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CASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS11CASESTUDY2THESUPERMARKET11INTRODUCTIONAFAMILIAREXAMPLEOFAQUEUINGSYSTEMISATSUPERMARKETCHECKOUTSWHEREQUEUESAREAWELLKNOWNPHENOMENONESPECIALLYONSATURDAYS,THESEQUEUESARETHECAUSEOFANNOYANCEANDDELAYSFORTHECUSTOMERSAFEWSOLUTIONSTOTHISISSUEAREOPENINGEXTRACHECKOUTSCAPACITYINCREASETHROUGHMOREPERSONNEL,TOPENINGANDCLOSINGCHECKOUTSACCORDINGTOTHENUMBEROFCUSTOMERSQUEUINGVARIABLECAPACITYORINTRODUCINGEXPRESSCHECKOUTSDISTINCTIONINTHETYPEOFCUSTOMERSINTHEFOLLOWINGEXAMPLE,WEWILLLOOKATANUMBEROFDIFFERENTSTRATEGIESANDEXAMINETHEEFFECTONWAITINGTIMEANDQUEUELENGTH12DESCRIPTIONOFTHESITUATIONINOURLOCALSUPERMARKETTHEREAREEIGHTCHECKOUTLANESAVAILABLEONSATURDAY,THEDAYWHENTHESTUDYISCONDUCTED,THECHECKOUTSAREOPENFROM0900TO1700HOURSFORTHEPURPOSESOFTHESEEXERCISES,WEWILLIGNOREANYTHINGTHATHAPPENSAFTER1700ANAVERAGEOF1400SHOPPERSARRIVEDURINGTHEDAYONARANDOMBASISAFTERTHECUSTOMERSHAVEDONETHEIRSHOPPING,THEYGOTOTHECHECKOUTSANDCHOOSEAQUEUESOMETIMESACUSTOMERWILLCHANGEQUEUESIFANOTHERQUEUEAPPEARSTOBEGOINGFASTERTHISISCALLEDJOCKEYINGANDITCANREDUCEQUEUESANDSPREADTHELOADACROSSCHECKOUTOPERATORSMOREEVENLYALTHOUGHINREALITYTHEORDERINWHICHCUSTOMERSARESERVEDISSLIGHTLYCHANGEDBYJOCKEYINGINOURMODEL,WEINITIALLYOPTFORACENTRALQUEUEWHERECUSTOMERSARESERVEDONAFIRSTINFIRSTOUTBASISFURTHERMORE,WEASSUMETHATALLTHECHECKOUTOPERATORSWORKATTHESAMESPEEDIDENTICALCOUNTERSCUSTOMERSAREALREADYCOMPLAININGABOUTTHEWAITINGTIMESATTHECHECKOUTS,ANDTHEMANAGERWANTSTOSTUDYTHEPROBLEMINDETAILTHEFEELINGISTHATATHOROUGHEXAMINATIONOFTHEPROBLEMWOULDALSOHELPTOSOLVESIMILARPROBLEMSELSEWHEREINTHEBUSINESSTHERESEARCHWILLFOCUSONTHEEFFECTOFDIFFERENTQUEUINGSTRATEGIESONCUSTOMERWAITINGTIMESANDQUEUELENGTHSSTRATEGY1FIXEDPERSONNEL,SERVICETIMEINDEPENDENTOFTHENUMBEROFGROCERIESINTHISCASE,ALLCHECKOUTSAREOPENANDTHESERVICETIMEFOREACHCUSTOMERISTAKENFROMANEGATIVEEXPONENTIALDISTRIBUTIONWITHANAVERAGEOF25MINUTESSUPERMARKET1MODSTRATEGY2FIXEDPERSONNEL,SERVICETIMEDEPENDENTONTHENUMBEROFGROCERIESTHISISAVARIATIONOFTHEFIRSTSTRATEGYWHERETHESERVICETIMEDEPENDSONTHENUMBEROFITEMSPURCHASEDWEASSUMETHATTHESCANNINGTIMEPERITEMIS6SECONDS,ANDTHATPAYMENTTAKES30SECONDSMEASUREMENTSHAVESHOWNTHATTHEFOLLOWINGEMPIRICALPROBABILITYDISTRIBUTIONCANBEUSEDFORTHENUMBEROFGROCERIESCASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS2NUMBEROFITEMSPROBABILITYINNUMBEROFITEMSPROBABILITYINNUMBEROFITEMSPROBABILITYIN121833512219336132203371422133815222339163233401732434118325342193262431103272441113282451123292461133302471143311481153321491163331501173341TABLE11PROBABILITYDISTRIBUTIONTHISREFINEMENTRESULTSINASECONDSIMULATIONMODELSUPERMARKET2MODSTRATEGY3FIXEDPERSONNEL,SERVICETIMEDEPENDENTOFTHENUMBEROFGROCERIESANDSEPARATIONOFCUSTOMERTYPESINTHISSTRATEGY,THEFIRSTCHECKOUTISANEXPRESSLANEONLYCUSTOMERSWITH10ITEMSORLESSAREALLOWEDTOUSETHISCHECKOUTINTHISCASE,WEASSUMETHATALLTHESECUSTOMERSWILLACTUALLYUSETHEEXPRESSLANESUPERMARKET3MODSTRATEGY4FIXEDPERSONNEL,SERVICETIMEDEPENDENTOFTHENUMBEROFGROCERIES,WITHPRIORITYTOTHECUSTOMERSWITHTHELEASTGROCERIESTHISALTERNATIVEISINTERESTINGFROMTHEPOINTOFVIEWOFFLOWS,BUTWOULDLEADTOMAJORPROBLEMSINSUPERMARKETSMODIFYTHESECONDMODELSOTHATCUSTOMERSWITHTHEFEWESTITEMSARESERVEDFIRSTSUPERMARKET4MODSTRATEGY5VARIABLEPERSONNEL,SERVICETIMEDEPENDENTONTHENUMBEROFPEOPLEWAITINGTHEAVAILABILITYOFCHECKOUTSISNOWLINKEDTOTHENUMBEROFCUSTOMERSINTHEQUEUEIF0TO3CUSTOMERSAREWAITING,CHECKOUT1OPENS,4TO6CUSTOMERS,CHECKOUT2ETCUPTOATOTALOF8CHECKOUTSFOR22CUSTOMERSORMOREWHENTHENUMBEROFCUSTOMERSQUEUINGDECREASES,THECORRESPONDINGNUMBEROFCHECKOUTSCLOSESUPERMARKET5MOD13ASSIGNMENTS1ANALYSEEACHSTRATEGYACCURATELYONTHEBASISOFTHEORETICALUTILIZATIONS,TRYTOESTIMATEWHICHSYSTEMWILLOPERATETHEMOSTEFFICIENTLY2BUILDSIMULATIONMODELSFORALLSTRATEGIESANDDEFINEFOREACHTHEAVERAGEQUEUEANDWAITINGTIMEINSTRATEGY3FORBOTHCUSTOMERTYPESCASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS33WHICHSYSTEMWOULDYOURECOMMENDCANTHEYBECOMPAREDWITHEACHOTHERARETHEREBETTERALTERNATIVESCASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS42SUGGESTIONSFORMODELLINGINEDTHEFIRSTMODELISEASYTOBUILDADDTHEAPPROPRIATEPFMSINTHE“EXPERIMENTWIZARD”ASYOULEARNTINTHETUTORIALFORTHEOTHERMODELS,WEADVISEYOUTOGOTHROUGHTHEUSEOFEMPIRICALDISTRIBUTIONSANDTHEFUNCTIONINGOFLABELSEXAMINEHOWYOUCANSORTCUSTOMERSINTHEQUEUEBYUSINGDIFFERENTQUEUEDISCIPLINESSTRATEGY5ISTHEMOSTDIFFICULTANDREQUIRESTHEEXTENSIVEUSEOF4DSCRIPTASSIGNMENT3REQUIRESYOUTOUSEYOUROWNINITIATIVETOIDENTIFYANDANALYSEWAYSINWHICHWAITINGTIMEANDQUEUELENGTHSCANBEREDUCEDALLSTUDIESARETOBECARRIEDOUTCAREFULLYANDACCORDINGTOASIMULATIONMETHODOLOGYCASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS53WORKEDEXAMPLESTHESUPERMARKET31ASSIGNMENT1ACCORDINGTOTHEQUEUINGTHEORY,STRATEGY1ISDEFINEDASANM/M/8SYSTEMTHEARRIVALANDSERVICEPROCESSESAREBOTHPOISSONPROCESSESANDTHEREARE8WINDOWSTHEUTILIZATION,DEFINEDASTHEAVERAGEFLOWDIVIDEDBYTHEAVERAGESERVICECAPACITY,GIVESANINDICATIONFORTHELOADONTHESYSTEMIFTHEUTILIZATIONISCLOSETO1,LONGQUEUESCANBEEXPECTEDFURTHERMORE,THISMEASURECANGIVEANEARLYINSIGHTINTOWHICHSYSTEMWILLPERFORMTHEBESTTHEAVERAGEFLOWISOF1400CUSTOMERSADAYASERVICEOPERATIONTAKESANAVERAGEOF150SECONDSINTOACCOUNTACHECKOUTSSERVICECAPACITYIS3600/15024CUSTOMERSPERHOURINSTRATEGY1,THETOTALSERVICECAPACITYAMOUNTS8X24192CUSTOMERSPERHOURINAN8HOURWORKINGDAY,THISREPRESENTS1536CUSTOMERSTHISRESULTSIN11400/1536091ACONSIDERATIONOFSIDEISSUERELATINGTOTHEORETICALDISTRIBUTIONSISAPPROPRIATETHECALCULATEDUTILIZATIONSAREASSUMINGABALANCED,STEADYSTATESITUATIONTHISSTATEISONLYREACHEDAFTERAPERIODOFWARMUPTIME,ANDESPECIALLYINTHECASEOFHIGHUTILIZATIONS,THISTIMEMAYBEQUITEPROTRACTEDINTHESEEXAMPLES,THESYSTEMSTARTSANDFINISHESEMPTYTHEACTIVETIMEMAYBETOOSHORTFORASTEADYSTATETOBEREACHED,ANDIFTHISISTHECASETHEACTUALUTILIZATIONSMAYBELOWERTHANTHETHEORYPREDICTSFORALLOTHERSTRATEGIES,THEPROBABILITYDISTRIBUTIONOFTHENUMBEROFITEMSISIMPORTANTTHEREARE50POSSIBLERESULTS,EACHWITHAPROBABILITYVARYINGFROM1TO3PERCENTTHEAVERAGEVALUEOFTHENUMBEROFGROCERIESIS205THISCANBECALCULATEDBYFACTORINGEVERYQUANTITYBYITSPROBABILITYANDTAKINGTHETOTALUSINGTHEABOVEAPPROACHWECANCALCULATETHATTHEAVERAGESERVICETIMEWILLBEROUGHLY150SECONDS6X20530153THISGIVESUSAWORKLOADANDUTILIZATIONCOMPARABLETOSTRATEGY1,THOUGHTHEUNPREDICTABILITYOFTHEEXPONENTIALDISTRIBUTIONISSMOOTHEDSOMEWHATINTHISCASETHESERVICETIMEWILLMOREORLESSBEUNIFORMLYDIVIDEDBETWEEN36SECONDS1ITEMAND330SECONDS50ITEMSINTHECASEOFTRATEGY3,THEREARETWOCUSTOMERTYPESTHEAVERAGENUMBEROFITEMSFORTHECUSTOMERSWITHUPTO10ITEMSIS1X0022X0025X0026X0037X00310X003X415X46ITEMSTHEFACTOROF4INTHEEQUATIONISREQUIREDBECAUSE25OFTHEFULLGROUPWILLHAVE10ITEMSORLESSTHISISTHESUMOFTHEPROBABILITIESFORITEMSFROM1TO10ASTHISGROUPREPRESENT100OFTHELOADFORTHEEXPRESSCHECKOUT,WEMUSTADJUSTTHEPROBABILITIESBY100/25OR4THISRESULTSINANAVERAGESERVICETIMEATTHEEXPRESSCHECKOUTOFSECONDS630THEAVERAGENUMBEROFITEMSFORTHEOTHERCUSTOMERSNOWINCREASESUPTOAPPROXIMATELY25,LEADINGTOANAVERAGESERVICETIMEOFAPPROXIMATELY3MINUTESFROMTHE1751400/8ARRIVINGCUSTOMERSPERHOUR,2544CUSTOMERSWILLUSETHEEXPRESSLANEAND75131CUSTOMERSTHEOTHERCHECKOUTSCASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS6ATTHEEXPRESSCASHREGISTER,THESERVICECAPACITYWILLREACH3600/66545CUSTOMERSPERHOUR,BRINGINGTHETHEORETICALUTILIZATIONTOAPPROXIMATELY44/545OR81THISISANIMPROVEMENTFORTHISTYPEOFCUSTOMERCOMPAREDTOTHEPREVIOUSSITUATIONTHEOTHERCUSTOMERSARESUFFERINGTHECONSEQUENCESOFTHISAFLOWOF131ONAVERAGEPERHOURCOMPAREDTOAJOINTCAPACITYOF140PERHOURTHEUTILIZATIONGOESUPTO94,ADETERIORATIONFORTHISTYPEOFCUSTOMERCOMPAREDTOTHESITUATIONDEPICTEDINSTRATEGY2,ANDTHISWILLRESULTINLONGERQUEUESINVARIANTSTRATEGY4,THEUTILIZATIONISEQUALTOTHATOFSTRATEGY2,BECAUSETHEQUEUEDISCIPLINEISTHEONLYFACTORALTEREDHOWEVER,THEFASTESTCUSTOMERSARESERVEDFIRSTHERE,WHICHWILLHAVEAPOSITIVEANDDIFFICULTTOCALCULATEEFFECTONTHEFLOWCOMPAREDTOSTRATEGY2,STRATEGY5IMPLIESLESSCAPACITYRESOURCESANDTHUSLONGERQUEUESCONCLUSIONSTRATEGY4ISEXPECTEDTOTURNOUTASTHEBESTFUNCTIONINGSYSTEMHOWEVERTHEIMPLEMENTATIONOFSUCHASYSTEMINPRACTICEWOULDCREATEMANYPROBLEMSWETHEREFORESUGGESTTHATYOUEXPERIMENTWITHALTERNATIVESTRATEGIESSUCHASCHANGINGTHENUMBEROFITEMSTOALLOWATTHEEXPRESSCHECKOUT,CREATINGMORECUSTOMERGROUPSANDSOON32ASSIGNMENTS24AND3321STEP1PROBLEMFORMULATIONANDOBJECTIVETHESUPERMARKETCUSTOMERSCOMPLAINABOUTLONGQUEUESATTHECHECKOUTSTHEMANAGEMENTWANTTOINVESTIGATETHESECOMPLAINTSANDUSETHISSTUDYATOSEARCHFORALTERNATIVEWORKINGMETHODSTOTHISEND,5STRATEGIESHAVEBEENFORMULATEDFOREACHSTRATEGY,THEAVERAGEQUEUESANDWAITINGTIMESWILLBESTUDIED,WITHOUTANYCONSTRAINTSDEFINEDBEFOREHANDTHEOBJECTIVEOFTHEINVESTIGATIONISTHECOMPARISONOFTHESECHARACTERISTICSINTHEDIFFERENTSTRATEGIESIFTHEMANAGEMENTWANTTOLIMITTHEIRINVESTIGATIONTOTHESE5STRATEGIESONLY,THEOBJECTIVEOFTHESTUDYCANBEDEFINEDASFOLLOWSTHEDETERMINATIONOFTHEAVERAGEWAITINGTIMEANDQUEUEOFCUSTOMERGROUPSFORTHESUGGESTEDSTRATEGIESOFCOURSE,INREALLIFEOTHERELEMENTSHAVETOBETAKENINTOCONSIDERATIONSUCHASTHECOSTSRELATINGTOPOTENTIALADJUSTMENTS,BUTTHEYWILLNOTBECONSIDEREDINTHISCASESTUDY322STEP2MODELLINGASYSTEMDESCRIPTIONWHENTHECUSTOMERSHAVECOMPLETEDTHEIRSHOPPING,THEYARRIVEATTHECHECKOUTSTHEMOTIMEOFARRIVALISTHEMOMENTWHENTHECUSTOMERSJOINSAQUEUENORMALLY,CUSTOMERSPICKTHESHORTESTQUEUEATONEOFTHE8CHECKOUTSANDWILLSWITCHQUEUESNOWANDTHENWHENANOTHERONEISGOINGFASTERTHEORDEROFSERVICEINAQUEUEISFIFOAFTERPAYMENT,THECUSTOMERSLEAVETHESYSTEMTHISPROCESSISIDENTICALINSTRATEGY2,EXCEPTTHATTHEPROCESSINGTIMEFORPAYMENTISNOWLINKEDTOTHENUMBEROFITEMSOFGROCERIESASOPPOSEDTOSTRATEGY2,THEFIFOQUEUEDISCIPLINEINSTRATEGY4ISNOTVALIDCUSTOMERSARESORTEDINTHEQUEUEONTHEBASISOFTHENUMBEROFITEMSPURCHASED,WITHTHECUSTOMERSWITHTHEFEWESTITEMSPLACEDATTHEFRONTOFTHEQUEUECASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS7INSTRATEGY3,TWOTYPESOFCUSTOMERANDCHECKOUTAREUSED,EACHONEWITHTHEIROWNQUEUESFINALLY,STRATEGY5ISQUITESIMILARTOSTRATEGY2,EXCEPTTHATCHECKOUTSCANOPENANDCLOSEACCORDINGTOTHELENGTHOFTHEQUEUESBDATACOLLECTIONALLNECESSARYINFORMATIONISTOBEFOUNDINTHECASESTUDYDATARELATINGTOINTERARRIVALTIMESANDTHEPROCESSINGTIMECANBEMEASUREDINAREALSITUATIONQUITEEASILYCONVERSIONTOAPPROPRIATEPROBABILITYDISTRIBUTIONSHASALREADYBEENDONECREPRESENTATIONOFTHESYSTEMINAMODELITHASBEENINDICATEDINTHECASESTUDYTHATACENTRALQUEUE,WHERETHECUSTOMERSARESERVEDONAFIFOBASIS,WILLSUFFICEFORTHEMODELCUSTOMERSDONOTSWITCHQUEUES,ANDTHEYLEAVETHESYSTEMAFTERHAVINGPAIDTHISDISTORTIONWITHRESPECTTOREALITYHASALREADYBEENDISCUSSEDEARLIERTHEDIFFICULTYAPPEARSONHOWTODEVELOPRULESFORJOCKEYINGANDDETERMINETHROUGHPUTTIMESBETWEENCHECKOUTSTHETIMEUNITINEDISTHESECONDAWORKINGDAYCONSISTSOF8HOURS,THATISFROM0900TO1700HOURSINREALITY,THESUPERMARKETISSTILLOPENAFTER1700HOURS,BUTTHISISNOTTAKENINTOCONSIDERATIONFORTHEMODELTHISOMISSIONWILLNOTINFACTHAVEMUCHEFFECTONTHERESULTSDERIVEDFROMTHEMODELTHEMOSTIMPORTANTMODELDATAARE1ARRIVALPATTERN1400CUSTOMERSADAYMEANSANAVERAGEINTERARRIVALTIMEOF206SECONDS,WHICHISTHEPARAMETEROFTHERELATEDEXPONENTIALDISTRIBUTION2BUFFERONEORTWOQUEUESSEESTRATEGY3ARETOBEFOUNDINTHEMODELTHEQUEUESREPRESENTTHECUSTOMERQUEUESFORWHICHACAPACITYOF100ISAMPLYSUFFICIENTWEASSUMETHATPHYSICALSPACELIMITATIONDOESNOTPLAYANYROLETHEEXITISLOCATEDBEHINDTHE8CHECKOUTSSERVERSORCOUNTERSTHISFINALBUFFERCONTAINSTHECUSTOMERSSERVEDTHEYARENOTINTHEACTUALSYSTEMANYMORE,BUTBYUSINGTHISMODELPATTERN,DATARELATINGTOTHENUMBEROFCUSTOMERSSERVEDCANBEGATHEREDEASILY3PROCESSTIMEDISTRIBUTIONSTHEONLYPROCESSINVOLVEDISPAYMENTINSTRATEGY1,THISPROCESSISEXPONENTIALLYDISTRIBUTEDWITHANAVERAGEOF150SECONDSASFARASTHEOTHERSTRATEGIESARECONCERNED,THEFOLLOWINGFORMULAISTOBEAPPLIEDPROCESSTIME6XNUMBEROFGROCERYITEMS30ASARESULT,ANUMBEROFITEMSMUSTBEALLOCATEDTOTHECUSTOMERATANEARLIERSTAGEINTHEMODELFORINSTANCE,THENUMBEROFITEMSCANRANDOMLYBEGIVENTOTHECUSTOMERARRIVINGINTHESYSTEMACCORDINGTOTHEDEFINEDEMPIRICALDISTRIBUTION4ROUTECHOICEWHENARRIVINGINTHESYSTEM,THECUSTOMERSCHOSEFORTHECENTRALQUEUESTRATEGIES1,2,4AND5STRATEGY3ISTHEONLYONEWHERE2QUEUESAREAVAILABLECUSTOMERSWITHLESSTHAN11GROCERIESAREFORWARDEDTOTHEEXPRESSCHECKOUTANDTHEOTHERSTOTHECENTRALQUEUEFORTHEOTHERCHECKOUTSCONSEQUENTLY,ACASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS8DISTRIBUTIONMECHANISMFORTHESEQUEUESISREQUIREDTHECUSTOMERSTHENWAIT,PAYFORTHEIRPURCHASESANDLEAVETHESYSTEM5QUEUEDISCIPLINETHEQUEUEDISCIPLINEINDICATESWHICHCUSTOMERISFORWARDEDFROMTHEQUEUETOANAVAILABLECHECKOUTINSTRATEGIES1,2,AND5WITHTHECENTRALQUEUE,ITISFIFOFIRSTIN,FIRSTOUTFORTHETWOQUEUESINSTRATEGY3,THEQUEUEDISCIPLINEFIFOISALSOAPPLICABLEINSTRATEGY4HOWEVER,THECUSTOMERWITHTHEFEWESTGROCERIESISPLACEDAHEADINTHEQUEUETHESORTINGOCCURSONTHEBASISOFASPECIFICLABEL,FOREXAMPLENUMBEROFITEMSINSTRATEGY5,ANEXTRAFEATUREHASTOBEINCLUDEDOPENINGANDCLOSINGCHECKOUTSWHENACUSTOMERARRIVESINORLEAVESTHEQUEUE,THELENGTHOFTHEQUEUEHASTOBECHECKED,RESULTINGINOPENINGORCLOSINGASPECIFICCHECKOUTDFROMMODELTOPROGRAMALLMODELSAREBUILTINEDANDSUPPLIEDTOGETHERWITHABRIEFEXPLANATIONWHERETHETRANSITIONFROMTHEPAPERMODELTOTHESELECTEDEDMODELSISMADETHEMODELSOFTHISCASESTUDYARETOBEFOUNDUNDERTHENAMESSUPERMARKET1MODTOSUPERMARKET5MOD,CORRESPONDINGTOTHEFIVESTRATEGIESAFTERLOADINGAMODELINED,YOUCANSEEHOWTHEMODELWASTRANSFORMEDINTOAPROGRAMNOTETHATMANYDIFFERENTCORRECTMODELSCANBEPRODUCED323DESIGNOFEXPERIMENTSTHEINFORMATIONWEWANTTORETRIEVEFROMTHEMODELSISTHEAVERAGEQUEUESANDTHEAVERAGEWAITINGTIMEOFTHECUSTOMERSACCORDINGTOTHEEXPERIMENTSWEWANTTOCARRYOUT,WENEEDTOMAKERELIABLEANDACCURATESTATEMENTSTHEFOLLOWINGPARAMETERSHAVETOBETAKENINTOCONSIDERATION1SELECTEDTIMESUBDIVISION2LENGTHOFSIMULATIONRUN3LENGTHOFWARMUPPERIOD4NUMBEROFSIMULATIONRUNS5OUTPUTVARIABLESINTHEMODELFORMULATION,THESECONDHASBEENCHOSENASSMALLESTTIMEUNITTHEWHOLESIMULATIONRUNCANNOWBERENDEREDINSECONDS,BUTITISMORECONVENIENTTOSELECTAMORESTRUCTUREDTIMESUBDIVISIONBASEDONREALITYTHEQUEUESYSTEMASDEFINEDINTHESTUDYCANBECHARACTERISEDASATERMINATINGSYSTEMEACHDAYALWAYSSTARTSWITHANEMPTYSYSTEMTHECONSEQUENCEOFATERMINATINGSYSTEMINTHESIMULATIONISTHATAWARMUPPERIODISSUPERFLUOUSANDTHATTHELENGTHOFARUNISFIXEDBECAUSETHEEVENTSOFONEDAYDONOTCARRYOVERTOTHEOTHERDAYS,AN8HOURDAYHASBEENCHOSENASLENGTHFORONESIMULATIONRUNCONSIDERINGTHENATUREANDTHERANGEOFTHESELECTIONCRITERION,MANYDAYSNEEDTOBERUNWEHAVECHOSEN50RUNSOFONEDAY,MEANING50SATURDAYSBYREPEATINGARUNASDESCRIBEDABOVE,INDEPENDENTOUTCOMESARISEINORDERTOCREATEACONFIDENCEINTERVAL,AMINIMUMOF5RUNSISREQUIREDTHECHOICEFOR50ISINTHISRESPECTAMPLYSUFFICIENTCASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS9THEOUTPUTVARIABLESHAVEALREADYBEENDEFINEDINTHEOBJECTIVESOFTHISSTUDYAVERAGEWAITINGTIMEANDAVERAGEQUEUEOTHERPARAMETERSSUCHASUTILIZATIONCANBEADDEDIFNEEDBE324ANALYSISOFTHEOUTPUTRESULTSONTHEBASISOFTHEFIRSTFOURSTEPSOFTHESTUDY,THERUNSFORTHE5MODELSHAVEBEENPERFORMEDTHERESULTSAREDISPLAYEDINTHEBELOWTABLE95CONFIDENCEINTERVALSHAVEBEENUSEDINALLCASESTHEAVERAGEQUEUEANDAVERAGEWAITINGTIMEINEACHMODELHAVEBEENMEASUREDVARIANTQUEUEWAITINGTIMEINSECONDS168101392025508112153CUSTOMERSWITH10ORLESSITEMS1602129133CUSTOMERSWITHMORETHAN10ITEMS63121713044206851252230845813TABLE31RESULTSOFTHERUNS325CONCLUSIONSANDRECOMMENDATIONSTHERESULTSDONOTCONTRADICTTHEANALYSISMADEBEFOREHANDSTRATEGIES1ANEWCUSTOMERISGENERATEDACCORDINGTOANEXPONENTIALDISTRIBUTIONQUEUE2QUEUEATTHECASHREGISTERSCAPACITY250THEQUEUECAPACITYALWAYSNEEDSTOBESUFFICIENTSENDTO4ARANDOMOPENCHANNELCHOOSEARANDOMCHANNELFROMALLTHEOPENOUTPUTCHANNELSWHENSEVERALCHECKOUTSAREAVAILABLE,ACHECKOUTISSELECTEDATRANDOMIFTHEYAREALLBUSY,THEFIRSTAVAILABLEISSELECTEDCHECKOUT1TO8THECHECKOUTSCYCLETIMENEGEXP150,THEAVERAGESERVICETIMEISOF150SECONDS25MINUTES,EXPONENTIALLYDISTRIBUTEDEXPERIMENTWIZARD,PFM1AVERAGEQUEUEATQUEUE2AVGCONTENTCSPFM2AVERAGEWAITINGTIMEATQUEUE2AVGSTAYCSPICTURE41LAYOUTSTRATEGIES2,4AND5CASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS11STRATEGY2SUPERMARKET2MODINTHISMODEL,THEEMPIRICALATOMHASBEENADDEDTHISATOMCANBEUSEDINORDERTOGENERATEANEMPIRICALDISTRIBUTIONTHEATOMCONTAINSATABLE,INWHICHANUMBEROFROWSAREFILLEDINWITHTHECUMULATIVEPROBABILITYPERCENTAGEANDRELATINGVALUESFORTHEPROBABILITYRELATINGTOTHEFIRST5ITEMS,THEROWSCANBEREPRESENTEDASFOLLOWSPICTURE42EMPIRICALDISTRIBUTIONTABLE202PROBABILITYOF1ITEM422PROBABILITYOF2ITEMS642PROBABILITYOF3ITEMS862PROBABILITYOF4ITEMS1082PROBABILITYOF5ITEMSETCINOUREXAMPLE,50ROWSWILLHAVETOBEENTEREDINTOTALBYGIVINGADISTRIBUTIONANAMECALLEDGROCERIES,A4DSCRIPTFUNCTIONISREGISTEREDUNDERTHATNAMETHISFUNCTIONWILLEXTRACTAVALUEOUTOFTHETABLECHECKOUT1TO8THECHECKOUTSCYCLETIME6GROCERIES30INTHISCASE,AVALUECALLED“GROCERIES”ISEXTRACTEDFROMTHEEMPIRICALDISTRIBUTIONITREPRESENTSTHENUMBEROFPRODUCTSTHECUSTOMERSHASTHENUMBEROFPRODUCTSISMULTIPLIEDBY6SECONDSSCANTIMEPERPRODUCTANDTHEN30SECONDSAREADDEDPAYMENTLOOKATTHETHIRDMODELFORANOTHERWAYTOSOLVETHISPROBLEMCASE2THESUPERMARKETINCONTROLENTERPRISEDYNAMICS12STRATEGY3SUPERMARKET3MODINTHISSTRATEGY,TWOQUEUESAREUSEDONEFORTHEEXPRESSCHECKOUTANDONEFORTHEOTHERCHECKOUTSALSO,TWOEXTRAPFMSHAVEBEENADDEDINORDERTOMEASUREBOTHQUEUESSEPARATELYTHEPICTUREBELOWSHOWSTHEMODELLAYOUTPICTURE43LAYOUTSTRATEGY3CUSTOMERSARRIVALGENERATOROFCUSTOMERSTRIGGERONCREATIONLABELITEMS,IGROCERIESATTHEMOMENTOFCREATION,EACHCUSTOMERNOWRECEIVESALABELCONTAININGTHENUMBEROFITEMSTHISCUSTOMERISGOINGTOBUYTHENUMBEROFGROCERIESITEMSISEXTRACTEDFROMTHEEMPIRICALDISTRIBUTIONATTHESAMETIMESENDTO8BYLABELVALUECONDITIONALIFTHEVALUEONTHELABELNAMEDITEMSOFTHE1STATOMINTHEQUEUEISTHEVALUE11THENSENDTOCHANNEL1ELSE2ALLCUSTOMERSWITHLESSTHAN11GROCERIESAREDIREC
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