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200666:100026788(2006)06201172072,,(,100083):2,.,/2.,,.:;2;;:N949:AModelandAlgorithmforSteelmaking2ContinuousCastingSchedulinginDHCRandCCREnvironmentLITie2ke,ZHOUJian,SUNLin(SchoolofManagement,UniversityofScienceandTechnologyBeijing,Beijing100083,China)Abstract:Acaststartingtimebasedmathematicalmodelconsideringbothmachineallocationandheatsequencingisestablishedforthesteelmaking2continuouscastingschedulingprobleminDHCR(directhotchargerolling)andCCR(coldchargerolling)environment.Themodelcancoordinatethecontinuouscastingandhot2rollingproductionstagesbyadjustingthevalueofpenaltycoefficientsonthedeviationofthecaststartingtimes.Forthemodelestablishedinthispaper,apracticalsolutionmethodbasedongeneticalgorithmandlinearprogrammingisdeveloped,andthecomputingexperiencewithdatafromapracticalproductionprocessisshown.Keywords:steelmaking2continuouscasting;hot2rolling;productionscheduling;geneticalgorithm:2005203231:(70371057):(1958-),,,,,,E2mal:tieke@public.bta.net.cn.12,2,,,2,.2,.2,[1,2]2;[3]2;[4](UML)2.2,[5]Petri2;[6]2;[7]2,;[8]2,,.,,2.[9,10]2.2,[11],[12]22.,2,,,,2.221121.(A)2(CC2CCR),;(B)2(CC2HCR),;(C)2(CC2DHCR);(D)2(CC2HDR).:1)CC2CCR,,.,2.2)CC2DHCR,(20),CC2HDR.CC2DHCRCC2HDR(),,22;3)CC2HCR,400700.,.122,.,2.2,,,.,.,.:1)[11];2)[12].(),,;,,,.,,,.,(),2.,/2.212;n(n=1,2,,N)|n|pij(in,j=1,2,3)n.n(n=1,2,,N)()Tn81120066.213,:hn,wnn/;i,,||;n,N,nn;j,,j=1,2,3;Mjj;pijij;tij,cijij;tFH(n),3n;Tnn();xijk=1,ijk;0,.yi1i2j=1,ji1i2;0,.C1nn;C2ii;U.2:[M1]minNn=1i,i+1nC1n(ti+1,3-ci3)+ij=1,2C2i(ti,j+1-cij)+Nn=1hnmax(0,Tn-tFH(n),3)+Nn=1wnmax(0,tFH(n),3-Tn)(1)s.t.Mjk=1xijk=1,Pi,j=1,2(2)ti2j-ci1j+(3-xi1jk-xi2jk-yi1i2j)U0,Pi1,i2,i1i2,j=1,2,k=1,2,,Mj(3)ti,j+1cij,Pi,j=1,2(4)ti+1,3ci3,Pi,i+1n,n=1,2,,N(5)yi1i2j+yi2i1j=1,Pi1,i2,i1i2,j=1,2(6)xijk=0,1,Pi,j=1,2,k=1,2,,Mj(7)yi1i2j=0,1,Pi1i2,i1i2,j=1,2(8)tij0,Pi,j=1,2,3(9),cij=tij+pij,Pi,j=1,2,3.(1)/.;/,/(hnwn).,(A)(B),hnwn;(C)(D),hnwn.(2)91162;(3);(4);(5),;(6)(9).32,()(),,2(hybridflowshop).,2.2.2,2:1)2,;2),2.31131111[13]HFSP.2,2,.m,3(),Mj(1j3),.,n,.:Rd=[a11ai1am1a12ai2am2]aij(1,Mj+1),ij(j=1or2)int(aij).int(aij)aij.,2,2:Tn(j=1)t3i1,FH(n)n1;t3i1=ii=FH(n)Pi3-3j=1pij(10)(j=1),t3i1,ijMk,CM(k)Mk,i:ti1=t3i1,k=1;ti1=max(t3i1,CM(k-1)),k1.(j=2,3),,,,aij,i:tij=ci,j-1,k=1;tij=max(ci,j-1,CM(k-1)),k1.311121),.2),015..3),SSM.ij,:i02120066,.,.31113fitness=1/fk,fkkMakespan.312LP,,Makespan,.,,(M2):[M2]min(1)s.t.tNH(i,j),jcij,Pi,j=1,2,3(11)(4),(9).M2,:zn=-min(0,tFH(n),3-Tn),yn=max(0,tFH(n),3-Tn)yn-zn=tFH(n),3-Tn:tFH(n),3=yn-zn+Tn,M2(M3):[M3]minNn=1i,i+1nC1n(ti+1,3-ci3)+ij=1,2C2i(ti,j+1-cij)+Nn=1(hnzn+wnyn)s.t.