運(yùn)籌學(xué)案例8培訓(xùn)講學(xué)

運(yùn)籌學(xué)案例8精品文檔精品文檔收集于網(wǎng)絡(luò)，如有侵權(quán)請(qǐng)聯(lián)系管理員刪除收集于網(wǎng)絡(luò)，如有侵權(quán)請(qǐng)聯(lián)系管理員刪除精品文檔收集于網(wǎng)絡(luò)，如有侵權(quán)請(qǐng)聯(lián)系管理員刪除運(yùn)籌學(xué)案例8報(bào)告組員晉榕榕尹琪徐凱文耿志強(qiáng)張晗模型假設(shè) 1問題分析 1模型求解 2LINGO程序部分： 2題目a 2題目b 4題目c 5程序運(yùn)行結(jié)果： 7題目a 7題目b 13題目c 19結(jié)果分析 25問題a 25問題b 26問題c 27附錄 28原問題的中文版本描述 28問題的英文原版描述 30模型假設(shè)首先我們假設(shè)每位藝術(shù)家作品數(shù)量都是4件,并將其中作品數(shù)目不足4件的藝術(shù)家的作品所對(duì)應(yīng)的變量xij的值取為0，同時(shí)，展品展出所需的費(fèi)用全部包含在表中所列價(jià)格中。問題分析通過討論分析，我們認(rèn)為題目a所要求解的是在艾西·布里格斯所提供的資金（400萬）的范圍內(nèi)，能夠展出的展品的最大數(shù)目以及展出的具體藝術(shù)家及其作品。題目b要求求解在保證展品數(shù)目不少于20件的條件下，使本次展覽所耗費(fèi)的資金數(shù)量最小的方案以及展出的具體作品。題目c是要求解在確保20件展品的情況下，求贊助人利塔·羅斯基所需要出資的最小的數(shù)目以及展出的具體作品。這一問題在所提供的中文版本的案例中的描述不夠準(zhǔn)確，所以我們查閱了英文原版案例。決策變量xiji=1,2,……,13j=1,2,3,4各變量的取值為0或1，當(dāng)展品展出時(shí)變量取值為1，否則取0。故此問題為0-1規(guī)劃。題目a目標(biāo)函數(shù)max約束條件由此建立模型如下max題目b目標(biāo)函數(shù)min約束條件由此建立模型如下題目c目標(biāo)函數(shù)min約束條件由此建立模型如下模型求解由上面分析可知此案例屬于0-1規(guī)劃問題，所以我們利用LINGO來求解各個(gè)問題。以下是每個(gè)問題對(duì)應(yīng)的LINGO程序以及結(jié)果。LINGO程序部分：題目a!案例8分配藝術(shù)品（ItroductiontoManagementScience,F.S.Hillier,Case9-2AssigningArt）;!a題;!所有的價(jià)格以萬元為單位;model:sets: artist/1..13/; piece/1..4/; link(artist,piece):price,x;endsets!目標(biāo)函數(shù);max=@sum(artist(I):@sum(piece(J):x(I,J)));!約束條件;x(3,2)+x(7,1)+x(12,1)+x(12,2)=1;!collage;@sign(@sum(piece(I)|I#le#3:x(1,I))-1)=@sign(@sum(piece(I)|I#le#2:x(2,I))-1);!wiremeshsculpture,computerpainting;@sum(piece(I)|I#le#2:x(6,I))+x(8,1)>=1;!photo-realistic;@sum(piece(I)|I#le#2:x(11,I))+x(8,2)>=1;!cubist;x(8,3)>=1;!expressionist;@sum(piece(I)|I#le#2:x(4,I))+@sum(piece(I)|I#le#4:x(13,I))>=1;!water-color;@sum(piece(I)|I#le#2:x(5,I))+@sum(piece(I)|I#le#2:x(9,I))+x(10,3)>=1;!油畫oil-paint;@sum(artist(I)|I#ne#1#and#I#ne#2#and#I#ne#3#and#I#ne#7#and#I#ne#10#and#I#ne#12:@sum(piece(J)|J#le#2:x(I,J)))+x(8,3)+x(10,3)+x(13,3)+x(13,4)<=2*(@sum(artist(I)|I#eq#1#or#I#eq#2#or#I#eq#3#or#I#eq#7#or#I#eq#12:@sum(piece(J):x(I,J)))+x(10,1)+x(10,2));!繪畫<=其他x2(painting<=2xother-form);!@sum(artist(I)|I#ne#1#and#I#ne#3#and#I#ne#7#and#I#ne#11#and#I#ne#12:@sum(piece(J):x(I,J)))+x(11,1)<=20;!繪畫<=20(這個(gè)條件在原書中沒有);@sum(piece(I)|I#le#4:x(13,I))=4;!allAsh;@sum(piece(I)|I#le#2:x(4,I))=2;!凱蒂作品全展出allCandy;@sum(piece(I)|I#le#4:x(6,I))=@sum(piece(I)|I#le#4:x(8,I));!戴維，里克作品數(shù)相等;@sum(piece(I)|I#le#4:x(6,I))>=1;!而且都大于1;@sum(piece(I)|I#le#4:x(12,I))<=1;!Ziggy的作品不多于1件;@sum(artist(I)|I#ne#2#and#I#ne#4#and#I#ne#7#and#I#ne#11:@sum(piece(J):x(I,J)))<=2*(@sum(artist(I)|I#eq#2#or#I#eq#4#or#I#eq#7#or#I#eq#11:@sum(piece(J):x(I,J))));!男<=女x2;@sum(piece(I)|I#le#2:x(3,I))>=1;!老年地球，浪費(fèi)資源;@sum(piece(I)|I#le#4:x(10,I))>=1;!Bill至少有一件;x(2,1)+x(2,2)+x(9,1)+x(9,2)>=1;!混沌至少一件;@sum(piece(I)|I#le#4:x(1,I))+x(3,1)+x(7,2)+x(7,3)<=4;!雕像<=4;@sum(artist(I):@sum(piece(J):x(I,J)))-(@sum(piece(I)|I#le#4:x(1,I))+x(3,1)+x(7,2)+x(7,3))<=20;!20painting,collage,drawing;x(7,2)>=x(12,2);!自戀，沉思;@sum(artist(I):@sum(piece(J):price(I,J)*x(I,J)))<=400;!總價(jià)格約束;total_price_used=@sum(artist(I):@sum(piece(J):price(I,J)*x(I,J)));!得到的總價(jià)格;total_display=@sum(artist(I):@sum(piece(J):x(I,J)));!總展出數(shù);!限制變量取值;x(1,4)+x(3,3)+x(3,4)+x(4,3)+x(4,4)+x(5,3)+x(5,4)+x(6,3)+x(6,4)+x(7,4)+x(8,4)+x(9,3)+x(9,4)+x(10,4)+x(11,3)+x(11,4)+x(12,3)+x(12,4)=0;!空缺部分;@for(artist(I):@for(piece(J):@bin(x(I,J))));!限制變量取值0-1;!數(shù)據(jù)部分;data: price=302512.50 40504055 7057.500 2022.500 151500 857500 4017.5450 5050500 656500 2535450 404000 303000 5555;enddataend題目b!案例8分配藝術(shù)品（ItroductiontoManagementScience,F.S.Hillier,Case9-2AssigningArt）;!b題;!所有的價(jià)格以萬元為單位;model:sets: artist/1..13/; piece/1..4/; link(artist,piece):price,x;endsets!目標(biāo)函數(shù);!max=@sum(artist(I):@sum(piece(J):x(I,J)));min=@sum(artist(I):@sum(piece(J):price(I,J)*x(I,J)));!最小花費(fèi);!約束條件;x(3,2)+x(7,1)+x(12,1)+x(12,2)=1;!collage;@sign(@sum(piece(I)|I#le#3:x(1,I))-1)=@sign(@sum(piece(I)|I#le#2:x(2,I))-1);!wiremeshsculpture,computerpainting;@sum(piece(I)|I#le#2:x(6,I))+x(8,1)>=1;!photo-realistic;@sum(piece(I)|I#le#2:x(11,I))+x(8,2)>=1;!cubist;x(8,3)>=1;!expressionist;@sum(piece(I)|I#le#2:x(4,I))+@sum(piece(I)|I#le#4:x(13,I))>=1;!water-color;@sum(piece(I)|I#le#2:x(5,I))+@sum(piece(I)|I#le#2:x(9,I))+x(10,3)>=1;!油畫oil-paint;@sum(artist(I)|I#ne#1#and#I#ne#2#and#I#ne#3#and#I#ne#7#and#I#ne#10#and#I#ne#12:@sum(piece(J)|J#le#2:x(I,J)))+x(8,3)+x(10,3)+x(13,3)+x(13,4)<=2*(@sum(artist(I)|I#eq#1#or#I#eq#2#or#I#eq#3#or#I#eq#7#or#I#eq#12:@sum(piece(J):x(I,J)))+x(10,1)+x(10,2));!繪畫<=其他x2(painting<=2xother-form);!@sum(artist(I)|I#ne#1#and#I#ne#3#and#I#ne#7#and#I#ne#11#and#I#ne#12:@sum(piece(J):x(I,J)))+x(11,1)<=20;!繪畫<=20(這個(gè)條件在原書中沒有);@sum(piece(I)|I#le#4:x(13,I))=4;!allAsh;@sum(piece(I)|I#le#2:x(4,I))=2;!