FMS之间工件传输有延迟的车间最优生产计划

200155:100026788(2001)0520038206FMS,,(,210096):FMS(FAW)L,L,L,,L,Matlab,ERPöMRPÊFAWFAWFMS,FMSL:;;;:TB11:AaOptimalProductionPlanningforWorkshopswithWorkpieceTransferringDelayBetweenFlexibleManufacturingSystemsYANHong2sen,ZHANGXiao2dong,ZHULi2feng(AutomationResearchInstitute,SoutheastUniversity,Nanjing210096,China)AbstractThepaperaddressestheproblemoftheoptimalproductionplanninginflexibleautomatedworkshops(FAWs)withworkpiecetransferringdelaybetweenflexiblemanufacturingsystems(FMSs).Adelay2interaction2basednonlinearprogrammingmodelofproductionplanninginaworkshopisbuiltupandthentransformedintoalinearprogrammingmodelbyaddingconstraints.Becausethescaleofthemodelforageneralworkshopistoolargetobesolvedinsimplexmethodonamicrocomputerwithinacceptabletime,aKarmarkar’salgorithmandaninteractionöpredictionalgorithmareusedtosolvethemodel,onthebasisofwhichthecorrespondingprogramshavebeenwritten.Throughproductionplanningexamples,theKarmarkar’salgorithm,interactionöpredictionalgorithmandlinearprogrammingmethodinMatlabarecompared.Thusweshowthattheproposedapproachesareverysuitablefordecomposingoptimallymedium2termplans(assignedtoanFAWbyERPöMRPÊ)intoshort2termplans(tobeexecutedbyFMSsintheFAW),especiallyforthecasethatworkpiecesaretransferredbetweenFMSsthroughashopstoragewithadelayofaperiod.Keywordsflexibleautomatedworkshop;productionplanning;Karmarkar’salgorithm;interactionöpredictionapproacha:1999209220:863öCIMS(863251129432005863251127082008).©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1,L(monolithic),[1-6]L,[1]L[2],L[3]L,(FAW)L[4],N,FAWFMS(,,),,FAWL[5][6]LFMS,L,()(),L,,,L,,,L,,L,,L,,,L,[7],FAW,,[7]L2FAWFAWMFMS,LFAWFMS,,,L,:J=6Mi=1aTixi(N+1)+6Mk=1(aTixi(k)+b+Ti[Tiui(k)-Bi(k)]++b-Ti[Bi(k)-Tiui(k)]+-c+Ti[yi(k)-di(k)]++c-Ti[di(k)-yi(k)]+)(1):MFMS;N;yi(k)FMSi1k,nf;nf;ui(k)FMSik(),ni;niFMSi;xi(k)FMSik(k=1,2,,N+1),ni;di(k)FMSi1k,nf;Bi(k)FMSik;mi;miFMSi;aiFMSi,ni;b+iFMSi,mi;b-iFMSi,mi;c+iFMSi,nf;c-iFMSi,nf;Timini,FMSikni;[]+max(0,)Z:1)935FMS©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.xi(k+1)=xi(k)-ui(k)+zi(k)+Gir(k)(2)xi(1)=xi1i=1,2,,M;k=1,2,,N:zi(k)FMSjkFMSi,,ni;r(k)k,nf;GininfZ2),FAWFMSZ,FMSjk-1FMSi,kFMSiZFMSj,FMSi,FMSiFMSj,ZFMSjFMSi,zi(k)=6Mj=1Lijuj(k-1)(3)uj(0)=uj0.:Lijninj,0,1,FMSjFMSiZ3)yi(k)=Ciui(k)(4):yi(k)FMSik,nf;Cinfni,FMSi,01,Z4)yi(k)=6kt=1yi(t)(5)5)di(k)=6kt=1di(t)(6):di(t)tFMSi,nfZ6)xi(k)E0,ui(k)E0(7),FMSFAWminJ=6Mi=1aTixi(N+1)+6Nk=1(aTixi(k)+b+Ti[Tiui(k)-Bi(k)]++b-Ti[Bi(k)-Tiui(k)]++c+Ti[yi(k)-di(k)]++c-Ti[di(k)-yi(k)]+)(8)s.t.