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附录附录1:英文文献LineBalancingintheRealWorldAbstract:LineBalancing(LB)isaclassic,well-researchedOperationsResearch(OR)optimizationproblemofsignificantindustrialimportance.Itisoneofthoseproblemswheredomainexpertisedoesnothelpverymuch:whateverthenumberofyearsspentsolvingit,oneiseachtimefacinganintractableproblemwithanastronomicnumberofpossiblesolutionsandnorealguidanceonhowtosolveitinthebestway,unlessonepostulatesthattheoldwayisthebestway.Hereweexplainanapparentparadox:althoughmanyalgorithmshavebeenproposedinthepast,anddespitetheproblem’spracticalimportance,justonecommerciallyavailableLBsoftwarecurrentlyappearstobeavailableforapplicationinindustriessuchasautomotive.WespeculatethatthismaybeduetoamisalignmentbetweentheacademicLBproblemaddressedbyOR,andtheactualproblemfacedbytheindustry.Keyword:LineBalancing,Assemblylines,Optimization

LineBalancingintheRealWorldEmanuelFalkenauerOptimalDesignAv.Jeanne19Aboîte2,B-1050Brussels,Belgium+32(0)264610741IntroductionAssemblyLineBalancing,orsimplyLineBalancing(LB),istheproblemofassigningoperationstoworkstationsalonganassemblyline,insuchawaythattheassignmentbeoptimalinsomesense.EversinceHenryFord’sintroductionofassemblylines,LBhasbeenanoptimizationproblemofsignificantindustrialimportance:theefficiencydifferencebetweenanoptimalandasub-optimalassignmentcanyieldeconomies(orwaste)reachingmillionsofdollarsperyear.LBisaclassicOperationsResearch(OR)optimizationproblem,havingbeentackledbyORoverseveraldecades.Manyalgorithmshavebeenproposedfortheproblem.Yetdespitethepracticalimportanceoftheproblem,andtheOReffortsthathavebeenmadetotackleit,littlecommerciallyavailablesoftwareisavailabletohelpindustryinoptimizingtheirlines.Infact,accordingtoarecentsurveybyBeckerandScholl(2004),thereappeartobecurrentlyjusttwocommerciallyavailablepackagesfeaturingbothastateoftheartoptimizationalgorithmandauser-friendlyinterfacefordatamanagement.Furthermore,oneofthosepackagesappearstohandleonlythe“clean”formulationoftheproblem(SimpleAssemblyLineBalancingProblem,orSALBP),whichleavesonlyonepackageavailableforindustriessuchasautomotive.Thissituationappearstobeparadoxical,oratleastunexpected:giventhehugeeconomiesLBcangenerate,onewouldexpectseveralsoftwarepackagesvyingtograbapartofthoseeconomies.ItappearsthatthegapbetweentheavailableORresultsandtheirdisseminationinToday’sindustry,isprobablyduetoamisalignmentbetweentheacademicLBproblemaddressedbymostoftheORapproaches,andtheactualproblembeingfacedbytheindustry.LBisadifficultoptimizationproblemevenitssimplestformsareNP-hard–seeGarryandJohnson,1979),sotheapproachtakenbyORhastypicallybeentosimplifyit,inordertobringittoalevelofcomplexityamenabletoORtools.Whilethisisaperfectlyvalidapproachingeneral,intheparticularcaseofLBitledsomedefinitionsoftheproblemhatignoremanyaspectsofthereal-worldproblem.Unfortunately,manyoftheaspectsthathavebeenleftoutintheORapproachareinfactcrucialtoindustriessuchasautomotive,inthesensethatanysolutionignoring(violating)thoseaspectsbecomesunusableintheindustry.Inthesequel,wefirstbrieflyrecallclassicORdefinitionsofLB,andthenreviewhowtheactuallinebalancingproblemfacedbytheindustrydiffersfromthem,andwhyasolutiontotheclassicORproblemmaybeunusableinsomeindustries.2ORDefinitionsofLBTheclassicORdefinitionofthelinebalancingproblem,dubbedSALBP(SimpleAssemblyLineBalancingProblem)byBeckerandScholl(2004),goesasfollows.Givenasetoftasksofvariousdurations,asetofprecedenceconstraintsamongthetasks,andasetofworkstations,assigneachtasktoexactlyoneworkstationinsuchawaythatnoprecedenceconstraintisviolatedandtheassignmentisoptimal.Theoptimalitycriteriongivesrisetotwovariantsoftheproblem:eitheracycletimeisgiventhatcannotbeexceededbythesumofdurationsofalltasksassignedtoanyworkstationandthenumberofworkstationsistobeminimized,orthenumberofworkstationsisfixedandthelinecycletime,equaltothelargestsumofdurationsoftaskassignedtoaworkstation,istobeminimized.AlthoughtheSALBPonlytakesintoaccounttwoconstraints(theprecedenceconstraintsplusthecycletime,ortheprecedenceconstraintsplusthenumberofworkstations),itisbyfarthevariantoflinebalancingthathasbeenthemostresearched.WehavecontributedtothateffortinFalkenauerandDelchambre(1992),whereweproposedaGroupingGeneticAlgorithmapproachthatachievedsomeofthebestperformanceinthefield.TheGroupingGeneticAlgorithmtechniqueitselfwaspresentedindetailinFalkenauer(1998).Howeverwellresearched,theSALBPishardlyapplicableinindustry,aswewillseeshortly.ThefacthasnotescapedtheattentionoftheORresearches,andBeckerandScholl(2004)definemanyextensionstoSALBP,yieldingacommondenominationGALBP(GeneralizedAssemblyLineBalancingProblem).Eachoftheextensionsreportedintheirauthoritativesurveyaimstohandleanadditionaldifficultypresentinreal-worldlinebalancing.WehavetackledoneofthoseaspectsinFalkenauer(1997),alsobyapplyingtheGroupingGeneticAlgorithm.ThemajorproblemwithmostoftheapproachesreportedbyBeckerandScholl(2004)isthattheygeneralizethesimpleSALBPinjustoneortwodirections.Therealworldlinebalancing,asfacedinparticularbytheautomotiveindustry,requirestacklingmanyofthosegeneralizationssimultaneously.3WhatDiffersintheRealWorld?AlthougheventhesimpleSALBPisNP-hard,itisfarfromcapturingthetruecomplexityoftheprobleminitsreal-worldincarnations.Ontheotherhand,smallinstancesoftheproblem,eventhoughtheyaredifficulttosolvetooptimality,areatrickytargetforlinebalancingsoftware,becausesmallinstancesoftheproblemcanbesolvedclosetoptimalitybyhand.Thatishowevernotthecaseintheautomotiveandrelatedindustries(Bus,truck,aircraft,heavymachinery,etc.),sincethoseindustriesroutinelyfeatureAssemblylineswithdozensorhundredsofworkstations,andhundredsorthousandsofOperations.Thoseindustriesarethereforetheprimetargetsforlinebalancingsoftware.Unfortunately,thosesameindustriesalsoneedtotakeintoaccountmanyoftheGALBPextensionsatthesametime,whichmayexplainwhy,despitetheimpressiveORWorkdoneonlinebalancing;onlyonecommerciallyavailablesoftwareseemstubecurrentlyavailableforthoseindustries.Weidentifybelowsomeoftheadditionaldifficulties(withrespecttoSALBP)thatmustbetackledinalinebalancingtool,inordertobeapplicableinthoseindustries.3.1DoNotBalancebutRe-balanceManyoftheORapproachesimplicitlyassumethattheproblemtobesolvedinvolvesanew,yet-to-be-builtassemblyline,possiblyhousedinanew,yet-to-be-builtfactory.Toouropinion,thisisthegravestoversimplificationoftheclassicORapproach,forinpractice,thisishardlyeverthecase.Thevastmajorityofreal-worldlinebalancingtasksinvolveexistinglines,housedinexistingfactories–infect,thetargetlinetypicallyneedstuberebalancedratherthanbalanced,theneedarisingfromchangesintheproductorthemixofmodelsbeingassembledintheline,theassemblytechnology,theavailableworkforce,ortheproductiontargets.Thishassomefar-reachingimplications,outlinedbelow.3.2WorkstationsHaveIdentitiesAspointedoutabove,thevastmajorityofreal-worldlinebalancingtasksinvolvesexistinglineshousedinexistingfactories.Inpractice,thisseemingly“uninteresting”observationhasonefar-reachingconsequence,namelythateachworkstationinthelinedoeshaveitsownidentity.Thisidentityisnotduetoany“incapacityofabstraction”onpartoftheprocessengineers,butrathertothefactthattheworkstationsareindeednotidentical:eachhasitsownspaceconstraints(e.g.aworkstationbelowalowceilingcannotelevatethecarabovetheoperators’heads),itsownheavyequipmentthatcannotbemovedsparehugecosts,itsowncapacityofcertainsupplies(pressedair),itsownrestrictionsontheoperationsthatcanbecarriedoutthere(e.g.donotplaceweldingoperationsjustbesidethepaintingshop),etc.3.3CannotEliminateWorkstationsSinceworkstationsdohavetheiridentity(asobservedabove),itbecomesobviousthatareal-worldLBtoolcannotaimateliminatingworkstations.Indeed,unlesstheeliminatedworkstationswereallinthefrontofthelineoritstail,theireliminationwouldcreategapingholesintheline,byvirtueoftheotherworkstations’retainingoftheiridentities,includingtheirgeographicalpositionsintheworkshop.Also,itsoftensthecasethatmanyworkstationsthatcouldpossiblybeeliminatedbythealgorithmareinfactnecessarybecauseofzoningconstraints.4ConclusionsTheconclusionsinspection3stemsfromourextensivecontactswithautomotiveandrelatedindustries,andreflectstheirtrueneeds.Other“exotic”constraintsmayapplyinanygivenreal-worldassemblyline,butlinebalancingtoolforthoseindustriesmustbeabletohandleatleastthoseaspectsoftheproblem.Thisisveryfarfromthe“clean”academicSALBP,aswellasmostGALBPextensionsreportedbyBeckerandScholl(2004).Infact,suchatoolmustsimultaneouslysolveseveral-hardproblems:•Findafeasibledefinedreplacementforallundefined(‘ANY’)ergonomicconstraintsonworkstations,i.e.Onecompatiblewiththeergonomicconstraintsandprecedenceconstraintsdefinedonoperations,aswellaszoningconstraintsandpossibledriftingoperations•Solvethewithin-workstationschedulingproblemonallworkstations,forallproductsbeingassembledontheline•Assigntheoperationstoworkstationstoachievethebestaveragebalance,whilekeepingthepeaktimesatamanageablelevel.Clearly,thereal-worldlinebalancingproblemdescribedaboveisextremelydifficulttosolve.Thisiscompoundedbytesizeoftheproblemencounteredinthetargetindustries,whichroutinelyfeatureassemblylineswithdozensorhundredsofworkstationswithmultipleoperators,andhundredsorthousandsofoperations.We’veidentifiedanumberofaspectsofthelinebalancingproblemthatarevitalinindustriessuchasautomotive,yetthathavebeeneitherneglectedintheORworkontheproblem,orhandledseparatelyfromeachother.Accordingtoourexperience,alinebalancingtoapplicableinthoseindustriesmustbeabletohandleallofthemsimultaneously.Thatgivesrisetoanextremelycomplexoptimizationproblem.Thecomplexityoftheproblem,andtheneedtosolveitquickly,mayexplainwhythereappearstobejustonecommerciallyavailablesoftwareforsolvingit,namelyoutlinebyOptimalDesign.MoreinformationonOutline,includingitsrichgraphicuserinterface,isavailableat.References1BeckerC.andScholl,A.(2004)`Asurveyonproblemsandmethodsingeneralizedassemblylinebalancing',EuropeanJournalofOperationsResearch,inpress.Availableonlineat:///doi:10.1016/j.ejor.2004.07.023.Journalarticle.2Falkenauer,E.andDelchambre,A.(1992)`GeneticAlgorithmforBinPackingandLineBalancing',Proceedingsofthe1992IEEEInternationalConferenceonRoboticsandAutomation,May10-15,1992,Nice,France.IEEEComputerSocietyPress,LosAlamitos,CA.Pp.1186-1192.Conferenceproceedings.3Falkenauer,E.(1997)`AGroupingGeneticAlgorithmforLineBalancingwithResourceDependentTaskTimes',ProceedingsoftheFourthInternationalConferenceonNeuralInformationProcessing(ICONIP’97),UniversityofOtego,Dunedin,NewZealand,November24-28,1997.Pp.464-468.Conferenceproceedings.4Falkenauer,E.(1998)GeneticAlgorithmsandGroupingProblems,JohnWiley&Sons,ChiChester,UK.Book.5Gary.R.andJohnsonD.S.(1979)ComputersandIntractability-AGuidetotheTheoryofNP-completeness,Co.,SanFrancisco,USA.Book.

