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

LineBalancingintheRealWorldEmanuelFalkenauerOptimalDesignAv.Jeanne19Abo?te2,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.

附錄2:中文文獻生產(chǎn)線平衡在現(xiàn)實世界摘要:生產(chǎn)線平衡(LB)是一個經(jīng)典的,細心探討的顯著工業(yè)重要性的運籌學(xué)(OR)優(yōu)化問題。這是其中一個所在領(lǐng)域的專業(yè)學(xué)問并沒有太大幫助的問題之一:無論花了多少年解決它,面對每一次麻煩的問題與可能的天文數(shù)字的解決方案都并不是關(guān)于如何解決這個問題的最好方法,除非你假定老方法是最好的方法。在這里,我們說明一個明顯的悖論:雖然很多算法已經(jīng)被提出,在過去,盡管該問題的實際重要性只是一個市場銷售的LB軟件。目前好像可用于工業(yè),如汽車中的應(yīng)用。我們推想,這可能是由于在學(xué)術(shù)LB問題之間的沒有通過運籌學(xué)路徑和生產(chǎn)業(yè)實際面對的問題。關(guān)鍵詞:生產(chǎn)線平衡,裝配生產(chǎn)線,優(yōu)化

生產(chǎn)線平衡在現(xiàn)實世界伊曼紐爾??夏螤杻?yōu)化設(shè)計地址:珍妮大道19A,2道,B-1050布魯塞爾,比利時+32(0)264610741引言裝配線平衡,或者簡稱生產(chǎn)線平衡(LB),是一個操作工作站沿著裝配線安排的問題,在這樣一種方式,該安排是在某種意義上最優(yōu)的。自從亨利?福特引進組裝生產(chǎn)線,LB已經(jīng)成為影響工業(yè)重要性的最優(yōu)化問題:在效率不同的最優(yōu)和次優(yōu)安排之間的差異可以產(chǎn)生經(jīng)濟(或奢侈)達到數(shù)百萬美元每年。LB是一個經(jīng)典的運籌學(xué)(OR)的優(yōu)化問題,已通過被運籌學(xué)解決達以上幾十年。很多算法已經(jīng)被提出了去解決這個問題。盡管問題的有實際重要性,并已經(jīng)取得了或努力,但很少的商業(yè)軟件是可以幫助行業(yè)優(yōu)化其生產(chǎn)線。事實上,依據(jù)最近貝克爾和紹爾(2004)的一項調(diào)查顯示,好像有目前只有兩個市場銷售的軟件包有特色,即是最先進的優(yōu)化算法的狀態(tài)和數(shù)據(jù)管理的用戶友好的界面。此外,這些軟件包,好像只處理“干凈”的提法的問題(簡潔裝配線平衡問題,或SALBP),這讓只有一個軟件包可用于工業(yè),如汽車業(yè)。這種狀況好像是自相沖突的,或者至少是意想不到的:給定的LB可以產(chǎn)生的巨大經(jīng)濟,人們能夠所期望的幾個軟件包爭先恐后地抓住這些經(jīng)濟體的一部分??磥恚F(xiàn)有的運籌學(xué)結(jié)果以及它們在傳播之間存在差距。當(dāng)今的工業(yè),很可能是由于在學(xué)術(shù)LB問題之間通過運籌學(xué)大多數(shù)的或接近解決,對于企業(yè)所面對的實際問題。LB是一個困難的優(yōu)化問題(即使是最簡潔的形式是NP-hard的形式見GAREY和約翰遜,1979),因此實行的運籌學(xué)方式通常被用以簡化它,為了把它的困難性聽從運籌學(xué)工具的水平。雖然這一般是一個特別有效的方法,在LB的特定狀況下,它導(dǎo)致了一些這種無視現(xiàn)實世界的問題的很多方面問題的定義。不幸的是,很多已經(jīng)離開了運籌學(xué)方面,實際在至關(guān)重要的行業(yè),如汽車,在這個意義上,任何解決方案忽視(違反)這些方面在使得在同行業(yè)中變得不行用。