuslines,webeginoureffortstoobserveanytrendsforthetimeframeweareevaluating.Figure2isanexampleofannualpassengercountfortheW-line,andsimilarplotsfortheG-andJ-linecanbereviewedinAppendixA-1. Thefigurehighlightsthe2015schoolyear,identifyingmajordatessuchasdurationofthequartersession,winterbreak,springbreak,
5CIMISisadatabasethatisintegratedintotheUniversityofCaliforniaStatewideIntegratedPestManagement(UCIPM)program.CIMISwasdevelopedbytheCaliforniaDepartmentofWaterResourcesandtheUniversityofCalifornia,atDavis.Itwasdesignedtoassistirrigatorsinmanagingtheirwaterresourcesmoreefficiently.
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andsummersession.Thetroughsareindicatorsofholidaysthatarerecognizedbytheuniversity,likeVeteran’sDay,ThanksgivingDay,MartinLutherKingDay,tonameafew.Thedatesthataremostimpactfultotheridershiparewinterbreakandspringbreak.Thisobservationisattributedtothelengthofthebreakbeingatleastoneweek,sostudentsaremorelikelytobeoutoftown.Theseseasonaltrendsarealsoobservedfortheportionofschoolyear2014,schoolyear2016,andpartof2017to-date.2.6DataCorrelationTemperatureandrainfallwasincludedinourevaluationtodeterminehowweatherimpactedridership,andthatisshowninFigure3.Thetemperatureandrainfallareseasonal,andtohelpbetterunderstandtrends,thecorrelationvalueswerecalculated,andprovidedinTable1forboardingwithtemperature,andboardingwithrainfall.Thiswascompletedforallthreebuslinesandeachhadsimilarvalues.Thecorrelationvaluessuggestedthatboardingandtemperaturehadaninverserelationship,sowhenthetemperaturedropsandit’scold,ridershipincreasesandviceversa.Asforpassengerandrainfall,ithadadirectrelationshipmeaningthatasrainfallincreasessodoesridership,andwhenrainfall
drops,sodoesridership.Thedirectrelationshipforrainfallandpassengersmakessensesincegoodweatherallowsforalternatemethodsforstudentstocommutetocampus,likeridingtheirbicyclesorevenwalking.Inthenextsection,wewilldiscussthemodelourmodelselectionprocess,themodelthatbestfitsourdata,andprovideinternalandfutureforecasts.
3.ModelAnalysisAfterreviewingthedataanditscharacteristicswemovedintochoosingtheappropriatemodelforthepurposeofforecastingridershipforthenext52weeks.Thisforecastwillbeusedforrecommendationsonbusservicesandstaffinglevels.Duetothehighlevelsofseasonalityinridership,greatcarewastakeninselectingthemodelwhichbothfitthedatabestanditsusecouldbereplicatedacrossalllinesofservicesforconsistentforecasting.
3.1ModelSelectionMultiplemodelswereconsideredforthebestpotentialforecast.TheMeanAbsoluteError6(MAPE)wasusedtonarrowdowntheselection(seeAppendixB-1).OtherthanWintersmodelandMultipleRegression,allmodelsproducedunacceptableerrors.DuetoclosesimilaritiesinerrorvaluestheWintersmodelandMultipleRegressionmodelswerechosenforexpandedevaluation.Tomakea
6TheMeanAbsolutePercentageErrorisameasureoftheaverageofabsolutedistancebetweenerrorsandactualorpredictedvalues.Thisratioallowsforcomparisonofmodels.Lowervaluesindicateamoreaccuratemodel.Delurgio,1998.pp.55-56.
Table1:CorrelationValuesforeachline. G-Line J-Line W-Line
Boarding Boarding BoardingTemp -35.4% -34.6% -32.7%Rain 26.8% 26.8% 22.5%
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determinationofwhichmodeltouseweconductedaninternalforecasttomeasurewhichmodelperformedbest.
WeperformedthesameinternalforecastsfortheWintersmodelandMultipleRegressionmodelsonalllinesofservicewewereevaluating.