附录2:中文文献生产线平衡在现实世界摘要:生产线平衡(LB)是一个经典的,细心探讨的显著工业重要性的运筹学(OR)优化问题。这是其中一个所在领域的专业学问并没有太大帮助的问题之一:无论花了多少年解决它,面对每一次麻烦的问题与可能的天文数字的解决方案都并不是关于如何解决这个问题的最好方法,除非你假定老方法是最好的方法。在这里,我们说明一个明显的悖论:虽然很多算法已经被提出,在过去,尽管该问题的实际重要性只是一个市场销售的LB软件。目前好像可用于工业,如汽车中的应用。我们推想,这可能是由于在学术LB问题之间的没有通过运筹学路径和生产业实际面对的问题。关键词:生产线平衡,装配生产线,优化

生产线平衡在现实世界伊曼纽尔福肯奈尔优化设计地址:珍妮大道19A,2道,B-1050布鲁塞尔,比利时+32(0)264610741引言装配线平衡,或者简称生产线平衡(LB),是一个操作工作站沿着装配线安排的问题,在这样一种方式,该安排是在某种意义上最优的。自从亨利•福特引进组装生产线,LB已经成为影响工业重要性的最优化问题:在效率不同的最优和次优安排之间的差异可以产生经济(或奢侈)达到数百万美元每年。LB是一个经典的运筹学(OR)的优化问题,已通过被运筹学解决达以上几十年。很多算法已经被提出了去解决这个问题。尽管问题的有实际重要性,并已经取得了或努力,但很少的商业软件是可以帮助行业优化其生产线。事实上,依据最近贝克尔和绍尔(2004)的一项调查显示,好像有目前只有两个市场销售的软件包有特色,即是最先进的优化算法的状态和数据管理的用户友好的界面。此外,这些软件包,好像只处理“干净”的提法的问题(简洁装配线平衡问题,或SALBP),这让只有一个软件包可用于工业,如汽车业。这种状况好像是自相冲突的,或者至少是意想不到的:给定的LB可以产生的巨大经济,人们能够所期望的几个软件包争先恐后地抓住这些经济体的一部分。看来,现有的运筹学结果以及它们在传播之间存在差距。当今的工业,很可能是由于在学术LB问题之间通过运筹学大多数的或接近解决,对于企业所面对的实际问题。LB是一个困难的优化问题(即使是最简洁的形式是NP-hard的形式见GAREY和约翰逊,1979),因此实行的运筹学方式通常被用以简化它,为了把它的困难性听从运筹学工具的水平。虽然这一般是一个特别有效的方法,在LB的特定状况下,它导致了一些这种无视现实世界的问题的很多方面问题的定义。不幸的是,很多已经离开了运筹学方面,实际在至关重要的行业,如汽车,在这个意义上,任何解决方案忽视(违反)这些方面在使得在同行业中变得不行用。在下面章节中,我们先简洁回顾一下经典运筹学对LB的定义,然后查看如何面对行业不同于他们的实际生产线平衡问题,为什么解决经典运筹学问题可能无法运用在一些行业。2生产线平衡的运筹学定义经典的运筹学定义的生产线平衡问题,被称为SALBP(简洁装配线平衡问题)由贝克尔和绍尔(2004)。特定一组不同期限的任务,任务之间的一组优先约束和一系列工作站,以这样一种方式安排给每个任务只有一个工作站,没有优先约束被违反和安排是最优的。最优标准产生该问题的两种变型:要么一个周期时间是考虑到不能超过了安排给任何工作站和数量的全部任务持续时间的总和工作站将被最小化,或工作站的数量是固定的线周期时间,等于任务安排给工作站的持续时间的总和最大的,是成为组合最小化。虽然SALBP只考虑两个约束条件(任一优先级约束加上循环时间,或优先约束加的数量工作站),它是迄今为止生产线平衡的变体,已经被探讨最多的。我们在Falkenauer和Delchambre促成了这一努力(1992),在那里我们建议取得一些最好的一个分组遗传算法的方法性能的领域。该分组遗传算法技术本身已提交具体见Falkenauer(1998)。但是深化探讨,SALBP几乎不适用于工业,就像我们将看到不久的时间内。事实上也没有逃脱运筹学探讨,和贝克尔的关注和绍尔(2004)定义了很多扩展到SALBP,产生了常用的单位GALBP(广义装配线平衡问题)。每个扩展报道在他们的权威调查旨在处理存在的另一个真实世界的生产线平衡困难。我们已经通过采纳分组遗传算法攻克了在Falkenauer(1997)的方面。与大多数报道贝克尔和舍尔的方法的主要问题(2004)是他们推广了在短短的一个或两个方向简洁SALBP。现实世界上生产线平衡,作为汽车行业所面临的特殊要求进行这些遗传算法。3在现实世界中有什么不同?但即使是简洁的SALBP是NP-hard的,它是远离捕获真实的困难性在现实世界中的化身的问题。另一方面,即使小的状况下的问题,他们以最优难以解决一个麻烦的目标对于平衡软件来说,因为这个问题的小实例,可以被近似的仿真。但是状况并非如此,在汽车及相关行业(公共汽车,卡车,飞机,重型机械等),因为这些行业的常规功能有几十个或上百个工作站,以及数以百计或数以千计的组装线操作。因此,这些行业对生产线平衡软件的首要市场目标。不幸的是,同样是这些行业也须要考虑到很多GALBP扩展的同时这也可以说明为什么尽管有令人印象深刻的运筹平衡所做的工作中,只有好像一个市场销售的软件是目前可用于这些行业。我们找出下面的一些额外的困难(相对于SALBP),该必需解决在生产线平衡的工具,以适用于这些行业。3.1不均衡,但再平衡很多运筹学方法隐含假定要解决的问题涉及一个新的,但将要建的装配生产线,或者有可能住在一个新的,但将要建立的工厂。在我们认为,这是一个经典的运筹学方法,做最严峻的

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