数学建模竞赛新手教程

MATHEMATICALMODELINGSHUMOSHUMO.COM2004.1Vol.1No.1MATHEMATICALMODELINGSPONSOREDBY:SHUMO.COMCOMPILEDBY:[e-mail]:[e-mail]:ScienceCollege,NUDT,ChangshaHunan410073POSTALCODE:410073²²..........................................................................1|...................................................3..............................................................6.................................................12........................................................15²²..........................................18........................................34..................................................47............................................60......................................78²²2004..........................................91III200411Vol.1No.1200411MathematicalModeling2004.11¤4100732000FloydInternet20015924¤SHUMO.COM200122004200211Vol.1No.1200411MathematicalModeling2004.11|¤430072¢¢¢¢¢¢CUMCM||GRE¤2004MCM200442004GRECUMCMRA|1|511Vol.1No.1200411MathematicalModeling2004.11¤4100731980100OKy¤SHUMO.COM2001y17¢¢¢¢¢¢|WordMicrosoftWPSWordVisioSmartDraw|801000200dbCPUUPS¢¢¢¢¢¢bird10¢¢¢¢¢¢2|82004WordVisioWord¢¢¢¢¢¢|MM3[1]1519192001z420019:)²5²MATLABC²533566UPSModemMATLABVisualC++MicrosoftWordWindows2000Visio²HPLaserJet6.0²¢¢¢¢¢¢8:00Down8:00/:)zSHUMO.COM102004x|WindowsconsoleDOSTurboC512512DOS32Windows¢¢¢¢¢¢¢¢¢¢¢¢42x111Word1.2.3.5[2]MATLABC++¢¢¢¢¢¢[1].[J].20041:1-2.[2].[J].20041:12-1411Vol.1No.1200411MathematicalModeling2004.11¤10087611.2.MATLAB3.LindoLingo4.5.6.7.8.9.10.MATLAB22.197A108¤SHUMO.COM2002113y2.298A94AMATLABMATLAB2.398BLindoLingo2.498B00B95DijkstraFloydPrimBellman-Ford2.592B97B98BACM2.697A00B01B89ABP86BP8903B2.7N[a;b]M+1a;a+(b¡a)=M;a+2¢(b¡a)=M;¢¢¢;b(M+1)N97A99BMATLABy20021420042.82.9MATLABMathematica2.1001ABMP98A03BMATLAB11Vol.1No.1200411MathematicalModeling2004.11¤1008761,23104¤SHUMO.COM20021620045¢¢¢¢¢¢6yB010216799AMATLABMathematicaC/C++Floydz8y2002z121179MATLABMATLABMATLAB10B11Vol.1No.1200411MathematicalModeling2004.11¤430072\\\Hu®manHu®manMATLAB1.R212.982.4MW3034953.1052.8MW35639.2%510Hu®man¤2004119121.2.AGCAGC3.4.5.6.7.8.3giiMWi=1;2;:::;8gi0iMWlijMWj=1;2;:::;6aijjibjjmjjMWrjj´jjviiMW/gmiiMWpi(gi)igi/MWhpM:/MWhPLMWE¢t1/444.1202004\4.2[1]32154.31.2.3.4.41.\2.03.4.\5.0011214.51.8Pi=1gi=PL2.gi0¡vi¢t·gi·gi0+vi¢t;i=1;2;:::;83.gmigi6gmi;i=1;2;:::;84.jljj¡mj0;j=1;2;:::;6;5.0jljj¡(1+rj)mj60;j=1;2;:::;655.133125.1.1lj=8Xi=1aijgi+j(1)lj=8Xi=1aijgi+bj+j(2)jj»N¡0;¾2j¢j=1;2;:::;6aijbj032222004(1)Lj=³l(0)j;l(1)j;¢¢¢;l(32)j´T;G=0BB@g(0)1g(0)2¢¢¢g(0)8¢¢¢¢¢¢¢¢¢¢¢¢g(32)1g(32)2¢¢¢g(32)81CCAAj=(a1j;a2j;¢¢¢;a8j)T;Ej=³(0)j;(1)j;¢¢¢;(32)j´TGTGAj=GTLj(3)(3)AjAj(2)G=[N...G]GN=(1;1;:::;1)T1£331Aj=[bj;Aj]AjAj(1)5.1.2ljg1;g2;:::;g8®j(j=1;2;:::;6)H0:a1j=a2j=a3j=a4j=a5j=a6j=a7j=a8j=0H1:i=1;2;:::;8aij6=0[2]1.FQQ=32Pk=0(l(k)j¡^l(k)j)2^l(k)j=8Pi=1aijg(k)iUU=32Pk=0(^l(k)j¡¹lj)2¹lj=(1=33)Pkl(k)jF=U=nQ=(m¡n¡1)n=8m=33F»F(n;m¡n¡1)®H0W=fFF1¡®(n;m¡n¡1)gFF1¡®(n;m¡n¡1)H0®2.R2R=pU=(U+Q),R2R21ljg1;g2;:::;g8®H0W=fR2R20g;R20=nF1¡®(n;m¡n¡1)m¡n¡1+nF1¡®(n;m¡n¡1)5.1.3MATLAB®=5%12(2)1235.1.412(2)(1)(2)\0(2)\1.\2.(2)(1)5.2\5.2.11.ikg(0)i;kp(0)i;kp(0)M(p(0)i;kp(0)M)g(1)i;kg(0)i;kg(1)i;kEi;k=(p(0)M¡p(0)i;k)(g(0)i;k¡g(1)i;k)¢t(4)2.ikg(0)i;k=0p(0)i;kp(0)Mg(1)i;k0Ei;k=(p(0)i;k¡p(0)M)(g(1)i;k¡g(0)i;k)¢t=(p(0)M¡p(0)i;k)(g(0)i;k¡g(1)i;k)¢t(5)E0=PiPkE0i;kE=°¢E0°01°=1(4)(5)g(1)i;k=g(0)i;kE5.2.2242004gtgt=PLp(0)Mp(1)Mp(2)ME=¢t³P(2)M¡P(0)M´¢PLp(2)M=(1¡µ)p(0)M+µp(1)Mµµ=15.2.31.2.3.pi;k=pME0i;k=0pi;k4.5.3Step1PLStep2gigigi0gi¡gi0vi¢¢tgi=gi0+vi¢¢tflagi=¡1gi¡gi06¡vi¢¢tgi=gi0¡vi¢¢tflagi=1giflagi=0Step3flagi0giiStep2g=PigiStep4g=PLgiigPLflagi1gPLflagi-1Step5Step5gPLflagi6=¡1Step2gPLflagi6=¡1Step21255.45.4.1\1.jljj¡mj0;j=1;2;:::;6(6)lj=8Pi=1aijgi+bj2.minEs.t.8:8Pi=1gi=PL;jljj¡mj0;gi0¡vi¢¢t6gi6gi0+vi¢¢t;gi6gmii=1;2;:::;8;j=1;2;:::;6(7)773.7j´j´j=jljj=mj¡1rjjljj=(1+rj´j)mj´j\(a)min½maxj´j¾s.t.8:Pigi=PLjljj¡(1+´jrj)mj0gi0¡vit6gi6gi0+vitgi6gmi´j61i=1;2;:::;8;j=1;2;:::;6(8)262004(8)f´¤jg6j=1(8)(b)(8)(8)minEs.t.8:Pigi=PLjljj¡(1+´jrj)mj0gi0¡vit6gi6gi0+vitgi·gmi´j6´¤j(9)(9)(8)(9)(8)(9)4.(7)maxXigis.t.8:gi0¡vit6gi6gi0+vitgi·gmijljj¡(1+rj)mj60i=1;2;:::;8;j=1;2;:::;6(10)5.4.21.(7)E=maxif(pi(gi)¡p(0)M)¢PLg;Gmaxipi(gi)j¤¡aij¤!aij¤i=1;2;:::;8aij¤minnmaxipi(gi)os.t.8:8Pi=1gi=PL;lj¡mj0;gi0¡vi¢¢t6gi6gi0+vi¢¢tgi6gmii=1;2;:::;8;j=1;2;:::;6127MATLAB[3]0(a)(b)[6](c)i.ii.aij¤jljmjfaijgG0p(0)MStep1G00G0igi¤Step2gi6gi¤maxXigis.t.8:lj6mjgi0¡vit6gi6gi0+vitgi6gi¤Step3PigiPLStep4Step2Step4Pigi=PLMATLAB452.(a)82820048aij¤min´s.t.8:Pigi=PLlj¡(1+´jrj)mj0gi0¡vit6gi6gi0+vitgi6gmi´j6´06´61i=1;2;:::;8;j=1;2;:::;615(g1;g2;:::;g8;´1;´2;:::;´6;´)(b)97minnmaxipi(gi)os.t.8:Pigi=PLlj¡(1+´jrj)mj0gi0¡vit6gi6gi0+vitgi6gmi´j6´¤ji=1;2;:::;8;j=1;2;: