2011年高教杯數(shù)學(xué)建模競賽題獲獎職業(yè)技術(shù)學(xué)院

二．符號說

為某一規(guī)格中第ij

為第ij jd 為第kk 為第k三．模型分（1（2（2（3，應(yīng)用3、應(yīng)用LINGO模型二針對要求（4）一中的原理建立線性規(guī)劃模型，并應(yīng)用LINGO軟件計算結(jié)果；LINGO四．模型的建立與求4.0計算三種規(guī)格成品的理想最大捆（1成品總長度允許有0.5的誤差。我們據(jù)此計算三種規(guī)格對應(yīng)的理論最大捆數(shù)。88.5，得出針對長度的最大捆數(shù)；用每種規(guī)格腸衣的總根數(shù)除以對應(yīng)規(guī)格每捆要求的數(shù)量dk(k1,2,3nLajb fmin{L,N},k1,2,3 ．n j

88.5fkLNajj 1854.1模型一，分別設(shè)計三種規(guī)格原料的搭配方（1（312123456783456123456787898920600012aiji1,2,m;j1,2,n,表示某一規(guī)格中，第ij檔次腸衣j檔次對應(yīng)的總根數(shù)為bj，每一種規(guī)格的成品捆數(shù)為m，xij表示第ij

表示第k品捆數(shù)，dk表示第k種規(guī)格中每捆要求的根數(shù)，且d120d28d35y表示（1（2得最大值，此時求出的xij就是最佳搭配方案。具體的線性規(guī)劃模型[1]如下

yaijbjxij

1mp且mNkkk88.5a21x21a22x22a2nx2n88.5am1xm1am2xm2amnxmn

nndk1xijdk,i1,2,3,,jmmxi1b1

mmxi2b2,

mmxinbn3（?。┽槍σ?guī)格一，將其數(shù)據(jù)帶入到模型②

yaijbjxij

1m14且mN88.53x113.5x1288.53x213.5x22888.53xm13.5xm2819xij20,ijmmxi1

mmxi2mmxi5

mmxi6將理想最大捆數(shù)m14代入模型，應(yīng)用LINGO計算[2模型的最優(yōu)解ymin52.5143所示（求6.13單位長捆34560010100006600000002600109050302330007800001005103010010000（ⅱA

B2[89.5,89.5,B'2b124,b224,,bj,b14 minyaijbjxij

B'TAXTB 7x8,iS.T

j

b,j 應(yīng)用LINGO計算結(jié)果，經(jīng)過驗證m37ymin428，即規(guī)6.2475895555數(shù)0000200010200041008000101200110028000003100020208000000101001100400800000000710000800200100100040800000212000120800010000070000800002011000400800110000020400800020000104100800031000000004800021000000500800002000300300800002002000001020280000021100220080000041000000380000040001100280000100320002080000000310000000048000000500001208000001100600008000210002000038000210000005008000210000005008000001001110022010800100004000200050080000100060000000508000000401003008000210000005008A

14.515 B3[89.589.5]1135，B'3b135,b229,bj,b24

yaijbjxij

(B')TAXTB 4x5,i

j

b,j LINGO計算結(jié)果，當m135ymin93，即規(guī)格三的最大成品捆數(shù)為135具體搭配方案如下表5（求解程序[3]及結(jié)果見附錄表 規(guī)格三搭配方14141515161617171818122222323242425252121221112212411112122122第十一第十二1第十三122第十四第十五第十六第十七第十八1112第十九1第二十11231122122第三十11111212第四十2241221231第五十112123221212第六十2311121112第13第七十32322第八十32212121221第九十221第一百23111211第一百234211112122221223122111212212113.2模型二，設(shè)計剩余原料的搭配方6678611514根據(jù)模型一中①式f

f61234567781514 nnmjmmm運用LINGOm3ymin344.58所示（6.4781020310041020103010039所示：123456678617用同樣的方法求解得，當m=2ymin28510所示（6.56780113.3模型求解最終11得出最終剩余腸衣原料如下 所示長度（米784五．模型說方案設(shè)計出來，并成功利用LINGO軟件計算出題目提供的三種規(guī)格腸衣的搭配30分鐘以內(nèi)，滿足題目（5參考文 六第一規(guī)格LINGO程序與求解結(jié)6.6.1求解程C=33.544.555.563456345634563456345634563456345634563456345634563456函數(shù)@FOR(WH(I):@SUM(VD(J):C(I,J)*X(I,J))<=89.5);!約束條件X(W4,X(W4,6.1.2運行結(jié)GlobaloptimalsolutionObjectiveExtendedsolver0TotalsolveriX(W1,X(W1,X(W1,X(W1,X(W1,X(W1,X(W1,X(W2,X(W2,X(W2,X(W2,X(W2,X(W2,X(W2,X(W2,X(W3,X(W3,X(W3,X(W3,X(W3,X(W3,X(W3,X(W3,X(W4,X(W4,X(W4,X(W4,X(W4,X(W4,X(W4,X(W4,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,第二規(guī)格LINGO求解程序與結(jié)求解程789789789789789789789789789789789789789789789789789789789789789789789X(W1,X(W1,789789789789789789789789789789789789789789;求解結(jié)GlobaloptimalsolutionObjective Extendedsolversteps: Totalsolveritions: ReducedX(W1,X(W1,X(W4,X(W4,X(W4,X(W4,X(W7,X(W7,X(W7,X(W7,X(W10,X(W10,X(W7,X(W7,X(W8,X(W8,X(W8,X(W8,X(W8,X(W8,X(W8,X(W8,X(W8,X(W8,X(W8,X(W8,X(W8,X(W8,X(W9,X(W9,X(W9,X(W9,X(W9,X(W9,X(W9,X(W9,X(W9,X(W9,X(W9,X(W9,X(W9,X(W9,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,X(W10,X(W14,X(W14,X(W14,X(W14,X(W17,X(W17,X(W17,X(W17,X(W20,X(W20,X(W20,X(W20,X(W23,X(W23,X(WX(WPAGE11,X(W26,X(W26,X(W26,X(W26,X(W29,X(W29,X(W29,X(W29,X(W32,X(W32,X(W32,X(W32,第三規(guī)格LINGO求解程序與求解結(jié)求解程1422.51422.51422.51422.51422.5141523.51523.51523.51523.51523.51422.51422.51422.51422.51422.5141523.51523.51523.51523.51523.5151624.51624.51624.51624.51624.5161717171717171415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.522.51422.51422.51422.51422.51422.523.51523.51523.51523.51522.51422.51422.51422.51422.51422.523.51523.51523.51523.51523.51523.524.51624.51624.51624.51624.51624.517171717171422.51422.51422.51422.51422.5141523.51523.51523.51523.51523.51422.51422.51422.51422.51422.5141523.51523.51523.51523.51523.5151624.51624.51624.51624.51624.5161717171717171415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.522.51422.51422.51422.51422.51422.523.51523.51523.51523.51522.51422.51422.51422.51422.51422.523.51523.51523.51523.51523.51523.524.51624.51624.51624.51624.51624.517171717171415161722.523.524.51415161722.523.524.51415161722.523.524.51415161722.523.524.5求解結(jié)5規(guī)格三的剩余原料降級至規(guī)格二的搭配方案程序及其結(jié)求解程求解結(jié)GlobaloptimalsolutionObjectiveExten