凱蒂作品全展出allCandy;@sum(piece(I)|I#le#4:x(6,I))=@sum(piece(I)|I#le#4:x(8,I));!戴維，里克作品數(shù)相等;@sum(piece(I)|I#le#4:x(6,I))>=1;!而且都大于1;@sum(piece(I)|I#le#4:x(12,I))<=1;!Ziggy的作品不多于1件;@sum(artist(I)|I#ne#2#and#I#ne#4#and#I#ne#7#and#I#ne#11:@sum(piece(J):x(I,J)))<=2*(@sum(artist(I)|I#eq#2#or#I#eq#4#or#I#eq#7#or#I#eq#11:@sum(piece(J):x(I,J))));!男<=女x2;@sum(piece(I)|I#le#2:x(3,I))>=1;!老年地球，浪費(fèi)資源;@sum(piece(I)|I#le#4:x(10,I))>=1;!Bill至少有一件;x(2,1)+x(2,2)+x(9,1)+x(9,2)>=1;!混沌至少一件;@sum(piece(I)|I#le#4:x(1,I))+x(3,1)+x(7,2)+x(7,3)<=4;!雕像<=4;@sum(artist(I):@sum(piece(J):x(I,J)))-(@sum(piece(I)|I#le#4:x(1,I))+x(3,1)+x(7,2)+x(7,3))<=20;!20painting,collage,drawing;x(7,2)>=x(12,2);!自戀，沉思;!@sum(artist(I):@sum(piece(J):price(I,J)*x(I,J)))<=400;!總價(jià)格約束;@sum(artist(I):@sum(piece(J):x(I,J)))>=20;!增加約束，展品數(shù)>=20;total_price=@sum(artist(I):@sum(piece(J):price(I,J)*x(I,J)));!總價(jià)格;total_display=@sum(artist(I):@sum(piece(J):x(I,J)));!總展品數(shù);!限制變量取值;x(1,4)+x(3,3)+x(3,4)+x(4,3)+x(4,4)+x(5,3)+x(5,4)+x(6,3)+x(6,4)+x(7,4)+x(8,4)+x(9,3)+x(9,4)+x(10,4)+x(11,3)+x(11,4)+x(12,3)+x(12,4)=0;!空缺部分;@for(artist(I):@for(piece(J):@bin(x(I,J))));!限制變量取值0-1;!數(shù)據(jù)部分;data: price=302512.50 40504055 7057.500 2022.500 151500 857500 4017.5450 5050500 656500 2535450 404000 303000 5555;enddataend題目c!案例8分配藝術(shù)品（ItroductiontoManagementScience,F.S.Hillier,Case9-2AssigningArt）;!c題;!所有的價(jià)格以萬元為單位;model:sets: artist/1..13/; piece/1..4/; link(artist,piece):price,x;endsets!目標(biāo)函數(shù);!max=@sum(artist(I):@sum(piece(J):x(I,J)));min=@sum(artist(I):@sum(piece(J):price(I,J)*x(I,J)));!最小花費(fèi);!約束條件;x(3,2)+x(7,1)+x(12,1)+x(12,2)=1;!collage;@sign(@sum(piece(I)|I#le#3:x(1,I)))=@sign(@sum(piece(I)|I#le#2:x(2,I)));!wiremeshsculpture,computerpainting;@sum(piece(I)|I#le#2:x(6,I))+x(8,1)>=1;!photo-realistic;@sum(piece(I)|I#le#2:x(11,I))+x(8,2)>=1;!cubist;x(8,3)>=1;!expressionist;@sum(piece(I)|I#le#2:x(4,I))+@sum(piece(I)|I#le#4:x(13,I))>=1;!water-color;@sum(piece(I)|I#le#2:x(5,I))+@sum(piece(I)|I#le#2:x(9,I))+x(10,3)>=1;!油畫oil-paint;@sum(artist(I)|I#ne#1#and#I#ne#2#and#I#ne#3#and#I#ne#7#and#I#ne#10#and#I#ne#12:@sum(piece(J)|J#le#2:x(I,J)))+x(8,3)+x(10,3)+x(13,3)+x(13,4)<=2*(@sum(artist(I)|I#eq#1#or#I#eq#2#or#I#eq#3#or#I#eq#7#or#I#eq#12:@sum(piece(J):x(I,J)))+x(10,1)+x(10,2));!繪畫<=其他x2(painting<=2xother-form);!