研究生录取问题的双向选择策略

35720057MATHEMATICSINPRACTICEANDTHEORYVol135No17July,2005,,:(,,,430072):.,0-1,,,;,,..:;;0-11(D)2,,:(1),,;(2),,;(3),A=017,L=017,B=017,w=015.3()4411,,.100.A,(1-A).500,SiMi:mi=Mi500100A,ABCD4321.Sifi,k(k=1,,5),fi,kvk(k=1,2,3,4,5),vk=1,Si:2004,ni=5k=1vkfi,kö(54)100(1-A),Sici=mi+ni.412,.:().,Lp,k(k=1,2,3,4),,:(1)Lk(k=1,,4),25;(2)Tplp,k=25Lp,köLk(p=1,,10);(3)Tp,lp,lp=25õ4k=1Lp,köLk;413Sifi,k,TpSiFip,k,k,Sifi,kTpFip,kKip,k,Kip,k=1fi.kFip.,kfi,kFip,kfi,kFip,ki=1,,15,p=1,,10,k=1,,4SiTp,gip,gip=15õ5k=1Kip,k51511Ej(j=1,,8)Sicijcgi=18õ8j=1cijSi.10.512A=(aip),:(1)Si10Dk(k=1,2,3):12,:D1D2D3.(2):a.;b..aB,b(1-B).(3),SiTp,tip,tip=Bõlp+(1-B)õgip,,Si.(4),SiSNip,Si7017,:aip=011(11-SNip).A=(aip)1010.513B=(bip),:(1)TpPk(k=1,,4),Tp12;.10Ck(k=1,2,3),:C1C2C3.(2),:a.;b..aL,b(1-L).(3),TpSi,ypi,ypi=Lci+5k=1Kip,kõ(1-L)5,,Tp.(4),TpTNpi,Tpbpi=011(11-TNpi),bip.B,B=(bip)1010.514XX=(xip)1010{0,1},TpSi.,10p=1xip=1.5150-1[1]:(1)maxAi(x)=10p=1aipõxipi=1,,10(2)maxBp(x)=10i=1bipõxipp=1,,10:(1)maxA(x)=10i=110p=1aipõxipi=1,,10(2)maxB(x)=10p=110i=1bipõxipp=1,,10publics.t:10p=1xip=1xip(1-xip)=0(i=1,,10;p=1,,10),5160-10-1,,.,w,(1-w),[2]:maxM(x)=110õ[max{wA(x)+(1-w)B(x)}]80135=110w10i=110p=1aipõxip+(1-w)10i=110p=1bipõxip:publics.t5170-1[3](1)X=(xip)10100-1,1010,,M(x)1010,M,.(2).M(x),aip=bip=1,SiTp,TpSi,aip=bip=1xip=1.1M(x),aip=bip=1,xip=1..()(3)A=(aip)1010B=(bip)1010,aip=bip=1,waip+(1-w)bipmax(waik+(1-w)bik)(k=1,,10;kp),M(x)xip=1,SiTp.2M(x),waip+(1-w)bipmax(waik+(1-w)bik)(k=1,,10;kp),xip=1..()(4),2,Si,.M=0196.626111,0-1:maxM(x)=wA(x)+(1-w)B(x)=w10i=110i=1aipõxip+(1-w)10i=110i=1bipõxip:publics.t10i=1xip=1(i=1,,10;p=1,,10)612NP,,.(1)1.A=(aip)1010B=(bip)1010,waip+(1-w)bipmax(walk+(1-w)blk)(kp,l=1,,10;li),xip=1;ipwamn+(1-w)bmnmax(walk+(1-w)blk)(k=1,,10;kn,p,l=1,,10;lm,i)xmn=1;..(2)X=(xip)1010,10!=36288009017,:,,M(x),M,,.,.,[4],.,,.,.,(3)A=(aip)1010B=(bip)1010,jaip=bip=1,SiTp,TpSi.jSiTp,(10-j)(10-j),(2),.jSiTp.,8-,,.73,,.71115:a.();b..aL,b(1-L).ab,100,TpSiyip=Lci+5k=1Kip,kõ100(1-L)5(i=1,,15;p=1,,10),TpSi.B=(bip)1015.712bi=110õ10p=1bip;bi,10.,10Si(i=1,,10),TpSibip(i=1,,10;p=1,,10).713E=(eip)1010Tpyip=Ldi+5k=1Kip,kõ100(1-L)5.,Tpyip.:110019011.TpSieip,E=(eip)101001135714Q=(qip)1010,Sitip=Bõlp+(1-B)õgip,Si10,:110019011.SiTpqip,Q=(qip)1010.715(1),qip=eip=1TpSi,j,D={d1,d2,dj},Tp(p|D)Si(i|D),Si(i|D)Tp(p|D)Qv=(qlip)(10-j)(10-j),Tp(p|D)Si(p|D)Ev=(egip)(10-j)(10-j),xqip,p|D,i|D.