摘（quadupecoadoe簡稱C（QC中的 Hanetal.[2]通過立體倉庫返回站點(diǎn)的排列提高了立體倉庫的工作能力，合理的排列返回Hanetal.所說的最大效率1所示。圖 圖 分別能存庫和出庫,所以堆垛機(jī)的兩個(gè)貨叉機(jī)構(gòu)能夠相互獨(dú)立運(yùn)行,具體結(jié)構(gòu)如圖3所示,這種3.為了估算正在設(shè)計(jì)的雙貨叉系統(tǒng)工作量的提高，我們引用Bozer和White[1]提出的有關(guān)單任務(wù)和雙任務(wù)指令所需時(shí)間理論和Hanetal.提出的最近有意義想法價(jià)值理論，這些理論家nm并分別把它們放置在指定的位置,在不同位置取兩件貨物并回到出入口,如圖4所示.上述工作HanS/R機(jī)器的新設(shè)計(jì)有二個(gè)航天飛機(jī)因此可能被操作如一個(gè)雙重的航天飛機(jī)系統(tǒng):45 Bozer,Y.A.andJ.A.White,"Travel-TimeModelsforAutomatedStorage/RetrievalSystems,"IIETransactions,Vol.16,No.4,1984,329-338.Elsayed,E.A.andO.I.Unal,"OrderBatchingAlgorithmsandTravelTimeEstimationforAutomatedStorage/RetrievalSystems,"InternationalJournalofProductionResearch,Vol.27,No.7,1989,1097-1114.Han,M.H.,L.F.McGinnis,J.S.Shieh,andJ.A.White,"OnSequencingRetrievalsInAnAutomatedStorage/RetrievalSystem,"IIETransactions,March1987,56-66.AnAnalysisOfDualShuttleAutomatedStorage/RetrievalAnAnalysisOfDualShuttleAutomatedStorage/RetrievalSystemsAdhinarayanKeserlaBrettA.PetersAugust1,Thisworkingpaperisnottobecopied,quoted,orcitedwithoutthepermissionoftheAddresscorrespondencetoBrettA.Peters,Dept.ofIndustrialEngineering,TexasA&MUniversity,CollegeStation,TX77843-3131oremailtobpeters@Thispaperaddressesthethroughputimprovementpossiblewiththeuseofadualshuttleautomatedstorageandretrievalsystem.Withtheuseofsuchasystem,travelbetweentimeinadualcommandcycleisvirtuallyeliminatedresultinginalargethroughputimprovement.Thedualshuttlesystemisthenextendedtoperformanequivalentoftwodualcommandsinonecycleinaquadruplecommandmode(QC).AheuristicthatsequencesretrievalstominimizetraveltimeinQCmodeisdeveloped.MonteCarlosimulationresultsareprovidedforevaluatingtheheuristic'sperformanceandshowthatitperformswell,achievinglargethroughputimprovementscomparedwiththatofthedualcommandcycleoperatingunderthenearestneighborretrievalsequencingAutomatedStorage/RetrievalSystemsDesign;AutomatedStorage/RetrievalSystemsOperation;MaterialHandlingSystems;PerformanceModelingandAnalysisAutomatedstorage/retrievalsystems(AS/RS)arewidelyusedinwarehousingandmanufacturingapplications.AtypicalunitloadAS/RSconsistsofstorageracks,S/Rmachines,linkconveyors,andinput/output(I/O)stations.Animportantsystemperformancemeasureisthethroughputcapacityofthesystem.Thethroughputcapacityforasingleaisleistheinverseofthemeantransactiontime,whichistheexpectedamountoftimerequiredfortheS/Rmachinetostoreand/orretrieveaunitload.TheservicetimeforatransactionincludesbothS/Rmachinetraveltimeandpickup/deposittime.ThistimetypicallydependsontheconfigurationofthestoragerackandtheS/Rmachinespecifications.Hanetal.[2]improvedthethroughputcapacityoftheAS/RSthroughsequencingretrievals.IntelligentlysequencingtheretrievalscanreduceunproductivetravelbetweentimewhentheS/Rmachineistravelingemptyandtherebyincreasethethroughput.TheydevelopanexpressionforthemaximumpossibleimprovementinthroughputiftravelbetweeniseliminatedforanAS/RSthatisthroughputboundandoperatesindualcommandmode.Inessence,thismeansthatiftheS/Rmachinetravelsinasinglecommandpathbutperformsbothastorageandaretrievaloperation,theabovethroughputimprovementcouldbeobtained.Inthispaper,weanalyzeanalternativedesignoftheS/RmachinethathastwoshuttlesinsteadofoneasinaregularAS/RS.Thenewdesigneliminatesthetravelbetweenthestorageandretrievalpointsandperformsbothastorageandaretrievalatthepointofretrieval,therebyachievingthemaximumthroughputincreasecalculatedbyHanetal.