@sum(artist(I)|I#ne#1#and#I#ne#3#and#I#ne#7#and#I#ne#11#and#I#ne#12:@sum(piece(J):x(I,J)))+x(11,1)<=20;!繪畫<=20(這個(gè)條件在原書中沒有);@sum(piece(I)|I#le#4:x(13,I))=4;!allAsh;@sum(piece(I)|I#le#2:x(4,I))=2;!凱蒂作品全展出allCandy;@sum(piece(I)|I#le#4:x(6,I))=@sum(piece(I)|I#le#4:x(8,I));!戴維，里克作品數(shù)相等;@sum(piece(I)|I#le#4:x(6,I))>=1;!而且都大于1;@sum(piece(I)|I#le#4:x(12,I))<=1;!Ziggy的作品不多于1件;@sum(artist(I)|I#ne#2#and#I#ne#4#and#I#ne#7#and#I#ne#11:@sum(piece(J):x(I,J)))<=2*(@sum(artist(I)|I#eq#2#or#I#eq#4#or#I#eq#7#or#I#eq#11:@sum(piece(J):x(I,J))));!男<=女x2;@sum(piece(I)|I#le#2:x(3,I))>=1;!老年地球，浪費(fèi)資源;@sum(piece(I)|I#le#4:x(10,I))>=1;!Bill至少有一件;x(2,1)+x(2,2)+x(9,1)+x(9,2)>=1;!混沌至少一件;@sum(piece(I)|I#le#4:x(1,I))+x(3,1)+x(7,2)+x(7,3)<=4;!雕像<=4;@sum(artist(I):@sum(piece(J):x(I,J)))-(@sum(piece(I)|I#le#4:x(1,I))+x(3,1)+x(7,2)+x(7,3))<=20;!20painting,collage,drawing;x(7,2)>=x(12,2);!自戀，沉思;!@sum(artist(I):@sum(piece(J):price(I,J)*x(I,J)))<=400;!總價(jià)格約束;@sum(artist(I):@sum(piece(J):x(I,J)))>=20;!增加約束，展品數(shù)>=20;!增加的約束條件;@sum(artist(I):@sum(piece(J):x(I,J)))=20;!總展品數(shù);@sum(piece(I)|I#le#4:x(2,I))=4;!allLoskey;total_price=@sum(artist(I):@sum(piece(J):price(I,J)*x(I,J)));!總價(jià)格;total_display=@sum(artist(I):@sum(piece(J):x(I,J)));!總展品數(shù);patron_pay=@sum(artist(I):@sum(piece(J):price(I,J)*x(I,J)))-400;!限制變量取值;x(1,4)+x(3,3)+x(3,4)+x(4,3)+x(4,4)+x(5,3)+x(5,4)+x(6,3)+x(6,4)+x(7,4)+x(8,4)+x(9,3)+x(9,4)+x(10,4)+x(11,3)+x(11,4)+x(12,3)+x(12,4)=0;!空缺部分;@for(artist(I):@for(piece(J):@bin(x(I,J))));!限制變量取值0-1;!數(shù)據(jù)部分;data: price=302512.50 40504055 7057.500 2022.500 151500 857500 4017.5450 5050500 656500 2535450 404000 303000 5555;enddataend程序運(yùn)行結(jié)果：題目aLocaloptimalsolutionfound.Objectivevalue:15.00000Objectivebound:15.00000Infeasibilities:0.000000Extendedsolversteps:2Totalsolveriterations:176VariableValueReducedCostTOTAL_PRICE_USED395.00000.000000TOTAL_DISPLAY15.000000.000000PRICE(1,1)30.000000.000000PRICE(1,2)25.000000.000000PRICE(1,3)12.500000.000000PRICE(1,4)0.0000000.000000PRICE(2,1)40.000000.000000PRICE(2,2)50.000000.000000PRICE(2,3)40.000000.000000PRICE(2,4)55.000000.000000PRICE(3,1)70.000000.000000PRICE(3,2)57.500000.000000PRICE(3,3)0.0000000.000000PRICE(3,4)0.0000000.000000PRICE(4,1)20.000000.000000PRICE(4,2)22.500000.000000PRICE(4,3)0.0000000.000000PRICE(4,4)0.0000000.000000PRICE(