U形生产线的分析与优化外文翻译Word文档下载推荐.docx

U形生产线的分析与优化外文翻译Word文档下载推荐.docx

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（ReceivedAugust21,1995;

RevisedJanuary16,1996）

AbstractInthejust-in-timecontext,partsareoftenprocessedbyasingle-unitproductionandconveyancesystem（called"

zkko-nagash?

inJapanese）withoutconveyors.TheU-shapedlayout,inwhicheachmultifunctionworkertakeschargeofseveralmachines,hasbeenintroducedasanimplementationofthisconcept.Presentlythelayoutisgaininganincreasingpopularityduetothelowrunningcost.

Inthispaper,firstwedealwiththeU-shapedproductionlinewithasinglemulti-functionworker.Wederivehiswaitingtimeandacycletimeofthelinewhenprocessingtimesofitems,operationtimes,andhiswalkingtimesbetweenmachinesareconstants.ThenwedealwithaU-shapedproductionlinewithmultipleworkers.Wederivetheoverallcycletimeofthisline,andconsideranoptimalworkerallocationproblemthatminimizestheoverallcycletimewhenthenumberofworkersisgiven.Inparticular,itisshownthattheU-shapedlayoutissuperiortothelinearlayoutforlineswithoneortwoworkers.Wealsodiscussthecasewherethoseprocessing,operationandwalkingtimesarestochastic.

1.Introduction

InaconveyorsystemformassproductionasintheFordsystem,eachstationprocessesjustoneiteminonecycletime,wherethecycletimeisthetime-intervalbetweentwosuccessiveoutputs.Thesumsofnecessaryoperationandprocessingtimesareintendedtobeequalamongthestations,theitemsareprocessedsynchronouslyamongthestations,andthereexistnoitemsbetweenadjacentstations.

Inthejust-in-time（JIT）productionsystem,theaboveconcept,whichiscalledasingleunitproductionandconveyance（"

ikko-nagashi,"

inJapanese）,isappliedtoaproductionlinewithoutconveyorswhichmanufacturesdifferentkindsofrelativelysmallparts（Monden[3],p.107）.Toachievethisatalowproductioncost,aU-shapedlayoutisusedwithmultifunctionworkers.TheU-shapedproductionlinewiththreeworkersandtenmachinesisshowninFigure1.WhentheentranceandexitofitemsarenearasshowninFigure1,wecallthislayoutaU-shapedlayout,andifthesameworkerhandlesbothmachinesattheentranceandexitintheU-shapedlayoutthenwecallthislayoutaU-shapedproductionline.

Themultifunctionworkertakeschargeofmultiplemachines,andvisitseachofthemounceinonecycle.Whenhearrivesatoneofthesemachines,hewaitsfortheendofprocessingoftheprecedingitemifitisnotcompleted,andthenoperatestheitemsandwalkstothenextmachine.Theoperationconsistsofdetachingtheprocesseditemfromthemachine,puttingitonachutetorollinfrontofthenextmachine,attachingthenewitemtothemachine,andswitchingiton.Thecycletimeoftheworkeristhetime-intervalbetweenhisconsecutivearrivalsathisfirstmachine,andconsistsofthewaitingtimesfortheendofprocessing,operationtimesandwalkingtimesbetweenmachines.

IntheJITproductionsystem,twokindsofKanbans,thatis,aproductionorderingandawithdrawalKanbansareusedastoolstocontrolproductionandwithdrawalquantitiesineachproductionline.IntheU-shapedline,thesameworkerinputsanewitemandoutputsacompletedproduct.Consequently,hecanobservechangesoftwokindsofKanbansandrespondtothempromptly.Sinceanewitementersthesystemonlyafteronecompletedproductexits,thework-in-processinthesystemisalwaysconstant.Further,thereexistmorepossibleallocationsoftheworkerstomachinesthaninthelinearlayout.Therefore,whenthedemandchangeswecanmoreappropriatelyreallocatetheworkerstomachinessothatthecycletimesofworkersarebalanced.Thatis,theU-shapedlayoutcanbemoreproperlyadaptedtothechangesofthecircumstancesthanthelinearlayout.

Inthispaper,wefirstconsidertheU-shapedproductionlinewithjustonemulti-functionworker.Weanalyzehiswaitingtimeandthecycletime.ThenweconsidertheoverallcycletimeoftheU-shapedlinewithmorethanonemulti-functionworker,whichisthemaximumofthecycletimesofallworkers.Itisnotedthatitsreciprocalgivesthethroughput,ortheproductionrateoffinishedproducts.Moreover,weconsideranoptimalworkerallocationproblemthatminimizestheoverallcycletime.

InSection2,weexplaintheU-shapedproductionlinewithasingleworker,andanalyzehiswaitingtimeandthecycletimeofthisline,whentheoperation,walkingandprocessingtimesareconstants.Weshowthatthen-thcycletimebecomesconstantforn>

2,andthatafterseveralcyclestheworkerwaitsforthecompletionofprocessingofatmostonespecifiedmachine.