(2)-(7)3(8)[]+,,Z,,,Z,$+Bi(k)=max{0,Tiui(k)-Bi(k)}=[Tiui(k)-Bi(k)]+(9)$-Bi(k)=max{0,Bi(k)-Tiui(k)}=[Bi(k)-Tiui(k)]+(10)$+di(k)=max{0,yi(k)-di(k)}=[yi(k)-di(k)]+(11)$-di(k)=max{0,di(k)-yi(k)}=[di(k)-yi(k)]+(12)(8),(9)-(12)$+Bi(k)E0,$-Bi(k)E0(13)0420015©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.$+Bi(k)-$-Bi(k)=Tiui(k)-Bi(k)(14)$+di(k)E0,$-di(k)E0(15)$+di(k)-$-di(k)=yi(k)-di(k)(16),(8)minJ=6Mi=1aTixi(N+1)+6Nk=1[aTixi(k)+b+Ti$+Bi(k)+b-Ti$-Bi(k)+c+Ti$+di(k)+c-Ti$-di(k)](17)s.t.(2)-(7),(13)-(16),(17)yi(k),yi(k)di(k)Z(4)(5)yi(k)=6kt=1Ciui(t)(18)(6)(18)(16)$+di(k)-$-di(k)=6kt=1Ciui(t)-6kt=1di(t)(19),(17)minJ=6Mi=1aTixi(N+1)+6Nk=1[aTixi(k)+b+Ti$+Bi(k)+b-Ti$-Bi(k)+c+Ti$+di(k)+c-Ti$-di(k)](20)s.t.(2),(3),(7),(13)-(15),(19)4,(20)Z,(20),Z(20),,[7]Z,(3)(2)zi(k),,(20)minJ=6Mi=1aTixi(N+1)+6Nk=1[aTixi(k)+b+Ti$+Bi(k)+b-Ti$-Bi(k)+c+Ti$+di(k)+c-Ti$-di(k)](21)s.t.-xi(k)+xi(k+1)-6Mj=1Lijuj(k-1)+ui(k)=Gir(k)(22)Tiui(k)-$+Bi(k)+$-Bi(k)=Bi(k)(23)6kt=1Ciui(t)-$+di(k)+$-di(k)=6kt=1di(t)(24)xi(1)=xi1,uj(0)=uj0(25)xi(k)E0,ui(k)E0,$+Bi(k)E0,$-Bi(k)E0,$+di(k)E0,$-di(k)E0(26)(22)-(24),(21)-(26):minbTy(27)s.t.ATy=c(28)yE0(29)AmnmEn,cn,bymZ145FMS©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(27)-(29),mv,,[7]É[7]Z,Z,Z,,[7]Z5,FMS,,Z,,Zz=z3,(20)MFMSZ,FMSi:minJi=aTixi(N+1)+6Nk=1[aTixi(k)+b+Ti$+Bi(k)+b-Ti$-Bi(k)+c+Ti$+di(k)+c-Ti$-di(k)](30)s.t.-xi(k)+xi(k+1)+ui(k)=z3i(k)+Gir(k)(31)Tiui(k)-$+Bi(k)+$-Bi(k)=Bi(k)(32)6kt=1Ciui(t)-$+di(k)+$-di(k)=6kt=1di(t)(33)xi(1)=xi1(34)xi(k)E0,ui(k)E0,$+Bi(k)E0,$-Bi(k)E0,$+di(k)E0,$-di(k)E0(35)(30)-(35)Zui(k),,,z3i(k)Z[z3i(k)]l+1=6Mj=1Lijuj(k-1)li=1,2,,M;k=1,2,,N(36)l,uj(0)=uj0Z,(20)FMSFAW:1FAW:Step1l=1,zi(k)=z3i(k),,i=1,2,,M;k=1,2,,NZStep2(30)-(35),xi(k)(k=2,,N+1)ui(k)(k=1,2,,N),i=1,2,,MZStep3z3i(k)-6Mj=1Lijuj(k-1)2Z,Step5,Step4ZStep4(36)z3i(k),l=l+1,Step2LStep5,FMSiu3i(k),y3i(k)x3i(k)Z1,(20)MFMS,,,Z6VC++5.0,Pentium266Win98,ZZ1FAWFMS,FMS3-4,2420015©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.ERPöMRPÊFAW6,P12,1,3FMS,P21,4,2FMS,P33,1,4FMS,P44,2,3FMS,P52,4,1FMS,P63,1,2FMS,63,5,4,6,5,4,2.14,4.00,4.27,4.45,3.64,3.28,60,80,50,100,90,70Z,,FMS42,49,35,42()Z,6,8,5,10,9,7Zx11=(60597)T,x21=(081007)T,x31=(60100)T,x41=(8509)T,v-j0Z1,(28)A1120560,2150Z32MPentium266,35.15,23,FMSu31(k)=(68597)T,u32(k)=(681097)T,u33(k)=(65107)T,u34(k)=(85109)Tx3i(k)(kE2),J3=415.21Z,(1)56.24,6,u3i(k),x3i(k)J3Z,MatlabcE48Z,102,A224112,358,Matlab5.0578.09,1.7Z2FAW6FMS,FMS6-8,201250,xi1,vj0Z2,(28)A50002500,11574Z64MPentium266,973.5,23u3i(k),x3i(k)J