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第1页翻译部分英文原文AnAnalysisofDualShuttleAutomatedStorage/RetrievalSystemsAnAnalysisofDualShuttleAutomatedStorage/RetrievalSystemsAdhinarayanKeserlaBrettA.PetersAbstractThispaperaddressesthethroughputimprovementpossiblewiththeuseofadualshuttleautomatedstorageandretrievalsystem.Withtheuseofsuchasystem,travelbetweentimeinadualcommandcycleisvirtuallyeliminatedresultinginalargethroughputimprovement.ThedualshuttlesystemisthenextendedtoperformanequivalentoftwodualcommandsinonecycleinaquadruplecommandmodeQC.AheuristicthatsequencesretrievalstominimizetraveltimeinQCmodeisdeveloped.MonteCarlosimulationresultsareprovidedforevaluatingtheheuristicsperformanceandshowthatitperformswell,achievinglargethroughputimprovementscomparedwiththatofthedualcommandcycleoperatingunderthenearestneighborretrievalsequencingheuristic.KeywordsAutomatedStorage/RetrievalSystemsDesignAutomatedStorage/RetrievalSystemsOperationMaterialHandlingSystemsPerformanceModelingandAnalysisIntroductionAutomatedstorage/retrievalsystemsAS/RSarewidelyusedinwarehousingandmanufacturingapplications.AtypicalunitloadAS/RSconsistsofstorageracks,S/Rmachines,linkconveyors,andinput/outputI/Ostations.Animportantsystemperformancemeasureisthethroughputcapacityofthesystem.Thethroughputcapacityforasingleaisleistheinverseofthemeantransaction第2页time,whichistheexpectedamountoftimerequiredfortheS/Rmachinetostoreand/orretrieveaunitload.TheservicetimeforatransactionincludesbothS/Rmachinetraveltimeandpickup/deposittime.ThistimetypicallydependsontheconfigurationofthestoragerackandtheS/Rmachinespecifications.Hanetal.2improvedthethroughputcapacityoftheAS/RSthroughsequencingretrievals.IntelligentlysequencingtheretrievalscanreduceunproductivetravelbetweentimeswhentheS/Rmachineistravelingemptyandtherebyincreasethethroughput.TheydevelopanexpressionforthemaximumpossibleimprovementinthroughputiftravelbetweeniseliminatedforanAS/RSthatisthroughputboundandoperatesindualcommandmode.Inessence,thismeansthatiftheS/Rmachinetravelsinasinglecommandpathbutperformsbothstorageandaretrievaloperation,theabovethroughputimprovementcouldbeobtained.Inthispaper,weanalyzeanalternativedesignoftheS/RmachinethathastwoshuttlesinsteadofoneasinaregularAS/RS.Thenewdesigneliminatesthetravelbetweenthestorageandretrievalpointsandperformsbothstorageandretrievalatthepointofretrieval,therebyachievingthemaximumthroughputincreasecalculatedbyHanetal.3.ThedualshuttleAS/RSisanewdesignaimedatimprovingS/Rmachineperformance.MoststudiesonAS/RSsystemshavebeenbasedonasingleshuttledesign.InouranalysisofthedualshuttleAS/RSperformance,webuilduponthesepreviousresearchresults.1AlternativeS/RMachineDesignAtypicalunitloadAS/RShasanS/Rmachineoperatingineachaisleofthesystem.TheS/Rmachinehasamastwhichissupportedatthefloorandtheceilingandtravelshorizontallywithintheaisle.Connectedtothismastisashuttlemechanismthatcarriestheunitloadandmovesverticallyupanddownthemast.Theshuttlemechanismalsotransfersloadsinandoutofstoragelocationsintherack.Figure1providesanillustrationofthesingleshuttleS/Rmachine.Figure1.SingleShuttleS/RMachineDesignAtypicalsingleshuttleAS/RScanperformasinglecommandcycleoradualcommandcycle.Asinglecommandcycleconsistsofeitherstorageorretrieval.Forstorage,thetimeconsistsofthetimetopickuptheloadattheI/Opoint,travel第3页tothestoragepoint,deposittheloadatthatpoint,andreturntotheI/Opoint.Thetimeforretrievalisdevelopedsimilarly.Adualcommandcycleinvolvesbothstorageandretrievalinthesamecycle.ThecycletimeinvolvesthetimetopickuptheloadattheI/Opoint,traveltothestoragelocation,placetheloadintherack,travelemptytotheretrievallocation,retrieveaload,returntotheI/Opoint,anddeposittheloadattheI/Opoint.IfwecriticallyanalyzethedualcommandcycleoftheS/RmachineshownbythesolidlineinFigure2,apotentialopenlocationforafuturestorageiscreatedwhenaretrievalisperformed.Furthermore,ifbotharetrievalandastorageareperformedatthesamepoint,thetravelbetweentimeTBiseliminated,andthetraveltimewillbeequaltothesinglecommandtraveltime.WiththeexistingAS/RSdesign,thismodeofoperationisnotpossibletherefore,analternativetotheS/Rmachine,adualshuttleR/Smachine,isproposed.Figure2.DualCommandTravelPathsofS/RandR/SMachines2R/SMachineOperationsConsideranS/Rmachinewithtwoshuttlemechanismsinsteadofone.ThisnewS/Rmachinecouldnowcarrytwoloadssimultaneously.Eachshuttlemechanismcouldoperateindependentlyoftheother,sothatindividualloadscanstillbestoredandretrieved.AnillustrationofthedualshuttleS/RmachineisshowninFigure3.ThisnewS/Rmachinewouldoperateasdescribedbelow.Figure3.DualShuttleS/RMachineDesignTheS/RmachinepicksuptheitemtobestoredfromtheI/Opoint,loadsitintothefirstshuttle,andmovestotheretrievallocation.Afterreachingtheretrievallocation,thesecondshuttleispositionedtopickuptheitemtoberetrieved.Afterretrieval,theS/Rmachinepositionsthefirstshuttleanddepositstheload.TheS/RmachinethenreturnstotheI/Opoint.TheoperationcaneasilybeseenasasinglecommandoperationplusasmalltraveltimeforrepositioningtheS/Rmachinebetweentheretrievalandstorageaswellastheadditionalpickupanddeposittimeassociatedwiththesecondload.Therefore,theS/RmachinenowoperatesasanR/Smachineperformingaretrievalfirstthenastorageinadualcommandcycle.SincetheR/Smachinehastwoshuttles,thepositionoftheshuttleshasaroleintheoperationofthesystem.Withtwoshuttles,theR/Smachineisabletoperformadualcommandcycleatonelocationintherack.Thisoperationis第4页accomplishedbyfirstretrievingtheloadontotheemptyshuttle,transferringthesecondshuttleintoposition,andstoringtheloadintotheemptylocationintherack.However,thechoiceofshuttleconfigurationdoesnotimpacttheanalysisinthispaper.Toperformtheseoperations,theR/Smachinemustmovethesecondshuttleintopositionafterthefirstshuttlehascompletedtheretrieval.Duetothesmalldistanceinvolved,theR/Smachinewilluseaslowercreepspeedforpositioning,butthistraveltimeisgenerallysmall.Furthermore,anamountofcreeptimeisusuallyincludedinthepickupanddeposittimetoaccountforthisrequiredpositioning.AseconddesigncharacteristicisthatadditionalclearancebeyondthefirstandlastrowandcolumnoftherackmustbeprovidedforovertraveloftheR/Smachinetoaccommodatebothshuttlemechanisms.3ThroughputImprovementToestimatethethroughputimprovementbythedualshuttlesystemoverexistingdesigns,weusetheexpressionsforsinglecommandanddualcommandcycletimesdevelopedbyBozerandWhite1andthetabulatedvaluesforthenearestneighborheuristicfromHanetal.4.Indevelopingtheexpressions,theauthorsin1and4madeseveralassumptions.Thesameassumptionsholdforthenewdesignandincludethefollowing.1TherackisconsideredtobeacontinuousrectangularpickfacewheretheI/Opointislocatedatthelowerlefthandcorneroftherack.2Theracklengthandheight,aswellastheS/Rmachinevelocityinthehorizontalandverticaldirections,areknown.3TheS/Rmachinetravelssimultaneouslyinthehorizontalandverticaldirections.Incalculatingthetraveltime,constantvelocitiesareusedforhorizontalandverticaltravel.Accelerationanddecelerationeffectsareimplicitlyaccountedforineitherareducedtopspeedoranincreasedpickupanddeposittime.Acreepspeedisusedforrepositioningthedualshuttle.4Pickupanddeposittimesassociatedwithloadhandlingareassumedconstantand,therefore,thesecouldbeeasilyaddedintothecycletimeexpressions.5TheS/Rmachineoperateseitheronasingleordualcommandbasis,i.e.,multiplestopsintheaislearenotallowed.ThisassumptionislaterrelaxedforthenewR/Smachinetoperformaquadruplecommandcycle.
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