3.1.1WintersModelFirst,wedidaninternalforecastonallthreebuslinesusing48weeksofdata.FortheWintersmodel,
onlythetotalnumberofweeklypassengersovertimewereutilizedinbuildingthemodelandtheforecast.WecreatedaforecastforbuslinesJ(Figure4).LineJshowsaclearlackoffitfortheforecastandthesubsequenterrorcalculationsconfirmthisfinding.WeperformedthesameanalysisforlinesGandW(AppendixB).LineGissimilartoLineJalthoughthefitisslightlybetter.TheerrorsassociatedwithLineGwerehigherthanwewouldhavepreferred.Lastly,weperformedtheforecastonLineW.Forthislineourfitwassignificantlybetter.Theerrorvalueswerealsosignificantlybetterforthisbusline.Despitetheissueswiththefirsttwoforecastswe
thoughtitwaspossiblethattheWintersmodelingmethodwouldbeusefulforourpurposes.
3.1.2MultipleRegressionModelAgain,justaswiththeWintersmodel,weperformedforecastson48weeksofridershipdataforLinesJ,GandW.ThemultipleregressiondiffersfromtheWintersmodelinthattherearemoreindependentvariablesconsideredinthecreationofthemodel.Inadditiontothenumberofpassengersperweek,weutilizedaverageweeklytemperature(°F),andtotalrainfall(inches),allovertime.Sinceweweresimulatingaforecast,weusedaveragesforbothtemperatureandrainfallinsteadofactualsforeachweek.Thismethodologyalignswithhowwewouldperformtheactualforecastandthereforegiveusthebestideaofhowwellthemodelfunctions.WestartedwithLineJanditwasquicklyapparentthatitfittheforecastsignificantlybetter(Figure5).Theerrorcalculationswerealsolow.WeperformedthesameanalysisforlinesGandW(AppendixB-2andB-4).WeevaluatedLineGandfoundasimilarresulttolineJ.Thepredictedvalueswerelowerthantheactuals,however,theyfollowtheweeklytrendnicelyandthecalculatederrorswerenotacauseforconcern.Lastly,weevaluatedLineWandsawasimilartrendtoLineGexceptinsteadofunderestimatingslightlythemodelisoverestimatingslightly.
Nowthatwehaveevaluatedbothmodelswewilldeterminethebestmodelforourpurposes.
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Figure4:LineJInternalForecastWinters
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Figure5:LineJInternalForecast
Weeklyboardings AVGFITS
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3.1.3ModelComparisonAsmentionedpreviously,allthreebuslinesexhibitedsimilarerrorsduringtheinitialmodelbuildingforbothWintersmodelandMultipleRegression.Wethereforedecidedthatthemodelwhichperformedbestattheinternalforecastwouldbethebestfitforouranalysis.ErrorcomparisonscanbefoundinAppendixB-4.OneofthemaindifferencesbetweentheWintersmodelandtheMultipleRegressionisthattheMultipleRegressionconsistentlyfollowedtheweeklytrendwheretheWintersmodelwasunreliablefortwoofthethreebuslines.DespiteLinesGandWhavingaslightlybetterMAPEvaluefortheWintersmodel,weultimatelydecidedtoutilizetheMultipleRegressionmodelforthefollowingreasons:
• Highcorrelationbetweenridershipandtemperatureandrain.
• Consistentinternalforecastsforallthreelines.
• MoreeasilyreplicableacrossallUnitranslines.
Nowthatwehadchosenamodelweneededtobuildthefullmodelsandinterprettheresults.
3.2ModelInterpretationAfterselectingtheMultipleRegressionmodelforourfinalforecastweusedallthedatapointstocreateafull,robustformulaforprediction.Thetruncated(fullequationscanbefoundinAppendixB-3)equationsareasfollows:
• LineJModel
WeeklyBoardings=1,410-11.1*AveTemp-5.65*Time+874*WeeklyPrecipitation+WeeklyIndex*Week.
• LineGModel
WeeklyBoardings=3,473-45.8*AveTemp-10.88*Time+342*WeeklyPrecipitation+WeeklyIndex*Week.