(2),2,maxM(xq)=110w10-ji=110-jp=1qlipõxqip+(1-w)10-ji=110-jp=1egipõxqip+js.t10-ji=1xqip=110-jp=1xqip=1xip(1-xip)=1i=1,,10-jp=1,,10-j716(1),jqip=eip=1.jSiTp,(10-j)(10-j),2.(2)2.,,.(3)(10-j)!,,M(xq),M,.848115,5.,A=(aip)1510.ap=15i=1aipö15,ap,5.5Tp(p=1,,5).812101,Tp15yip=Lci1117,:+5k=1Kip,kõ100(1-L)ö5(i=1,,15;p=1,,5)B=(bip)155.,bi=5p=1bipö5;bi,10.10Si(i=1,,10).813,2:maxM(x)=w10i=15p=1aipõxip+(1-w)10i=15p=1bipõxips.t10p=1xip=110i=1xip=2xip(1-xip)=0(i=1,,10;p=1,,5)814,510,1010,5.Av=(A,A)1010,Bv=(B,B)1010,X=(xip)1010,:maxM(x)=w10i=110p=1alipõxip+(1-w)10i=110p=1blipõxip:publics.t10i=1xip=1(i=1,,10;p=1,,10),2,.,,.10!,,M(x),M,.95911,,,.,,.,.,.91214(),21135,,,.,,.,.:(1);(2).(1),(1)(2),;,.:(1)1510A=(aip)1510B=(bip)1510,,.(2)10,10,15.10,155,10,1,Mi.(3),.(C515=3003).Md=max{M1,M2,,M3003},Md,,.9135[5]1,5Uk,i1,i2,i3,i4,i5,10p=1xi1p=0,10p=1xi2p=0,10p=1xi3p=0,10p=1xi4p=0,10p=1xi5p=0.Uk,Mk:Mk=110maxw15i=110p=1aipõxip+(1-w)15i=110p=1bipõxips.t10p=1xijp=0(ij{1,2,,15};j=1,2,3,4,5)10p=1xip=1(iik)xip(1-xip)=0(i{1,2,,15};p{1,2,,10}):Md=max{M1,M2,,Mk,,M3003}9145.5,A=(aip)1010B=(bip)1010,waip+(1-w)bipmax(waik+(1-w)bik),xip=1,SiTp.,2,Si,.,Mk,3003MkMd=max{M1,M2,,Mk,,M3003}.3117,:101:10196201893016640194501971,:1),;2),;3),,.:[1],.()[M].,19984.[2].[M].,1998.[3].()[M].:,199013.[4].[C]..[5],.[M].,20013.Two-waySelectingStrategyonPostgraduateRecruitmentProblemCAOBao2hua,CHENYan2zhou,GUOLan2yingAdvisor:GUOCheng2xiu(NationalLaboratoryofSoftwareEngineering,CollegeofCivilConstruction,MathematicandStatisticSchool,WuhanUniversity,WuhanHubei430072,China)Abstract:Thepostgraduaterecruitmentproblemunderdifferentconditionsisanalyzedinthispaperaccordingtothebackgroundandrequirementofthisquestion.Underdifferentcondi2tions,atwo2wayselecting0-1planningmodelhasbeenputforwardaswellasthecorrespond2ingcalculatingapplicationprogramonthisproblem.Theoptimumprogramgainedfromopti2mumsolutionisachievedthroughcalculationofeveryquestion.Thismodelhasguidancetothepracticalmathcalculationandmathematicalmodelingoftheuniversitystudent.Keywords:postgraduaterecruitmentproblem;Two2waySelectingStrategy;0-1planningmodel41135