[3].ThedualshuttleAS/RSisanewdesignaimedatimprovingS/Rmachineperformance.moststudiesonAS/RSsystemshavebeenbasedonasingleshuttledesign.InouranalysisofthedualshuttleAS/RSperformance,webuilduponthesepreviousresearchresults.AlternativeS/RMachineAtypicalunit-loadAS/RShasanS/Rmachineoperatingineachaisleofthesystem.TheS/Rmachinehasamastwhichissupportedatthefloorandtheceilingandtravelshorizontallywithintheaisle.Connectedtothismastisashuttlemechanismthatcarriestheunitloadandverticallyupanddownthemast.Theshuttlemechanismalsotransfersloadsinandoutofstoragelocationsintherack.Figure1providesanillustrationofthesingleshuttleS/Rmachine.Figure1.SingleShuttleS/RMachineAtypicalsingleshuttleAS/RScanperformasinglecommandcycleoradualcommandcycle.Asinglecommandcycleconsistsofeitherastorageoraretrieval.Forastorage,thetimeconsistsofthetimetopickuptheloadattheI/Opoint,traveltothestoragepoint,deposittheloadatthatpoint,andreturntotheI/Opoint.Thetimeforaretrievalisdevelopedsimilarly.Adualcommandcycleinvolvesbothastorageandaretrievalinthesamecycle.ThecycletimeinvolvesthetimetopickuptheloadattheI/Opoint,traveltothestoragelocation,placetheloadintherack,travelemptytotheretrievallocation,retrieveaload,returntotheI/Opoint,anddeposittheloadattheI/Opoint.IfwecriticallyanalyzethedualcommandcycleoftheS/Rmachine(shownbythesolidlineinFigure2),apotentialopenlocationforafuturestorageiscreatedwhenaretrievalisperformed.Furthermore,ifbotharetrievalandastorageareperformedatthesamepoint,thetravelbetweentime(TB)iseliminated,andthetraveltimewillbeequaltothesinglecommandtraveltime.WiththeexistingAS/RSdesign,thismodeofoperationisnotpossible;therefore,analternativetotheS/Rmachine,adualshuttleR/Smachine,isproposed.Figure2.DualCommandTravelPathsofS/RandR/SMachinesR/SMachineOperationConsideranS/Rmachinewithtwoshuttlemechanismsinsteadofone.ThisnewS/Rmachinecouldnowcarrytwoloadssimultaneously.Eachshuttlemechanismcouldoperateindependentlyoftheother,sothatindividualloadscanstillbestoredandretrieved.AnillustrationofthedualshuttleS/RmachineisshowninFigure3.ThisnewS/RmachinewouldoperateasdescribedFigure3.DualShuttleS/RMachineTheS/RmachinepicksuptheitemtobestoredfromtheI/Opoint,loadsitintothefirstshuttle,andmovestotheretrievallocation.Afterreachingtheretrievallocation,thesecondshuttleispositionedtopickuptheitemtoberetrieved.Afterretrieval,theS/Rmachinepositionsthefirstshuttleanddepositstheload.TheS/RmachinethenreturnstotheI/Opoint.TheoperationcaneasilybeseenasasinglecommandoperationplusasmalltraveltimeforrepositioningtheS/Rmachinebetweentheretrievalandstorage(aswellastheadditionalpickupanddeposittimeassociatedwiththesecondload).Therefore,theS/RmachinenowoperatesasanR/Smachineperformingaretrievalfirstthenastorageinadualcommandcycle.SincetheR/Smachinehastwoshuttles,thepositionoftheshuttleshasaroleintheoperationofthesystem.Withtwoshuttles,theR/Smachineisabletoperformadualcommandcycleatonelocationintherack.Thisoperationisaccomplishedbyfirstretrievingtheloadontotheemptyshuttle,transferringthesecondshuttleintoposition,andstoringtheloadintotheemptylocationintherack.However,thechoiceofshuttleconfigurationdoesnotimpacttheanalysisinthispaper.Toperformtheseoperations,theR/Smachinemustmovethesecondshuttleintopositionafterthefirstshuttlehascompletedtheretrieval.Duetothesmalldistanceinvolved,theR/Smachinewilluseaslowercreepspeedforpositioning,butthistraveltimeisgenerallysmall.Furthermore,anamountofcreeptimeisusuallyincludedinthepickupanddeposittimetoaccountforthisrequiredpositioning.AseconddesigncharacteristicisthatadditionalclearancebeyondtheandlastrowandcolumnoftherackmustbeprovidedforovertraveloftheR/Smachinetoaccommodatebothshuttlemechanisms.ThroughputToestimatethethroughputimprovementbythedualshuttlesystemoverexistingdesigns,weusetheexpressionsforsinglecommandanddualcommandcycletimesdevelopedbyBozerandWhite[1]andthetabulatedvaluesforthenearestneighborheuristicfromHanetal.[4].Indevelopingtheexpressions,theauthorsin[1]and[4]madeseveralassumptions.Thesameassumptionsholdforthenewdesignandincludethefollowing.TherackisconsideredtobeacontinuousrectangularpickfacewheretheI/Opointislocatedatthelowerleft-handcorneroftherack.Theracklengthandheight,aswellastheS/Rmachinevelocityinthehorizontalandverticaldirections,areknown.TheS/Rmachinetravelssimultaneouslyinthehorizontalandverticaldirections.Incalculatingthetraveltime,constantvelocitiesareusedforhorizontalandverticaltravel.Accelerationanddecelerationeffectsareimplicitlyaccountedforineitherareducedtopspeedoranincreasedpickupanddeposittime.Acreepspeedisusedforrepositioningthedualshuttle.Pickupanddeposittimesassociatedwithloadhandlingareassumedconstantand,therefore,thesecouldbeeasilyaddedintothecycletimeexpressions.TheS/Rmachineoperateseitheronasingleordualcommandbasis,i.e.,multiplestopsintheaislearenotallowed.(ThisassumptionislaterrelaxedforthenewR/Smachinetoperformaquadruplecommandcycle.)Forthenearestneighborheuristic,ablockofnretrievalsisavailableforsequencingandthereareminitialopenlocationsintherackface.DualShuttleS/RThenewdesignoftheS/Rmachinehastwoshuttlesandthereforecouldbeoperatedasadualshuttlesystem:carryingtwoloadsanddepositingthem,retrievingtwoloads,andreturningtotheI/OpointtodeliverthemasshowninFigure4.Theaboveoperationcanbeperformedbystoringandretrievingtheloadsatfourdifferentlocations.Therefore,thetraveltimewouldconsistofthetimeforasinglecommandtravelplusthreetravelbetweentimes.Tomoreefficientlyperform4operations,aretrievalandstorageperformedatonelocationisinterspersedwithadualcommandoperation.Thismodeofoperation,termedthequadruplecommand(QC)cycle,eliminatesonetravelbetweenandismoreefficientthanthepreviousmodementionedabove(seeFigure5).TheQCcyclecanbeperformedwithstoragesatrandomizedlocationsandretrievalsprocessedinafirst-come-first-served(FCFS)manner.However,byintelligentlysequencingtheretrievallist,thetraveltimeinperformingthefouroperationscanbesignificantlyreduced.ThistypeofanalysiswasusedbyHanetal.[4]toimprovethethroughputofasingleloadAS/RS.Inourpaper,webuildontheresultsoftheiranalysis.Thenotationandtheassumptionsmentionedinsection2.2.stillhold,exceptthatmultiplestopsoftheS/Rmachinearenowallowed.Figure4.S/RMachinePathPerformingFourOperationsAtFourFigure5.S/RMachinePathPerformingFourOperationsAtThreeLocations.Thispaperperformsananalysisofdualshuttleautomatedstorageandretrievalsystems.contributionshavebeenmadeincludingtheThroughputimprovementsintherangeof40-45%canbeobtainedusingthequadruplecommandcyclerelativetodualcommandcycleswithasingleshuttlesystem.Withthedualshuttledesign,travelbetweenisvirtuallyeliminatedforadualc