• LineWModel
WeeklyBoardings=-1+1.8*AveTemp+8.82*Time+722*WeeklyPrecipitation+WeeklyIndex*Week.
Thewiderangesofridershiponaweektoweekbasis,whichcloselycorrelatestotheUCDavisacademiccalendar,causedustoevaluatethemodelonaweekbyweekseasonalitybasis.Theseasonalityvalueswereconsistentinscaleforeachequation.Forexample,weobservedhighervaluesinweeks5,6and7acrossallmodels,whichcorrespondstothebeginningofthespringquarter.BothLinesJandGarenegativelyimpactedbyanincreaseintemperaturewhereLineWisbasicallyneutral.AllthreeLinesexperienceanincreaseinridershipduringweeksofheavyrain.Lastly,linesJandGareexperiencingadeclineintotalridershipovertimeasindicatedbythenegativevariableforTime.ConverselyLineWisexperiencinganincreaseinridershipovertime.
Nextwewantedtoensurethatourdatafitourassumptionsoflinearity,homoscedasticityandotherdiagnosticmeasures.
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3.3ModelDiagnosticsToensuretherewerenosurpriseswiththedataweperformedadditionaldatadiagnostics(SeeAppendixA-2).Thedatatestedwithinallappropriateranges.Wethereforedeterminedthatitwasappropriatetomoveforwardwithouranalysis.
Next,wewillusethesemodelstodeterminetheexpectedridershipbyweekforthethreebuslines.
3.4ForecastNowthatwehaveestablishedourpredictionmodelswecanaccuratelydeterminetheridershipoverthenext52weeks(week5/21/2017toweek5/13/2018).Sincewedonothaveactualtemperatureandprecipitationdataforthefuture52weekswedevelopedmodelsforthesevalueswhichlookatthe
average,maximum(hightemperature/lowrainfall)andminimum(lowtemperature/highrainfall)valuesforeachvariable.WehavelabeledtheminimumasElNinoyearsandmaximumasdroughtyears.Intuitively,ahigheraveragetemperatureinDavis,CAwouldcorrespondtolowerprecipitationvaluesandviceversa.UsingtheequationforLineWweforecast52weeksahead(Figure6).Itcanbeobservedthatduringthesummerwheretemperaturesarehighandschoolisoutofsessionthatallthreeforecastsfolloweachotherclosely.ThelowestpointofridershipcomesduringChristmasbreakwhenschool
activityisatitslowestandmanystudentshavegonehomefortheholidays.
UsingthisinformationweareabletomaketheappropriaterecommendationsforUnitransinhowtobestmaximizetheiroperations.
4. SummaryandRecommendations
Fromouranalysis,wehavethreeclimatebasedscenariosforUnitranstoconsider.Wecategorizetheseas:ElNino(wet)year,Normalyear,andDroughtyear.AnElNinoyearcorrespondstooursituationwherethereislowtemperaturesandhighrainfallthroughouttheyear.Anormalyearcontainsaveragetemperaturesandrainfall.Adroughtyeariswheretherearehightemperaturesandlowrainfall.Theseclimateconditionsdirectlycorrespondtothethreeforecastsscenariosthatweexplored.UnitranscanexpecttoexperienceElNinoyearsevery2-7years7,or4yearsonaverage.Droughtyearsoccuronasimilarcycleandarecharacterizedbytheeffectcalled“LaNina8”thatpushesprecipitationnorthcausingadryerseasoninCalifornia.ThesethreeclimatesituationscanbereadilygottenfromlongtermmeteorologicalpredictionsforeachyearandUnitranscanusetheinformationtoadjusttheiroperationsasnecessary.