(11)(4)(9).,cij=tij+pij,(Pi,j=1,2,3),tNH(i,j),jiji.M3,.313C++,LINDOM3,.333(2,1).,,4810.,200,300,2800MHz,512MB15,1000,37.,.,().,.1jMjiC2in=1,T1=85,c11=15,h1,w1=10n=2,T2=120,c12=15,h2,w2=10n=3,T3=160,c13=10,h3,w3=512345678910111213141522222222221111113233-pij454545454545454545454545454545404040404040404040403535353535353535353535353535354040404040,1,.1,,2.,2(a),2(b)2.121622(a)2(b)4,.,.2,;,/;,,.:[1]SatoS,YamaokaT,AokiY,UedaT.Developmentofintegratedproductionschedulingsystemforironandsteelworks[J].InternationalJournalofProductionResearch,1977,15(6):539-52.[2]LarryB,BieglerL,heneinA.Amodelforsequencingacontinuouscastingoperationtominimizecosts[J].Iron&steel,1987,10:53-70.[3],,.2[J].,1996,12:663-667.TangLixin,YangZihou,WangMengguang.Researchonframeworkofsteelmaking2continuouscastingproductionplanningandscheduling[J].JournalofNortheasternUniversity,1996,12:663-667.[4],,.UML2[J].,2003,25(6):532-536.LiuWei,LiTieke,ZhouZhi.ModelingofaUML2basedschedulingsystemforsteelmaking2continuouscastingproduction[J].JournalofUniversityofScienceandTechnologyBeijing,2003,25(6):532-536.[5],.Petri[J].,1999,1:79-82.FangYuwei,HanZengjin.Petrinetsbasedreal2timeschedulingmodelofsteelmaking2continuouscastingprocess[J].TsinghuaUniv(Sci&Tech),1999,1:79-82.[6],,,.[J].,2001,11:1657-1662.LiXiaofeng,XuLiyun,ShaoHuihe,RenDexiang.Dynamicmodelofsteelmakingandcontinuouscastingsystemandhierarchicalgorithmofdynamicscheduling[J].JournalofShanghaiJiaotongUniversity,2001,11:1657-1662.[7]IiroHarjunkoski,IgnacioE.Grossmann.Adecompositionapproachfortheschedulingofasteelplantproduction[J].Computers22120066andChemicalEngineering,2002,25:1647-1660.[8],.2[J].,2002,6:44-48.LiuGuanghang,LiTieke.Asteelmaking2continuouscastingproductionschedulingmodelanditsheuristicalgorithm[J].SystemsEngineering,2002,6:44-48.[9],,.2[J].,2000,5:409-413.SunFuquan,ZhengBinglin,CuiJianjiang,WangDingwei.Theresearchofproductionplanningofintegratedmanagementinsteelmaking2hotrolling[J].ActaAutomaticaSinica,2000,5:409-413.[10],,,.[J].,2002,2:25-28.PengQichun,BaoYanping,TianNaiyuan,etal.Designofsteelmakingplanningsubsysteminintegratedproductionmanagementsystem[J].JournalofUniversityofScienceandTechnologyBeijing,2002,2:25-28.[11],,.2[J].,1998,24(1):9-14.TanGLixin,YangZihou,WangMengguang.Researchonsteelmakingandcontinuouscastingproductionscheduling[J].ActaAutomaticaSinica,1998,24(1):9-14.[12],.22[J].,2003,1:33-36.ZhuBaolin,YuHaibin.Productionschedulingmodelandalgorithmforsteelmaking2continuouscasting2hot