5,1)15.000000.000000PRICE(5,2)15.000000.000000PRICE(5,3)0.0000000.000000PRICE(5,4)0.0000000.000000PRICE(6,1)85.000000.000000PRICE(6,2)75.000000.000000PRICE(6,3)0.0000000.000000PRICE(6,4)0.0000000.000000PRICE(7,1)40.000000.000000PRICE(7,2)17.500000.000000PRICE(7,3)45.000000.000000PRICE(7,4)0.0000000.000000PRICE(8,1)50.000000.000000PRICE(8,2)50.000000.000000PRICE(8,3)50.000000.000000PRICE(8,4)0.0000000.000000PRICE(9,1)65.000000.000000PRICE(9,2)65.000000.000000PRICE(9,3)0.0000000.000000PRICE(9,4)0.0000000.000000PRICE(10,1)25.000000.000000PRICE(10,2)35.000000.000000PRICE(10,3)45.000000.000000PRICE(10,4)0.0000000.000000PRICE(11,1)40.000000.000000PRICE(11,2)40.000000.000000PRICE(11,3)0.0000000.000000PRICE(11,4)0.0000000.000000PRICE(12,1)30.000000.000000PRICE(12,2)30.000000.000000PRICE(12,3)0.0000000.000000PRICE(12,4)0.0000000.000000PRICE(13,1)5.0000000.000000PRICE(13,2)5.0000000.000000PRICE(13,3)5.0000000.000000PRICE(13,4)5.0000000.000000X(1,1)0.0000000.000000X(1,2)0.0000000.000000X(1,3)1.0000000.000000X(1,4)0.0000001.000000X(2,1)1.000000-2.000000X(2,2)0.000000-2.000000X(2,3)0.000000-1.000000X(2,4)0.000000-1.000000X(3,1)0.000000-1.000000X(3,2)1.0000000.000000X(3,3)0.0000001.000000X(3,4)0.0000001.000000X(4,1)1.0000000.000000X(4,2)1.0000000.000000X(4,3)0.0000001.000000X(4,4)0.0000001.000000X(5,1)1.000000-1.000000X(5,2)0.000000-1.000000X(5,3)0.0000001.000000X(5,4)0.0000001.000000X(6,1)0.000000-2.000000X(6,2)1.000000-2.000000X(6,3)0.0000000.000000X(6,4)0.0000000.000000X(7,1)0.0000000.000000X(7,2)1.000000-1.000000X(7,3)0.000000-1.000000X(7,4)0.0000001.000000X(8,1)0.0000000.000000X(8,2)0.0000000.000000X(8,3)1.0000000.000000X(8,4)0.0000002.000000X(9,1)0.000000-1.000000X(9,2)0.000000-1.000000X(9,3)0.0000001.000000X(9,4)0.0000001.000000X(10,1)1.000000-1.000000X(10,2)0.000000-1.000000X(10,3)0.000000-1.000000X(10,4)0.0000001.000000X(11,1)1.000000-1.000000X(11,2)0.000000-1.000000X(11,3)0.0000001.000000X(11,4)0.0000001.000000X(12,1)0.0000000.000000X(12,2)0.0000000.000000X(12,3)0.0000001.000000X(12,4)0.0000001.000000X(13,1)1.000000-1.000000X(13,2)1.000000-1.000000X(13,3)1.000000-1.000000X(13,4)1.000000-1.000000RowSlackorSurplusDualPrice115.000001.00000020.0000001.00000030.0000001.00000040.0000000.00000050.0000000.00000060.0000000.00000075.0000000.00000080.0000000.00000090.0000000.000000100.0000000.000000110.0000001