7https://www.wildlife.ca.gov/conservation/marine/el-nino8https://www.nationalgeographic.org/encyclopedia/la-nina/
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Figure6:3scenarioLineW52WeekForecast
BoardingsForecastAvg BoardingsForecastMax BoardingsForecastMin
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OurAnalysisandforecastsalsorevealsspecificweekswhereUnitranswillexperiencehigherthanaverageridershipontheJ,GandWlines.Betweeneachofthethreeforecastscenariosacrossallthreelines,wehavefoundkeyweekswhereridershipwas26%orhigherthanaverage.Thesepeakweeksnotonlycorrespondtoperiodsofinclementweather,butalsotouniqueperiodsoftheschoolyear.Forexample,weeks2,15,and41representthebeginningofaquarterwhenstudentsreturnandridershipincreases.Asimilarincreaseoccurstowardstheendofaquarterwhenexamsarescheduledinweeks11and49.AfulllistingofthesepeakweekscanbefoundinappendixB-7.
NowthatwehaveestablishedsomekeyinsightintothepotentialfutureoperationofUnitrans’topthreelines,wehavetwotypesofaugmentationsthatwerecommend.ThefirstaugmentationisregardingUnitrans’annualbudget.Becauseoftheincreaseinminimumwage,Unitransmustincreasetheirbudgetby$200,000eachyeartocovertheiroperationallabor.Werecommendincreasingthisamountby6%,or$212,000,eachyearuntil2021.The6%increasecorrespondswiththedifferenceinridershipfromthelowestscenariotothehighestridershipscenarioofawetyear.ThiswillallowUnitranstoincreasetheirdriverpooltocovertheincreaseindemand.However,wedonotrecommendUnitransincreasetheirworkforceimmediately.The6%increaseshouldbeplacedinreserveandwhenanElNinoyearispredicted,Unitransshouldactivelyrecruitandtrainadditionaldriverstofilltheextraneed.OncetheElNinoyearpasses,Unitranscanallowtheirworkforcetoreducetonormallevelsfromattritionasdriversgraduateandleavetheuniversity.
Becauseofourrecommendation,Unitranswillhaveabudgetgapof$848,000startingin2021.Toclosethisgap,wehaveanumberofoptionsthatUnitransshouldtake.Firstisanincrementalincreaseinfaresfrom$1to$2thatshouldbecompleteby2021.The$2farewillgenerateanadditional$265,000inrevenueassumingcurrentpaidridershipstaysthesame.TheincreasedfareisacompetitivefareasotherlocaltransitsystemssuchasSacramentoRTorSanFranciscoMUNIhavefaresof$2.75.Unitranswouldstillbealowcostoption.Thisleaves$583,000thatneedtofound.UnitranscanlobbytheASUCDtocoverthisgapbyraisingtheTransportationFeeby$16perstudent.Thisisafairlyreasonablerequest,butifUnitranswouldliketobesensitivetoeveryincreasingstudentfees,theycanseektofindadditionalfundingfromothermeans.Thiscanincluderaisingtheiradvertisingfeestogeneratehigheradrevenue.UnitranscanalsoapplyforhigherfundingformtheFederaltransitprogram.Additionally,theycanlobbytheCityofDavisandYoloCountytoincreasetheircontributionsaswell.Ingeneral,Unitranshasmanyoptionstocovertheirincreaseinoperationallaborcosts.
ThesecondaugmentationthatwerecommendtoUnitransisregardingtheirbusschedulesandoperations.Theserecommendationsderivefromthethreeclimatescenariosthattheycanface.
ElNinoYear
• Switchtoa3or4tripperbussystem.Thiswillallowformoreflexibilitytoincreasecapacityondemand.
• MovedoubledeckerbusesfromotherlinestoJandGlineduringpeakperiods.Thiswillincreasecapacityonarunfrom120passengersto160or200passengersdependingonbuscombinations.
• RuntwotripperbusesonpeakdemandfortheW-line.• Increasemaintenancecycletoallowtheextratripperstobeavailableduringthesepeakperiods.
NormalYear
• SameoperationalchangesasElNinoYear.
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• However,dependingonobserveddemand,UnitransmaynotneedtomovedoubledeckerbusestotheJandGlineandusesingledecktrippersinstead.Thiswouldallowcapacityonotherlinesthatusethedoubledeckerbusestonottobediminished.
DroughtYear
• ConsiderreducingthenumberofbusrunsonJ,GandWlineby2.5%.Thiscorrespondstothereducedforecastedridershipinadroughtyearcomparedtoanormalyear.
