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ELEVATORPLANNINGWITHSTOCHASTICMULTICRITERIAACCEPTABILITYANALYSISABSTRACTMODERNELEVATORSYSTEMSINHIGHRISEBUILDINGSCONSISTOFGROUPSOFELEVATORSWITHCENTRALIZEDCONTROLTHEGOALINELEVATORPLANNINGISTOCONFIGUREASUITABLEELEVATORGROUPTOBEBUILTTHEELEVATORGROUPMUSTSATISFYSPECIFICMINIMUMREQUIREMENTSFORANUMBEROFSTANDARDPERFORMANCECRITERIAINADDITION,ITISDESIRABLETOOPTIMIZETHECONFIGURATIONINTERMSOFOTHERCRITERIARELATEDTOTHEPERFORMANCE,ECONOMYANDSERVICELEVELOFTHEELEVATORGROUPDIFFERENTSTAKEHOLDERSINVOLVEDINTHEPLANNINGPHASEEMPHASIZEDIFFERENTCRITERIAMOSTOFTHECRITERIAMEASUREMENTSAREBYNATUREUNCERTAINSOMECRITERIACANBEESTIMATEDBYUSINGANALYTICALMODELS,WHILEOTHERS,ESPECIALLYTHOSERELATEDTOTHESERVICELEVELINDIFFERENTTRAFFICPATTERNS,REQUIRESIMULATIONSINTHISPAPERWEFORMULATETHEELEVATORPLANNINGPROBLEMASASTOCHASTICDISCRETEMULTICRITERIADECISIONMAKINGPROBLEMWECOMPARE10FEASIBLEELEVATORGROUPCONFIGURATIONSFORA20FLOORBUILDINGWEEVALUATETHECRITERIARELATEDTOTHESERVICELEVELINDIFFERENTTRAFFICSITUATIONSUSINGTHEKONEBUILDINGTRAFFICSIMULATOR,ANDUSEANALYTICALMODELSANDEXPERTJUDGMENTSFOROTHERCRITERIATHERESULTINGDECISIONPROBLEMCONTAINSMIXEDTYPECRITERIASOMECRITERIAAREREPRESENTEDBYTHEMULTIVARIATEGAUSSIANDISTRIBUTION,OTHERSBYDETERMINISTICVALUESANDORDINALRANKINGINFORMATIONTOIDENTIFYCONFIGURATIONSTHATCANBESTSATISFYTHEGOALSOFTHESTAKEHOLDERS,WEANALYZETHEPROBLEMUSINGTHESTOCHASTICMULTICRITERIAACCEPTABILITYANALYSISSMAAMETHODKEYWORDSSTOCHASTICMULTICRITERIAACCEPTABILITYANALYSISSMAAELEVATORPLANNINGMULTICRITERIASIMULATIONARTICLEOUTLINE1INTRODUCTION2ELEVATORPLANNING3THESMAAMETHODS4SIMULATIONMODELANDSIMULATIONRESULTS5DECISIONMAKINGPROBLEMANDSMAAANALYSIS6CONCLUSIONSACKNOWLEDGEMENTS1INTRODUCTIONINMODERNHIGHRISEBUILDINGSWORKERSANDINHABITANTSARETRANSPORTEDBETWEENFLOORSMAINLYBYMEANSOFMULTIPLEELEVATORSELEVATORSAREUSUALLYOPERATEDBYELEVATORGROUPCONTROLSYSTEMSINORDERTOPROVIDEEFFICIENTTRANSPORTATIONWHENAHIGHRISEBUILDINGISDESIGNED,ASUITABLECONFIGURATIONFORTHEELEVATORGROUPHASTOBEDESIGNEDTHEDECISIONMAKERSDMSSHOULDCONSIDERPERFORMANCEASWELLASPRICEANDOTHERNONPERFORMANCECRITERIAOFALTERNATIVEELEVATORGROUPCONFIGURATIONSBECAUSEANALYTICALMETHODSARELIMITEDTOTHEUPPEAKTRAFFICSITUATIONANDCANNOTEVALUATETHEEFFECTOFAGROUPCONTROLALGORITHM,THEPERFORMANCEHASTOBEMEASUREDUSINGCOMPUTERSIMULATION,WHICHPRODUCESSTOCHASTICMEASUREMENTSFORTHEPERFORMANCECRITERIAOFALTERNATIVECONFIGURATIONSTHEPERFORMANCEOFANELEVATORGROUPCANBEMEASUREDUSINGSEVERALCRITERIA,SUCHASTHEAVERAGEWAITINGTIMEWTORTHEAVERAGERIDETIMEOFTHEPASSENGERSTHEPRICEANDOTHERNONPERFORMANCECRITERIACANUSUALLYBEASSESSEDWITHSUFFICIENTACCURACYORBYRANKINGTHEALTERNATIVESDIFFERENTDMSMAYHAVEDIFFERENTPREFERENCESFORTHECRITERIAFOREXAMPLE,SOMEDMSPAYATTENTIONTOTHEAVERAGEWTWHILEOTHERSTHINKTHATTHEPERCENTAGEOFLONGWTSISMOREIMPORTANTSINCEITREPRESENTSTHEFAIRNESSINSERVICETHEBUILDERMAYSTRESSTHEAMOUNTOFFLOORSPACEUSEDBYTHEELEVATORSYSTEMTHEREAREUSUALLYSOMETRADEOFFSANDDEPENDENCIESBETWEENCRITERIATHEPROBLEMOFELEVATORPLANNINGCANTHUSBECONSIDEREDASADISCRETEMULTICRITERIADECISIONMAKINGPROBLEMWITHMULTIPLEDMSANDSTOCHASTICCRITERIAMEASUREMENTSWEAREINTERESTEDINFINDINGACOMPROMISESOLUTIONWHICHTAKESINTOACCOUNTDIFFERENTPOSSIBLEPREFERENCESOFDMS,ANDTHUSWEHAVECHOSENTOANALYZETHEPROBLEMUSINGTHESMAAMETHODSMAAMETHODSHAVEBEENDEVELOPEDFORDISCRETEMULTICRITERIADECISIONMAKINGPROBLEMS,WHERECRITERIAMEASUREMENTSAREUNCERTAINORINACCURATEANDWHEREITISFORSOMEREASONDIFFICULTTOOBTAINACCURATEORANYPREFERENCEINFORMATIONFROMTHEDMS1USUALLYTHEPREFERENCEINFORMATIONISMODELLEDBYDETERMININGIMPORTANCEWEIGHTSFORCRITERIATHESMAAMETHODSAREBASEDONEXPLORINGTHEWEIGHTSPACEINORDERTODESCRIBETHEPREFERENCESTHATWOULDMAKEEACHALTERNATIVETHEMOSTPREFERREDONE,ORTHATWOULDGIVEACERTAINRANKFORASPECIFICALTERNATIVEINTHEORIGINALSMAAMETHOD2THEWEIGHTSPACEANALYSISISPERFORMEDBASEDONANADDITIVEUTILITYORVALUEFUNCTIONANDSTOCHASTICCRITERIAMEASUREMENTSTHESMAA2METHOD1GENERALIZEDTHEANALYSISTOAGENERALUTILITYORVALUEFUNCTION,TOINCLUDEVARIOUSKINDSOFPREFERENCEINFORMATIONANDTOCONSIDERHOLISTICALLYALLRANKSTHESMAAOMETHOD3EXTENDSSMAA2FORTREATINGMIXEDORDINALANDCARDINALCRITERIAINACOMPARABLEMANNERSMAAISSUITABLEFORSOLVINGPROBLEMSALSOWHENTHEUNCERTAINTIESOFCRITERIAMEASUREMENTSAREDEPENDENT4ELEVATORPLANNINGRESEARCHHASALONGHISTORYTHEOPERATIVEPERFORMANCEHASBEENSTUDIEDOVERDECADES5AND6THEUPPEAKINTERVALANDTHEUPPEAKHANDLINGCAPACITYHASBEENANALYZEDINMANYPUBLICATIONSINTHE1960S,SEE,EG7,8AND9THEPATIENCEOFPASSENGERSANDWHATSHOULDBECONSIDEREDGOODSERVICEINDIFFERENTTYPESOFBUILDINGSHASBEENSTUDIEDSINCE1940SACCORDINGTO10EARLIESTAPPLICATIONSOFSIMULATIONTOELEVATORPLANNINGAREFROMTHE1960S11AND12THEREAREALSOMORERECENTAPPLICATIONSINALLAREASOFELEVATORPLANNING,BUTINPRACTICENORMALELEVATORGROUPSARESTILLDESIGNEDUSINGMETHODSFROMTHE1960SINTHISPAPERWEPRESENTAMULTICRITERIAMETHODTHATALLOWSTOUSESTOCHASTICSIMULATOROUTPUTINTHEDECISIONANALYSISWECONSIDERAREALISTICELEVATORPLANNINGPROBLEM,WHICHCONSISTSOFA20FLOORBUILDINGFORWHICHONEOF10POSSIBLEELEVATORGROUPCONFIGURATIONSHASTOBECHOSENWEWILLANALYZETHEALTERNATIVECONFIGURATIONSUSINGTHEKONEBUILDINGTRAFFICSIMULATORBASEDONTHEOUTPUTOFTHESIMULATOR,WEFORMAMULTICRITERIADECISIONMAKINGPROBLEM,WHICHWEANALYZEUSINGSMAATOOURBESTKNOWLEDGE,WEARETHEFIRSTTOAPPLYASTOCHASTICMCDAMETHODINELEVATORPLANNINGWEHAVECHOSENTOUSESMAAINTHEDECISIONANALYSIS,BECAUSEITISTHEONLYMCDAMETHODOLOGYTHATALLOWSMULTIVARIATEGAUSSIANDISTRIBUTEDCRITERIAMEASUREMENTSTHISPAPERISORGANIZEDASFOLLOWSSECTION2INTRODUCESTHEREADERTOTHEAREAOFELEVATORPLANNING,ANDSECTION3TOSMAAMETHODSINSECTION4,WEPRESENTTHESIMULATORTHATISUSEDTOGENERATETHEDATA,ANDTHESIMULATIONRESULTSWEDEFINETHEDECISIONMAKINGPROBLEMANDPRESENTTHESMAAANALYSISINSECTION5SECTION6ENDSTHISPAPERWITHCONCLUSIONS2ELEVATORPLANNINGTHEGOALINELEVATORPLANNINGISTOFINDASUITABLEELEVATORGROUPTOSERVETHETRAFFICOFAHIGHRISEBUILDINGBECAUSETHEBUILDINGSDONOTEXISTATTHEPLANNINGSTAGE,THETRAFFICMUSTBEESTIMATEDBYUSINGTHEBUILDINGSPECIFICATIONSTHENUMBEROFFLOORS,THEIRHEIGHTS,THEFLOORAREAANDTHEBUILDINGTYPETHETRAVELHEIGHTCANBECALCULATEDFROMTHENUMBEROFFLOORSANDTHEIRHEIGHTS,ANDTHETOTALPOPULATIONCANBEESTIMATEDACCORDINGTOTHETYPEOFBUILDINGANDTHEFLOORAREABUILDINGTYPESHAVECHARACTERISTICTRAFFICPROFILESFOREXAMPLE,OFFICEBUILDINGSTYPICALLYHAVEUPPEAKTRAFFICINTHEMORNINGWHENEMPLOYEESENTERTHEBUILDING,INTENSETWOWAYORINTERFLOORTRAFFICDURINGTHELUNCHTIME,ANDDOWNPEAKTRAFFICWHENEMPLOYEESEXITTHEBUILDING13THEPERFORMANCEOFAGROUPOFELEVATORSISMAINLYDETERMINEDBYTHENUMBERANDSIZEOFTHECARSANDTHEIRSPEEDALSOACCELERATION,DOORTYPESANDTHEGROUPCONTROLALGORITHMAFFECTPERFORMANCEUSUALPERFORMANCECRITERIAARETHEHANDLINGCAPACITYANDTHEINTERVALCALCULATEDINTHEUPPEAKSITUATIONTHEUPPEAKHANDLINGCAPACITYISTHEPERCENTAGEOFPOPULATIONPER5MINTHATCANBETRANSPORTEDFROMTHELOBBYTOTHEUPPERFLOORSITISASSUMEDTHATELEVATORSAREFILLEDTO80OFRATEDLOADALTHOUGHITISPOSSIBLETOFILLELEVATORUPTORATEDLOADTHATDOESNOTHAPPENINPRACTICETHEUPPEAKINTERVALISANINTERVALBETWEENTWOSTARTSFROMTHELOBBYTHEINTERVALISALSORELATEDTOTHEWTTHEUPPEAKISUSEDSINCEITISTHEMOSTDEMANDINGSITUATIONCONSIDERINGELEVATORHANDLINGCAPACITYATLEASTINOFFICEBUILDINGS,ANDBECAUSETHEREAREANALYTICALFORMULASFORCALCULATINGTHEUPPEAKHANDINGCAPACITYANDINTERVAL14THEUSUALRECOMMENDATIONSSTATETHATTHEUPPEAKHANDLINGCAPACITYFORANOFFICEBUILDINGSHOULDBE1117ANDINTERVAL2030S15NONPERFORMANCECRITERIA,SUCHASCOSTANDOCCUPIEDFLOORAREASHOULDALSOBECONSIDEREDTHECOSTOFANELEVATORSYSTEMCONSISTSOFBUILDANDMAINTENANCECOSTSTHEFLOORAREAOCCUPIEDBYTHEELEVATORGROUPCONSISTSOFTHESHAFTSPACEANDTHEWAITINGAREAFORPASSENGERSINHIGHRISEBUILDINGSTHEPOPULATIONISLARGEANDDISTANCESARELONG,THUSTHEPORTIONOFSHAFTSISLARGECOMPAREDTOTHETOTALFLOORAREATHISMEANSMORECOSTS,SINCETHERENTABLEAREAISREDUCEDINSOMECASESTHEBUILDINGDESIGNCONSTRAINSTHEOCCUPIEDAREA,SOMETIMESTHEREISMOREFREEDOMTOUSESPACETHEELEVATORPLANNINGISNOTINDEPENDENTOFBUILDINGDESIGNTHEARCHITECTSHOULDTAKEADVICEFROMTHEELEVATORPLANNERINSTEADOFCONSIDERINGONLYUPPEAKTRAFFIC,WETAKEINTOACCOUNTTHEENTIREDAILYTRAFFICANDCONSIDERALLCRITERIASIMULTANEOUSLYINTHESTUDYPRESENTEDINTHISPAPERWECONSIDERTHEFOLLOWINGSIXCRITERIATHECOSTANDAREACRITERIATAKEINTOACCOUNTTHEBUILDINGOWNERSPOINTOFVIEWPASSENGERSPOINTOFVIEWISTAKENINTOACCOUNTBYWT,JOURNEYTIMEJT,THEPERCENTAGEOFWTSEXCEEDING60SWT60,ANDTHEPERCENTAGEOFJTSEXCEEDING120SJT120THEWTISMEASUREDFROMTHEMOMENTAPASSENGERENTERSTHEWAITINGAREATOTHEMOMENTHE/SHEENTERSTHEELEVATORTHEJTISTHETOTALTIMEFROMENTERINGTHEWAITINGAREATOEXITINGTHEELEVATORTHELASTTWOCRITERIAMEASUREUNSATISFACTORYSERVICE,WHICHMAYHAPPENESPECIALLYININTENSETRAFFICPEAKS3THESMAAMETHODSTHESMAA2METHOD1HASBEENDEVELOPEDFORDISCRETESTOCHASTICMULTICRITERIADECISIONMAKINGPROBLEMSWITHMULTIPLEDMSSMAA2APPLIESINVERSEWEIGHTSPACEANALYSISTODESCRIBEFOREACHALTERNATIVEWHATKINDOFPREFERENCESMAKEITTHEMOSTPREFERREDONE,ORPLACEITONANYPARTICULARRANKTHEDECISIONPROBLEMISREPRESENTEDASASETOFMALTERNATIVESX1,X2,XMTHATAREEVALUATEDINTERMSOFNCRITERIATHEDMSPREFERENCESTRUCTUREISREPRESENTEDBYAREALVALUEDUTILITYORVALUEFUNCTIONUXI,WTHEVALUEFUNCTIONMAPSTHEDIFFERENTALTERNATIVESTOREALVALUESBYUSINGAWEIGHTVECTORWTOQUANTIFYDMSSUBJECTIVEPREFERENCESSMAA2HASBEENDEVELOPEDFORSITUATIONSWHERENEITHERCRITERIAMEASUREMENTSNORWEIGHTSAREPRECISELYKNOWNUNCERTAINORIMPRECISECRITERIAAREREPRESENTEDBYSTOCHASTICVARIABLESIJWITHJOINTDENSITYFUNCTIONFXINTHESPACEXRMNWEDENOTETHESTOCHASTICCRITERIAMEASUREMENTSOFALTERNATIVEXIWITHITHEDMSUNKNOWNORPARTIALLYKNOWNPREFERENCESAREREPRESENTEDBYAWEIGHTDISTRIBUTIONWITHJOINTDENSITYFUNCTIONFWWINTHEFEASIBLEWEIGHTSPACEWTOTALLACKOFPREFERENCEINFORMATIONISREPRESENTEDINBAYESIANSPIRITBYAUNIFORMWEIGHTDISTRIBUTIONINW,THATIS,FWW1/VOLWTHEWEIGHTSPACECANBEDEFINEDACCORDINGTONEEDS,BUTTYPICALLY,THEWEIGHTSARENONNEGATIVEANDNORMALIZED,THATISTHEWEIGHTSPACEISANN1DIMENSIONALSIMPLEXINNDIMENSIONALSPACE1THEVALUEFUNCTIONISUSEDTOMAPTHESTOCHASTICCRITERIAANDWEIGHTDISTRIBUTIONSINTOVALUEDISTRIBUTIONSUI,WBASEDONTHEVALUEDISTRIBUTIONS,THERANKOFEACHALTERNATIVEISDEFINEDASANINTEGERFROMTHEBESTRANK1TOTHEWORSTRANKMBYMEANSOFARANKINGFUNCTION2WHERETRUE1ANDFALSE0SMAA2ISTHENBASEDONANALYZINGTHESTOCHASTICSETSOFFAVORABLERANKWEIGHTS3ANYWEIGHTRESULTSINSUCHVALUESFORDIFFERENTALTERNATIVES,THATALTERNATIVEXIOBTAINSRANKRTHEFIRSTDESCRIPTIVEMEASUREOFSMAA2ISTHERANKACCEPTABILITYINDEX,WHICHMEASURESTHEVARIETYOFDIFFERENTPREFERENCESTHATGRANTALTERNATIVEXIRANKRITISTHESHAREOFALLFEASIBLEWEIGHTSTHATMAKETHEALTERNATIVEACCEPTABLEFORAPARTICULARRANK,ANDITISMOSTCONVENIENTLYEXPRESSEDPERCENTAGEWISETHERANKACCEPTABILITYINDEXISCOMPUTEDNUMERICALLYASAMULTIDIMENSIONALINTEGRALOVERTHECRITERIADISTRIBUTIONSANDTHEFAVORABLERANKWEIGHTSAS4THEMOSTACCEPTABLEBESTALTERNATIVESARETHOSEWITHHIGHACCEPTABILITIESFORTHEBESTRANKSTHECENTRALWEIGHTVECTORISTHEEXPECTEDCENTEROFGRAVITYCENTROIDOFTHEFAVORABLEFIRSTRANKWEIGHTSOFANALTERNATIVETHECENTRALWEIGHTVECTORREPRESENTSTHEPREFERENCESOFATYPICALDMSUPPORTINGTHISALTERNATIVETHECENTRALWEIGHTSOFDIFFERENTALTERNATIVESCANBEPRESENTEDTOTHEDMSINORDERTOHELPTHEMUNDERSTANDHOWDIFFERENTWEIGHTSCORRESPONDTODIFFERENTCHOICESWITHTHEASSUMEDPREFERENCEMODELTHECENTRALWEIGHTVECTORISCOMPUTEDNUMERICALLYASAMULTIDIMENSIONALINTEGRALOVERTHECRITERIADISTRIBUTIONSANDTHEFAVORABLEFIRSTRANKWEIGHTSUSING5THECONFIDENCEFACTORISTHEPROBABILITYFORANALTERNATIVETOOBTAINTHEFIRSTRANKWHENTHECENTRALWEIGHTVECTORISCHOSENTHECONFIDENCEFACTORISCOMPUTEDASAMULTIDIMENSIONALINTEGRALOVERTHECRITERIADISTRIBUTIONSUSING6CONFIDENCEFACTORSCANSIMILARLYBECALCULATEDFORANYGIVENWEIGHTVECTORSTHECONFIDENCEFACTORSMEASUREWHETHERTHECRITERIAMEASUREMENTSAREACCURATEENOUGHTODISCERNTHEEFFICIENTALTERNATIVESTHEUNCERTAINTYOFTHECRITERIAMEASUREMENTSCANBEMODELLEDVERYFLEXIBLYINSMAAMETHODSBYUSINGANAPPROPRIATEJOINTDISTRIBUTIONFXIFTHEUNCERTAINTIESAREINDEPENDENT,THENSEPARATEDISTRIBUTIONSFIJIJCANBEUSEDFOREACHMEASUREMENTSIMPLEPARAMETRICDISTRIBUTIONS,SUCHASTHEUNIFORMANDNORMALDISTRIBUTIONMAYBESUITABLEINMANYAPPLICATIONSWHENTHEUNCERTAINTIESOFTHECRITERIAMEASUREMENTSAREDEPENDENT,THENTHEDEPENDENTPARAMETERSCANBEREPRESENTEDBYAJOINTDISTRIBUTIONTHEMULTIVARIATEGAUSSIANNORMALDISTRIBUTIONISPARTICULARLYSUITABLE,BECAUSEITISTHEORETICALLYWELLUNDERSTOODANDYETITAPPROXIMATESWELLMANYREALLIFEPHENOMENAUSEOFTHEMULTIVARIATEGAUSSIANDISTRIBUTIONWITHSMAAISDESCRIBEDINMOREDETAILIN4THEREARESEVERALDIFFERENTWAYSTOHANDLEPARTIALPREFERENCEINFORMATIONINSMAAMETHODS1INTHEDECISIONMAKINGPROBLEMCONSIDEREDINTHISPAPER,WEAPPLYINTERVALCONSTRAINTSFORWEIGHTSFORMOREINFORMATIONABOUTTHISTECHNIQUE,SEE164SIMULATIONMODELANDSIMULATIONRESULTSTOOBTAINSTOCHASTICCRITERIAMEASUREMENTSFORTHEPERFORMANCECRITERIA,WEEXECUTEDSIMULATIONSWITHTHEKONEBUILDINGTRAFFICSIMULATOR17AND18THESIMULATIONMODELCONSISTSOFTHEELEVATORMODELANDTRAFFICGENERATIONFEATURESOFTHEMODELAREFLOORSHAVELANDINGCALLBUTTONSENTERINGPASSENGERGIVESACALLTOTHEUP/DOWNDIRECTIONWHEREHEISHEADINGTHEGROUPCONTROLALGORITHMALLOCATESTHECALLTOTHEMOSTSUITABLEELEVATORTHEALGORITHMISAGENETICALGORITHM19,WHICHOPTIMIZESWTSTHEGROUPCONTROLHASALSOARETURNINGALGORITHMWHICHSENDSTHEELEVATORBACKTOTHELOBBYTOWAITFORACALLTHERETURNINGALGORITHMISNECESSARYINTHEINCOMINGTRAFFICSITUATIONASTOPPINGELEVATOROPENSDOORS,EXITINGPASSENGERSGETOUT,ENTERINGPASSENGERSGETINANDTHEDOORSARECLOSEDTHESIMULATORHASDELAYSRELATEDTODOOROPENING,ENTRANCE,EXITANDDOORCLOSINGANELEVATORCANTAKEPASSENGERSUPTOTHEMAXIMUMLOAD,WHICHISABOUT80OFTHECARSRATEDLOADIFTHELOADEXCEEDSBYPASSLOADABOUT80OFMAXIMUMLOAD,ANELEVATORDOESNOTACCEPTNEWLANDINGCALLSTHELOADSAREEXPRESSEDINPERSONSANELEVATORCANNOTREVERSEDIRECTIONWITHPASSENGERSABOARDANELEVATORACCELERATESSMOOTHLYTOTHERATEDSPEED,PROVIDEDTHATTHEDISTANCEISLONGENOUGHTHESMOOTHNESSISMODELLEDBYTHEACCELERATIONDERIVATIVEJERK,WHICHISTHEDECELERATIONISANINVERSETOTHEACCELERATIONPHASETHEPASSENGERSARRIVETODIFFERENTFLOORSAPPROXIMATELYACCORDINGTOAPOISSONPROCESSTHISMEANSTHATTHEINTERARRIVALTIMESFOLLOWTHEEXPONENTIALDISTRIBUTION,FXEX,WHEREISTHEARRIVALRATETHEREISONEENTRANCEFLOORANDRESTOFTHEFLOORSAREPOPULATEDFLOORSTRAFFICCONSISTSOFTHREECOMPONENTSINCOMING,OUTGOINGANDINTERFLOORCOMPONENTSINCOMINGPASSENGERSTRAVELFROMANENTRANCEFLOORTOPOPULATEDFLOORS,OUTGOINGPASSENGERSFROMPOPULATEDFLOORSTOTHEENTRANCEFLOORANDINTERFLOORPASSENGERSBETWEENPOPULATEDFLOORSINTENSITYOFTRAFFICANDTHEPERCENTAGESOFINCOMING,OUTGOINGANDINTERFLOORPASSENGERSAREDETERMINEDBYTRAFFICPARAMETERSTHETRAFFICPROFILEDETERMINESTHEINTENSITYANDTHEPORTIONSOFTRAFFICCOMPONENTSATEACHMOMENTTHEINTENSITYISEXPRESSEDASPORTIONOFPOPULATIONPERTIMEUNITTHEPASSENGERSAREGENERATEDASFOLLOWS1THESIMULATORGENERATESTHEEXPECTEDNUMBEROFPASSENGERSTOA5MINPERIODANDASSIGNSTHEMRANDOMENTRYTIMESTHENUMBEROFPASSENGERSISTHETOTALPOPULATIONMULTIPLIEDBYTHETRAFFICINTENSITY2THETRAFFICCOMPONENTOFPASSENGERINCOMING,OUTGOINGORINTERFLOORISCHOSENRANDOMLYACCORDINGTOTHETRAFFICPROFILE3THECOMPONENTDETERMINESWHETHERTHEARRIVALANDDESTINATIONFLOORSAREENTRANCEORPOPULATEDFLOORSAIFTHEFLOORISAPOPULATEDFLOOR,THEPROBABILITYOFTHEFLOORISPROPORTIONALTOTHEFLOORPOPULATIONBIFINDEPENDENTLYGENERATEDARRIVALANDDESTINATIONFLOORSHAPPENTOBEEQUALCANHAPPENWITHANINTERFLOORPASSENGER,THEFLOORGENERATIONISREPEATEDTABLE1SHOWSCHARACTERISTICSOFTHESIMULATEDBUILDINGTHEBUILDINGHASALOBBYFLOORAND19POPULATEDFLOORSTHEESTIMATEDNUMBEROFPEOPLEIS60PERFLOORTABLE1CHARACTERISTICSOFTHESIMULATEDBUILDINGCHARACTERISTICVALUEFLOORS20FLOORHEIGHTM42TRAVELM78FLOORAREAM2/FLOOR1000RENTABLEAREAM2/FLOOR800PERSONSPERFLOOR60PERSONSTOTAL1140FIG1SHOWSTHEINTENSITIESOFINCOMING,OUTGOINGANDINTERFLOORPASSENGERSDURINGTHEDAYFROM7AMTO715PMTHETRAFFICPROFILEISMEASUREDFROMANOFFICEBUILDINGTHEPROFILESHOWSTYPICALMORNING,LUNCHTIMEANDAFTERNOONTRAFFICPEAKSWHENPASSENGERSAREGENERATEDACCORDINGTOTHETRAFFICPROFILE,THEEXPECTEDNUMBEROFPASSENGERSARE11502SINCETOTALPOPULATIONOFTHEBUILDINGISUNCERTAIN,THETRAFFICISVARIEDBETWEEN80AND120OFFORECASTEDTRAFFICWITHTHESEPARAMETERS,WEGENERATED21TRAFFICSITUATIONSACCORDINGTOTHETRAFFICPROFILETHESAMEPASSENGERSWEREUSEDFORALL10ALTERNATIVESINORDERTOREDUCETHECOVARIANCEBETWEENTHEMEASUREMENTSOFDIFFERENTALTERNATIVESFIG1TRAFFICPROFILEOFTHESIMULATEDBUILDING13SIIKONENML,LEPPLJELEVATORTRAFFICPATTERNRECOGNITIONINPROCEEDINGSOFTHEFOURTHWORLDCONGRESSOFTHEINTERNATIONALFUZZYSYSTEMSASSOCIATION,BRUSSELS,BELGIUM1991P195813TABLE2SHOWS10ALTERNATIVECONFIGURATIONSTHENUMBEROFELEVATORSVARIESBETWEEN6AND8,RATEDLOADFROM13TO24ANDSPEEDFROM35TO5M/SAREAISTHESHAFTSPACEPLUSWAITINGAREASPACETHEEXACTCOSTSAREUNKNOWNTHECOSTSARERANKEDFROM1TO10,WHERE1ISTHECHEAPESTAND10ISTHEMOSTEXPENSIVEALLALTERNATIVESAREFEASIBLEWITHRESPECTTOUPPEAKHANDLINGCAPACITYANDINTERVALTABLE2ALTERNATIVECONFIGURATIONSOFTHEELEVATORGROUPNAMEELEVATORSRATEDLOADSPEEDM/SACCELERATIONM/S2AREAM2COSTE6L17S461740106981E6L21S462140107742E6L17S561750107143E6L24S462440108724E7L17S3571735088755E7L17S471740108756E7L13S571350107607E7L17S571750108958E8L13S3581335087949E8L17S35817350893510SIMULATIONRESULTSAREPRESENTEDINFIG2,FIG3,FIG4ANDFIG5ASWTS,JTS,PERCENTAGEOFWTEXCEEDING60SANDPERCENTAGEOFJTSEXCEEDING120STHEPASSENGERTRANSFERTIMESARECLOSERTOREALITYTHANTHEVALUESNORMALLYUSEDINELEVATORPLANNINGTHISLOWERSTHEHANDLINGCAPACITYANDLENGTHENSTHEWAITINGANDJTSESPECIALLYWHENTHETRAFFICISINTENSIVETHEHORIZONTALAXISSHOWSTHENUMBEROFGENERATEDPASSENGERSINEACHOFTHE21TRAFFICSITUATIONSTHEFIGURESSEEMQUITESIMILAR,SINCETHEORDEROFALTERNATIVESISAPPROXIMATELYTHESAMEWITHALLCRITERIAANDALLINTENSITIESTHEGROUPSWITHEIGHTELEVATORSAREMOREEFFICIENTTHANTHESMALLERGROUPSFIG2WAITINGTIMESFIG3JOURNEYTIMESFIG4PERCENTAGEOFWAITINGTIMESOVER60SFIG5PERCENTAGEOFJOURNEYTIMESOVER120S5DECISIONMAKINGPROBLEMANDSMAAANALYSISTHEUNCERTAINTIESOFTHEPERFORMANCECRITERIAWEREASSESSEDBASEDONTHESIMULATIONSFOREACHOFTHE10CONFIGURATIONSBASEDONTHESIMULATIONRESULTSWEESTIMATEDTHEPARAMETERSFORAMULTIVARIATEGAUSSIANDISTRIBUTION,IETHEEXPECTEDVALUEOFEACHCRITERIAMEASUREMENTANDTHECOVARIANCEMATRIXFORTHEUNCERTAINTYDEPENDENCIESTHEUNCERTAINTIESOFTHEPERFORMANCECRITERIAWEREQUITEDEPENDENT,WITHMULTIVARIATECORRELATIONSINTHEINTERVAL08,1THECROSSCORRELATIONMATRIXISNOTPRESENTEDHEREBECAUSEOFITSSIZE4040THECOSTWASMODELLEDASANORDINALCRITERIONSEE3,BECAUSEEXACTPRICEINFORMATIONWASNOTAVAILABLETHEREQUIREDFLOORAREAWASMEASUREDONACARDINALSCALEWITHUNCERTAINTYFORALLALTERNATIVESTHEMEASUREMENTSFORCOSTANDAREACRITERIAAREPRESENTEDINTABLE2THECRITERIAMEASUREMENTSFORTHEPERFORMANCECRITERIAAREPRESENTEDINTABLE3TABLE3VALUESFORPERFORMANCECRITERIAOFALTERNATIVESMEANSTDEVALTERNATIVEWTJTWT60JT120E6L17S47152435813100476322959283116829E6L21S44208191210553246317628112964783E6L17S57119462313002504622579553060852E6L24S43917160110487218717277453048755E7L17S353546178492622224123072322
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