.000000120.000000-1.000000130.0000000.000000141.0000000.000000150.0000000.000000160.0000000.000000170.0000000.000000180.0000000.000000192.0000000.000000207.0000000.000000211.0000000.000000225.0000000.000000230.0000000.000000240.0000000.000000250.0000002.000000題目bLocaloptimalsolutionfound.Objectivevalue:560.0000Objectivebound:560.0000Infeasibilities:0.6888934E-13Extendedsolversteps:0Totalsolveriterations:17VariableValueTOTAL_PRICE560.0000TOTAL_DISPLAY20.00000PRICE(1,1)30.00000PRICE(1,2)25.00000PRICE(1,3)12.50000PRICE(1,4)0.000000PRICE(2,1)40.00000PRICE(2,2)50.00000PRICE(2,3)40.00000PRICE(2,4)55.00000PRICE(3,1)70.00000PRICE(3,2)57.50000PRICE(3,3)0.000000PRICE(3,4)0.000000PRICE(4,1)20.00000PRICE(4,2)22.50000PRICE(4,3)0.000000PRICE(4,4)0.000000PRICE(5,1)15.00000PRICE(5,2)15.00000PRICE(5,3)0.000000PRICE(5,4)0.000000PRICE(6,1)85.00000PRICE(6,2)75.00000PRICE(6,3)0.000000PRICE(6,4)0.000000PRICE(7,1)40.00000PRICE(7,2)17.50000PRICE(7,3)45.00000PRICE(7,4)0.000000PRICE(8,1)50.00000PRICE(8,2)50.00000PRICE(8,3)50.00000PRICE(8,4)0.000000PRICE(9,1)65.00000PRICE(9,2)65.00000PRICE(9,3)0.000000PRICE(9,4)0.000000PRICE(10,1)25.00000PRICE(10,2)35.00000PRICE(10,3)45.00000PRICE(10,4)0.000000PRICE(11,1)40.00000PRICE(11,2)40.00000PRICE(11,3)0.000000PRICE(11,4)0.000000PRICE(12,1)30.00000PRICE(12,2)30.00000PRICE(12,3)0.000000PRICE(12,4)0.000000PRICE(13,1)5.000000PRICE(13,2)5.000000PRICE(13,3)5.000000PRICE(13,4)5.000000X(1,1)0.000000X(1,2)1.000000X(1,3)1.000000X(1,4)0.000000X(2,1)1.000000X(2,2)1.000000X(2,3)1.000000X(2,4)0.000000X(3,1)0.000000X(3,2)1.000000X(3,3)0.000000X(3,4)0.000000X(4,1)1.000000X(4,2)1.000000X(4,3)0.000000X(4,4)0.000000X(5,1)1.000000X(5,2)1.000000X(5,3)0.000000X(5,4)0.000000X(6,1)0.000000X(6,2)1.000000X(6,3)0.000000X(6,4)0.000000X(7,1)0.000000X(7,2)1.000000X(7,3)0.000000X(7,4)0.000000X(8,1)0.000000X(8,2)0.000000X(8,3)1.000000X(8,4)0.000000X(9,1)0.000000X(9,2)0.000000X(9,3)0.000000X(9,4)0.000000X(10,1)1.000000X(10,2)1.000000X(10,3)0.000000X(10,4)0.000000X(11,1)1.000000X(11,2)0.000000X(11,3)0.000000X(11,4)0.000000X(12,1)0.000000X(12,2)0.000000X(12,3)0.000000X(12,4)0.000000X(13,1)1.000000X(13,2)1.000000X(13,3)1.000000X(13,4)1.000000RowSlackorSurplus1560.000020.00000030.00000040.00000050.00000060.00000075.00000081.00000097.000000100.000000110.000000120.000000130.000000141.000000151.000000160.000000171.000000