• Thisreductionwillachievea$33,296savingsinoperationcosts.
Duetothelimitedscopeofourreportandanalysis,wehavesomenextstepsforUnitranstotake.First,Unitransshouldperformasimilaranalysisasoursontheotherbuslinesintheirsystem.WeobservedareductioninridershipacrosstheJ,GandWlinesbutanincreaseinridershipacrosstheentiretransitsystems.FurtheranalysiswilldeterminewhichbuslinesarecontributingtothisincreaseandmodelingbasedonthosebuslineswillgiveUnitransmoretoolstobetterutilizetheirresources.Additionally,Unitransshouldre-evaluateourmodelsonanannualbasistointegratenewridershipandweatherdata,furtherimprovingtheaccuracyoftheforecastsfromthemodels.
Byfollowingourrecommendationsandnextsteps,wefeelthatUnitranscangreatlyimprovetheirresourceutilization.Withamoreefficienttransitsystem,Unitranswillhavemorecustomersatisfactionandincreasedridership.
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AppendixThisappendixcontainsadditionalinformationregardingdatacharacteristicsandsupportinginformationforourmodelandforecastpredictions.
AppendixA-SupplementalinformationforModelStructureandDiagnosticsA-1AdditionalTrendDataforBusG-andW-LineFigureA-1andFigureA-2areprovidedtoshowthatthetrendobservedforridershipoftheG-lineandJ-line,respectively.BoththeG-andJ-linehavesimilartrendstotheW-linewhichwaspresentedinthedatacharacteristicssection.
A-2AssumptionTestingofDataSetforRegressionInorderforalinearregressionmodeltobevalid,thereareseveralassumptionsaboutthedatathatwemusttake.Inthissection,wetestthefollowingassumptions:
1. Normality2. Homoscedasticity(ConstantVariance)3. Linearity4. Independence5. Multicollinearity
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Wefoundthatallassumptionshavebeenmetwithoutamendmentstothedata.Asummaryispresentedinthefollowingtable:
TableA-1DataassumptionsforlinearRegressionModelingAssumption TestStatus Comment/testusedNormality Pass Observationofbellshapedhistogramofresiduals9Homoscedasticity Pass ResidualPlotevaluationLinearity Pass ScatterPlotofimportsvstimeevaluationIndependence Pass Durbin&WatsonTest10
AppendixB–SupportinginformationforModelandForecastInappendixB,wepresentthemodelsthatwereconsideredfortheforecastoftheBusridershipaswellasthemodelthatwaschosen,MultipleRegressionModel.Additionally,wepresentacomparisonofthemodelstoshowwhywechoseourmodel.InappendixB-5,wepresentthedatausedtoforecastbusridershipaswellastheaverageforecastedvaluesforMay2017throughMay2018.B-1ModelComparisonsSeveralmodelswereconsideredduringthecourseofHATconsulting’sanalysisofUnitransdatasets.TheMeanAbsolutePercentageError11(MAPE)wasusedtocomparetherelativeaccuracyofeach
forecastingmodel.Byexaminingtheratiooferrorproducedbyeachmodelcomparedtoforecastedvalues,amoreaccuratedeterminationofmodelvaliditycanbeattained.HATConsultingdeterminedthattheWinter’smodelandMultipleRegressionmodelswerethestrongestcandidatesforfurtherevaluation.TheARIMAmodelwasnotaviablesolutionduetoasignificantdecreaseinridershipduringspringbreakeveryspringsemesterwhichpreventedtheARIMAmodeltonotdemonstrateanysignificance.
B-2Winter’sModelInternalForecastsforLinesGandWAninternalforecastwasperformedusingtheWinter’smodelfortheGandWlinedatasetstodeterminetheaccuracyoftheforecastmodel.HATConsultingwithheld48weeksofobserveddataandforecastedvalueswerecomparedtothoseobservationsforaccuracy.