在下面章節(jié)中,我們先簡潔回顧一下經(jīng)典運籌學(xué)對LB的定義,然后查看如何面對行業(yè)不同于他們的實際生產(chǎn)線平衡問題,為什么解決經(jīng)典運籌學(xué)問題可能無法運用在一些行業(yè)。2生產(chǎn)線平衡的運籌學(xué)定義經(jīng)典的運籌學(xué)定義的生產(chǎn)線平衡問題,被稱為SALBP(簡潔裝配線平衡問題)由貝克爾和紹爾(2004)。特定一組不同期限的任務(wù),任務(wù)之間的一組優(yōu)先約束和一系列工作站,以這樣一種方式安排給每個任務(wù)只有一個工作站,沒有優(yōu)先約束被違反和安排是最優(yōu)的。最優(yōu)標準產(chǎn)生該問題的兩種變型:要么一個周期時間是考慮到不能超過了安排給任何工作站和數(shù)量的全部任務(wù)持續(xù)時間的總和工作站將被最小化,或工作站的數(shù)量是固定的線周期時間,等于任務(wù)安排給工作站的持續(xù)時間的總和最大的,是成為組合最小化。雖然SALBP只考慮兩個約束條件(任一優(yōu)先級約束加上循環(huán)時間,或優(yōu)先約束加的數(shù)量工作站),它是迄今為止生產(chǎn)線平衡的變體,已經(jīng)被探討最多的。我們在Falkenauer和Delchambre促成了這一努力(1992),在那里我們建議取得一些最好的一個分組遺傳算法的方法性能的領(lǐng)域。該分組遺傳算法技術(shù)本身已提交具體見Falkenauer(1998)。但是深化探討,SALBP幾乎不適用于工業(yè),就像我們將看到不久的時間內(nèi)。事實上也沒有逃脫運籌學(xué)探討,和貝克爾的關(guān)注和紹爾(2004)定義了很多擴展到SALBP,產(chǎn)生了常用的單位GALBP(廣義裝配線平衡問題)。每個擴展報道在他們的權(quán)威調(diào)查旨在處理存在的另一個真實世界的生產(chǎn)線平衡困難。我們已經(jīng)通過采納分組遺傳算法攻克了在Falkenauer(1997)的方面。與大多數(shù)報道貝克爾和舍爾的方法的主要問題(2004)是他們推廣了在短短的一個或兩個方向簡潔SALBP?,F(xiàn)實世界上生產(chǎn)線平衡,作為汽車行業(yè)所面臨的特殊要求進行這些遺傳算法。3在現(xiàn)實世界中有什么不同?但即使是簡潔的SALBP是NP-hard的,它是遠離捕獲真實的困難性在現(xiàn)實世界中的化身的問題。另一方面,即使小的狀況下的問題,他們以最優(yōu)難以解決一個麻煩的目標對于平衡軟件來說,因為這個問題的小實例,可以被近似的仿真。但是狀況并非如此,在汽車及相關(guān)行業(yè)(公共汽車,卡車,飛機,重型機械等),因為這些行業(yè)的常規(guī)功能有幾十個或上百個工作站,以及數(shù)以百計或數(shù)以千計的組裝線操作。因此,這些行業(yè)對生產(chǎn)線平衡軟件的首要市場目標。不幸的是,同樣是這些行業(yè)也須要考慮到很多GALBP擴展的同時這也可以說明為什么盡管有令人印象深刻的運籌平衡所做的工作中,只有好像一個市場銷售的軟件是目前可用于這些行業(yè)。我們找出下面的一些額外的困難(相對于SALBP),該必需解決在生產(chǎn)線平衡的工具,以適用于這些行業(yè)。3.1不均衡,但再平衡很多運籌學(xué)方法隱含假定要解決的問題涉及一個新的,但將要建的裝配生產(chǎn)線,或者有可能住在一個新的,但將要建立的工廠。在我們認為,這是一個經(jīng)典的運籌學(xué)方法,做最嚴峻的

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