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371Vol.37,No.120111ACTAAUTOMATICASINICAJanuary,20111;21;21,,.,,,.,(Constantwork-in-process,CON-WIP)Kanban(Genericpull,GP),,.,,,,DOI10.3724/SP.J.1004.2011.00118ApplicationofaPullStrategyBasedonFuzzyControlforProductionControlofAssemblyLineMOJu-Hua1;2HUANGMin1;2WANGXing-Wei1AbstractDuetoitsrobustness,fuzzycontrolhasbeenincor-poratedintotheproductioncontrolsystemtoestablishapullstrategyforsingle-productassemblyline.Basedonaperiodicreviewmodelproposedtodescribetheoperationsoftheassem-blycontrolsystemandonthedesignsofthefuzzycontrollers,thebasicgeneticalgorithm(GA)hasbeenimprovedviareduc-ingmutationdomainstosolveamulti-objectiveprogram,whichminimizesthework-in-processleveland°uctuationlevelofor-derplacementwhilemeetingcustomer0sdemand,meanwhile,theparametersofthecontrolsystemhavebeenoptimized.Inordertoinvestigatetheperformanceoftheproposedfuzzycon-trolsystem,multi-CONWIP,Kanbanandgenericpullsystemshavebeencomparedwiththefuzzysystem,andtheresultsshowthatthefuzzyproductioncontrolsystemkeepsalowerwork-in-processlevel,andespeciallyaweakerplacement°uctuation.KeywordsProductioncontrol,assemblyline,fuzzycontrol,pullcontrol,placement°uctuation.(Materialrequirementplanning,MRP),Kanban(Constant2008-07-282010-03-17ManuscriptreceivedJuly28,2008;acceptedMarch17,2010(71071028,70931001,70721001,61070162),(20070145017,20100042110025),(N090504006,N090504003),SupportedbyNationalNaturalScienceFoundationofChina(71071028,70931001,70721001,61070162),SpecializedResearchFundfortheDoctoralProgramofHigherEducationofChina(20070145017,20100042110025),FundamentalResearchFundsfortheCentralUniversities(N090504006,N090504003),andScienceandTechnologyResearchFundofBureauofEducationofLiaoningProvince1.1100042.()1100041.CollegeofInformationScienceandEngineering,NortheasternUniversity,Shenyang1100042.LaboratoryofIntegratedAutoma-tionofProcessIndustry(NortheasternUniversity),MinistryofEd-ucation,Shenyang110004work-in-process,CONWIP)(Basestock)[1],,[2¡3].,,,,,.,,,,.,.:1);2),.,,,,:1)[4¡7];2)[8¡11];3)\[12¡13];4)[14].,,,,.11.1n,s,S=f1;2;¢¢¢;ng.sSS(s),PS(s).n(s),11.w(s),W(s)=f1;2;¢¢¢,n(s)g.w(s)1,OPw(s)Pw(s),Ow(s)Pw(s),Pw(s)Yw(s).SHw(s)w(s),s,w(s)s,SHw(s).1w(s)Fig.1Structureofnodew(s).,.,...1)A,A=(aij)n£n,aij=(1;i2PS(j)0;(1)2)QQ=(qij)n£n,qij=(1;ij0;(2)A,Q,,(3)[15].1:119Q=(I_A)^¢¢¢^(I_A)|{z}n¡1(3),I,_^.3)BB=(jjnXi=1aij=0;aij2A)(4),,.4)PSsPSs=n(s)Xw(s)=1Pw(s)(5),Yw(s).5)YSsYSs=n(s)Xw(s)=1Yw(s)(6),Yw(s)Yw(s).1.2,,,,;,.,,,.1)tFLCsMts=(nXv=s·PStv+YStvUC¸qsvjqsu=1);s2S;u¸s(7),,UC.2)tsOPFLCts=f(Mts;Ks)¢UC(8),KsMs,,.Ks.3)tsw(s)Ots;w(s)=OPt¡Ls;w(s)s;w(s)(9),Ls;w(s)sw(s).4)tsw(s)TYts;w(s)=Yts;w(s)+Ots;w(s)(10)5)tsw(s)OPts;w(s)=8:minnminvTYtv;n(v);OPFLCts;MLPs;w(s)Ls;w(s)o;v2PS(s);w(s)=1;s=2Bmin½OPFLCts;MLPs;w(s)Ls;w(s)¾;w(s)=1;s2Bmin½TYts;w(s)¡1;MLPs;w(s)Ls;w(s)¾;w(s)6=1(11),n(v)=jW(v)j,W(v)v.w(s),w(s);MLPs;w(s)=Ls;w(s)w(s).w(s),.w(s),w(s).6)tsw(s)SHts;w(s)=8:minfTYts;w(s);OPtcustg;s=n;w(s)=n(s)OPtv;1;v2SS(s);s6=n;w(s)=n(s)OPts;w(s)+1;w(s)6=n(s)(12),OPtcustt.Ots;w(s)SHts;w(s)Ots;w(s),SHts;w(s).7)tsw(s)Tts;w(s)=Yt¡1s;w(s)+Ots;w(s)¡SHts;w(s)(13)8)tsw(s)Pts;w(s)=Pt¡1s;w(s)+OPts;w(s)¡Ots;w(s)(14)9)tBt=Bt¡1+OPtcust¡SHtn;n(n)(15)2FLCsMsjMsj.m(s)Ms,k(s)2Ksm(s).m(s),SMB,\\\,2(a).2(b)OPFLCts,MLs;12[OPucost;MLPs;1=Ls;1],OPucost,MLPs;1=Ls;1s.,,,,,\,:1.1B,M;120372.2B,M;3.1B,1M,M;4.1B,1M,B.4:\,\;MB1/2,S0,,2M1B,S1S,1SnMnM,1SnBnB.(£;+),.,\[16],,.2Fig.2Membershipde¯nitionsofinputandoutput33.1,,(16)»(20).1)CSR=100¢µTPt=1OPtcust¡BT¶TPt=1OPtcust(16)2)AOP=TXt=1Xv2BOPtv;1T¢jBj(17)3)SDO=(18)vuut1(T¡1)¢jBjTXt=1Xu2BÃOPtu;1¡TXt=1Xv2BOPtv;1T¢jBj!24)()APY=TXt=1nXv=1PStv+YStvT;i=1;2;¢¢¢;n(19)5)AIC=TXt=1nXv=1PStv¢Pwiptv+YStv¢PmtvT;i=1;2;¢¢¢;n(20),PwiptvPmtvtv.,,.[17],..3.2,,.Little[18],,,,.,,,.,.[19],,,,,.,.,,,,,,.[16],,,.[20],,.[20],,..,minAIC(KKK)(21)minSDO(KKK)(22)s:t:CSR(KKK)¸CSR0(23),KKKKs,AIC,SDOCSRKKK,CSR0.,,,,:min!1AIC(KKK)+!2SDO(KKK)(24)s:t:CSR(KKK)¸CSR0(25),!1,!2.3.3,,.KKK,ki2KKK,kif1;2;¢¢¢;Kig,Ki1:121,,.,,FF=M¡[!1AIC(KKK)+!2SDO(KKK)]¡®(CSR0¡CSR(KKK))+(26),M,F,®..ki(ki2KKK)f1;2;¢¢¢;Kig,f1,2;¢¢¢;Kig,,,,,kiki=8:f1;¢¢¢;ki+¸g;ki·1+¸fki¡¸;¢¢¢;ki+¸g;1+¸ki·ki¡¸fki¡¸;¢¢¢;kig;kiki¡¸(27),¸.475,3,1.,Q,Q=0BBBBBB@10011010110010100011000011CCCCCCA1»5FLC1;FLC2;FLC3;FLC4FLC5,Q,5:FLC1:PS1+YS1;PS1+YS1+PS4+YS4;PS1+YS1+PS4+YS4+PS5+YS5.FLC2:PS2+YS2;PS2+YS2+PS4+YS4;PS2+YS2+PS4+YS4+PS5+YS5.FLC3:PS3+YS3;PS3+YS3+PS5+YS5.FLC4:PS4+YS4;PS4+YS4+PS5+YS5.FLC5:PS5+YS5.,PSiYSi,i=1,2,¢¢¢,5.,,T3000,,300,t=301.4.0,0.08.0,,1.0,2.0,3.04.0.CSR00.9,ki(i=1;2;¢¢¢;jKj)50.M,®,!1!230,20,0.10.9,0.4,0.08,200.4,653.8,,4.0.,CONWIP,Kan-ban(Genericpull,GP)[2].CONWIPCONWIP,,.Kanban,.Genericpull,,,,.2,.,,,.,,,.2,3.60,3:60=4:0=0:9,,.,,,,.,,,3Fig.3Structureoftheassemblyline122371Table1InitialdataofassemblylineiP0iY0iS0iO0iOP0iLiMLPiUCPmtiPwipti18124831301212812483130121381248313012148124831301215812483130121681248313012178124831301212Table2Comparisonofdi®erentcontrolstrategiesCSRAOPSDOAPYAIC(32,44,42,39,46,20,28,26,49,15,31)0.903.580.5014.5414.761.0CONWIP(8,4,8,4,4)0.903.580.6215.4516.