Recently,MiltenbergandWijngaard[2]consideredthelinebalancingproblemofthe

U-shapedlinewithconstantoperationtimes,nowaitingtimesandnowalkingtimes.Theydiscussedtheoptimalmachineallocationproblemtoworkers（whichtheycalledstations）undertheconstraintsontheordersofmachinesinwhichtheitemsareprocessed,liketheassemblylinebalancingproblems（Baybars[I],forexample）.IntheU-shapedline,however,thewalkingtimesshouldbetakenintoaccounttoderivetheexactcycletime.Inaddition,itispossiblefortheworkertowaitfortheendofprocessingatamachineforanallocation,becausethetimeintervalfromdeparturetonextarrivaloftheworkeratthemachinemayexceedtheprocessingtimeatthemachine.Therefore,theproblemwhichtheydiscusseddoesnotrepresenttherealfeaturesoftheU-shapedline.InSection3,weconsideraproductionlinewithIworkersandKmachines,andderivetheoverallcycletimeofthislineunderagivenallocationofworkerstomachines.Thenwediscusstheoptimalworkerallocationproblemthatminimizestheoverallcycletimeofthisline.Itisshownthattheproblemcanbeformulatedintoacombinatorialoptimizationproblem.WeexaminetheoptimalworkerallocationproblemwithoneortwoworkersinaproductionlinewithKmachinesplacedatthesamedistance.ThiswillrevealadvantagesoftheU-shapedlayoutoverthelinearlayout.

WecanfurtherreduceanoverallcycletimebyadmittingwhatToyotacallsmutualreliefmovement（[3],p.114）.Thismeansthataworkerwhohasfinishedhisownoperationsinonecyclehelpsanotheradjacentworker.This,however,isnottakenintoaccountinthispaper,becausetheproblembecomesmorecomplicated.

Ifmultiplekindsofitemsareprocessedinthisline,theprocessingtimesandoperationtimesarenotconstant.Inaddition,theoperationandwalkingtimesoftheworkermayfluctuatebecauseofhiswearinessandlearningeffect.InSection4,wedealwiththecasewheretheprocessesofoperation,walkingandprocessingtimesarestochastic.Inparticular,wediscussthecasewherethesequencesofrandomvariablesintheseprocessesareindependentandidenticallydistributedandthereisabottleneckmachinesuchthatthesumofprocessingandoperationtimesofthismachineislargerthanthatofanyothermachinewithprobabilityone.Itcanbeshownthattheworkerwaitsforthecompletionofprocessingatthebottleneckmachineinallcycles.

2.CycleandWaitingTimesofaMulti-FunctionWorker

InthissectionweconsidertheU-shapedproductionlinewithasinglemulti-function

worker,whichisshowninFigure2.Theworkerhandlesmachines1throughK.Thefacilityhasenoughrawmaterialinfrontofmachine1.Thematerialisprocessedatmachines1,2,...,K,sequentially,anddepartsfromthesystemasafinishedproduct.LetK={l,...,K}.Whentheworkerarrivesatmachinek∈K,iftheprocessingoftheprecedingitemiscompleted,thenheremovesitfrommachinek,sendsittomachinek+1,attachesthepresentitemtomachinekandswitchesiton.Aftertheoperationatmachinek,hewalkstomachinek+1.Iftheprecedingitemisstillinprocessathisarrival,thenhewaitsfortheendoftheprocessingbeforetheoperation.

Itisassumedasaninitialconditionthatattime0,thereisoneitemoneachmachine,whichhasbeenalreadyprocessedatthismachine.Thatis,inthefirstcycletheworkeroperateswithoutwaitingatallmachines.Inthisandnextsections,weassumethattheprocessing,operationandwalkingtimesareconstantsateachmachine.Thisassumptionissatisfiedwhenonekindofproductsareproducedandtheworkeriswellexperiencedintheoperation.Weusethefollowingnotations:

fork∈Kandn∈Z^={l,2,...},

ik:

theprocessingtimeatmachinek,

sk:

theoperationtimeoftheworkeratmachinek,

rk:

thewalkingtimefrommachinektomachinek+l（Ktol,ifk=K）,

Wk（n）:

thewaitingtimeoftheworkeratmachinekinthen-thcycle,

C（n）:

then-thcycletime,

a∨b=max{a,b},a∧b=min{a,b},[a]+=max{0,a}　.

Figure3illustratesthebehavioroftheworkerandtheabovedefinedvariables.The

initialconditionimpliesthat

Considerthen-thcycletimeforn>

2.Iftheworkerdoesnotwaitatanymachinethenthecycletimeissimplythesumofalloperationandwalkingtimes.Sinceoneitemisprocessedandoperatedateachmachineinonecycle,thecycletimemustbegreaterthanorequaltothemaximumofthesumsoftheprocessingandoperationtimesamongallthemachines.Iftheworkerstartsfromthemachinewiththemaximumsum,thenthecycletimewillbeequaltothemaximumofthemaximumsumandthesumofalloperationandwalkingtimes.Thatis,thecycletimewillbegivenby

andthenthetotalwaitingtimeoftheworkerinonecycleisgivenby

Inthefollowing,wederivethen-thwaitingtimeatmachinekforallkEKandnE-E+,andshowthat

（2）and（3）