9Residualsarethedifferencebetweenactualvaluesofyandthevaluescalculatedbytheregressionline.Keller,2012.Pp.650.10“TheDurbin-Watsontestallowsthestatisticspractitionertodeterminewhetherthereisevidenceoffirst-orderautocorrelation.”Keller,2012.Pp.716-71911TheMeanAbsolutePercentageErrorisameasureoftheaverageofabsolutedistancebetweenerrorsandactualorpredictedvalues.Thisratioallowsforcomparisonofmodels.Lowervaluesindicateamoreaccuratemodel.Delurgio,1998.Pp.55-56.
TableB-1ModelMAPEComparison
Model MAPE
SimpleRegression 137%
MovingAverage 58%
Holt’sMethod 124%
WintersMethod 11%
MultipleRegression 11%
ARIMA N/A
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B-3MultipleRegressionModelLineJFullModelEquationWeeklyRidership=1410-5.65Time-11.1AveTemp+874WeeklyPrecip+13717Week2+ 13599Week3+10868Week4+13219Week5+12036Week6+12582Week7+ 11095Week8+12514Week9+12797Week10+13015Week11+9350Week12+ 917Week13+11924Week14+12075Week15+11038Week16+12387Week17+ 12299Week18+11837Week19+12016Week20+11170Week21+9777Week22+ 10733Week23+5874Week24+2068Week25+5896Week26+5310Week27+ 5838Week28+5429Week29+5395Week30+5404Week31+5151Week32+ 4893Week33+4875Week34+4921Week35+4266Week36+4405Week37+ 3053Week38+6611Week39+11728Week40+13711Week41+13909Week42+ 12960Week43+12746Week44+12894Week45+11216Week46+13460Week47+ 6679Week48+12440Week49+11065Week50+3689Week51-18Week52.
LineGFullModelEquationWeeklyRidership=3473-45.8AveTemp+342WeeklyPrecip-10.88Time+10968Week2+ 10388Week3+8125Week4+9975Week5+9727Week6+9355Week7+7625Week8+ 10100Week9+9854Week10+9961Week11+7319Week12+1487Week13+ 10451Week14+11209Week15+11326Week16+9774Week17+10043Week18+ 9832Week19+9675Week20 + 9528Week21+8060Week22+8995Week23+ 5282Week24+2681Week25+4949Week26+4949Week27+4944Week28+ 5206Week29+4866Week30+5425Week31+4391Week32+4431Week33+ 4550Week34+4779Week35+4570Week36+4229Week37+3468Week38+ 7830Week39+8960Week40+11001Week41+10781Week42+10141Week43+ 10387Week44 + 10300Week45+8022Week46+10402Week47+ 5357Week48+10011Week49+7689Week50+3179Week51+363Week52.
LineWFullModelEquationWeeklyRidership=-1+1.8AveTemp+722WeeklyPrecip+8.82Time+14407Week2+ 14422Week3+11087Week4+14390Week5+13287Week6+12913Week7+ 10359Week8+11870Week9+13048Week10+13392Week11+9915Week12+ 725Week13+12519Week14+12650Week15+12941Week16+12083Week17
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FigureB-1LineGInternalForecastWinters
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FigureB-2LineWInternalForecastWinters
WeeklyBoardings FITS
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+ 12029Week18+11394Week19+11628Week20+10465Week21+9587Week22+ 10515Week23+5364Week24+1036Week25+4443Week26+4170Week27+ 4641Week28+4645Week29+4410Week30+4778Week31+3986Week32+ 4173Week33+4026Week34+4084Week35+3198Week36+3453Week37+ 1927Week38+5562Week39+11841Week40+14558Week41+14837Week42+ 14255Week43+13844Week44+14803Week45+11957Week46+14569Week47+ 7640Week48+14155Week49+10613Week50+3653Week51-256Week52.
B-4ComparisonofWinter’sMethodandMultipleRegressionErrorvalueswereusedasameanstocomparetheWinter’smodelandMultipleRegressionModel.Theseerrorhelptodeterminewhichofthetwomodelsmayprovidethemostaccurateforecasts.ErrorsusedforcomparisonwastheMeanError(ME)whichhelpstodetermineifthemodelsareunderoroverforecasting;MeanSquareError(MSE)istheaverageofsumofsquarederrors;MeanAbsoluteDeviation(MAD)istheisameasureoferrordispersionthatislesssensitivetooutliers.MSEandMADtakewithMAPE,providesaclearerpictureofforecastaccuracy12.MEValues
MultipleRegressionInternalForecast
Winter’sMethodInternalForecast
MultipleRegressionExternalForecast(DroughtScenario)
Winter’sMethodExternalForecast
J-Line 0.0000 8.78895 -1299.15 4978.19G-Line 0.0000 14.9356 -753.852 3014.45W-line 0.0000 -1.3772 -1441.39 61.1014
MSEValues
MultipleRegressionInternalForecast
Winter’sMethodInternalForecast
MultipleRegressionExternalForecast(DroughtScenario)
Winter’sMethodExternalForecast
J-Line 880,315 1,143,903 5,707,547 38,733,127G-Line 419,123 680,349 7,766,942 18,201,525W-line 962,107 1,706,536 5,883,683 3,573,154
MADValues
MultipleRegressionInternalForecast
Winter’sMethodInternalForecast
MultipleRegressionExternalForecast(DroughtScenario)
Winter’sMethodExternalForecast
J-Line 678.737 713 1691.28 5033.53G-Line 449.216 560 1636.94 3395.38W-line 632.489 923 1823.34 1213.88
MAPEValues
MultipleRegressionInternalForecast
Winter’sMethodInternalForecast
MultipleRegressionExternalForecast(DroughtScenario)
Winter’sMethodExternalForecast
J-Line 11.0620 11 34.1236 57.3597G-Line 11.2727 11 59.3978 50.3725W-line 10.6468 11 35.3824 20.0018
12Delurgio,1998.Pp.43-55.
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B-5DescriptivestatisticsofweatherconditionsforuseinForecastingThetablebelowshowsasamplingoftheassumedvaluesforweeklytemperatureandPrecipitationusedforforecastingridershiponUnitransbuses.FulltableofvaluescanberequestedfromHATConsulting.WeekStarting AvgTemp maxtemp mintemp AvgPrecip minprecip maxprecip5/21/17 83 86.5714 79.8571 0.04667 0 0.145/28/17 89.8095 95.2857 84.4286 0 0 06/4/17 91.2380 93.5714 87.8571 0 0 06/11/17 85.9524 91.7143 79.1429 0 0 06/18/17 91.4762 93.8571 87.8571 0.0033 0 0.01
⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞4/22/18 79.5714 85.8571 73.5714 0 0 04/29/18 78.0714 85.71428 74.5714 0.0375 0 0.135/6/18 80.6071 89.7143 73.1429 0 0 05/13/18 78.8036 84.2857 74.5 0.15 0 0.6
B-6AverageForecastedvaluesMay2017–May2018ForecastedAverageWeeklyRidership
Line/Year ElNino Normal DroughtJ-Line 7,385 7,175 7,082G-Line 6,458 6,103 5,824W-line 9,451 9,266 9,183Total 23,294 22,544 22,089
B-7WeeksoftheyearwithpeakRidershipAthresholdof26%increaseinridership,whichistheaverageofthecorrelationofprecipitationonridership,wasusedtodeterminepeakweeks.Commonalityofpeakperiodswerefoundamongallforecastedscenariosandthoseperiodsarepresentedinthetablebelow:
ForecastedPeakDemandWeeks2 3 5 6 7 910 11 15 17 18 4142 43 44 45 47 49
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References1. DeLurgo,StephenA.1998.ForecastingPrinciplesandApplications.Boston:Irwin/McGrawHill.2. Keller,G.(2012).Statisticsformanagementandeconomics10-thEd.Mason,OH:Cengage
Learning.3. Palmere,Anthony.September7,2016.UnitransGeneralManager’sReportFiscalYear2015-16.4. https://www.wildlife.ca.gov/conservation/marine/el-nino5. https://www.nationalgeographic.org/encyclopedia/la-nina/6. http://unitrans.ucdavis.edu/about/
