中國(guó)石油大學(xué)-建模作業(yè)

數(shù)學(xué)規(guī)劃上機(jī)實(shí)踐作業(yè)一1首先練習(xí)一下書中線性規(guī)劃案例。2某企業(yè)和用戶簽定了設(shè)備交貨合同，已知該企業(yè)各季度的生產(chǎn)能力、每臺(tái)設(shè)備的生產(chǎn)成本和每季度末的交貨量見下表，若生產(chǎn)出的設(shè)備當(dāng)季度不交貨，每臺(tái)設(shè)備每季度需要支付保管費(fèi)0.1萬(wàn)元，試問(wèn)在遵守合同的條件下，企業(yè)應(yīng)如何安排生產(chǎn)計(jì)劃，才能使年消耗費(fèi)用最低？季度工廠生產(chǎn)能力（臺(tái)）交貨量（臺(tái)）每臺(tái)設(shè)備生產(chǎn)成本（萬(wàn)元/臺(tái)）1251512.02352011.03302511.54202012.5變量定義：設(shè)第季度生產(chǎn)臺(tái)，；模型假設(shè)：，①每個(gè)季度都交貨交滿②第四季度交貨后無(wú)設(shè)備剩余；目標(biāo)函數(shù)：約束條件：，，，，。Lingo程序：model:min=12*x1+(x1-15)*0.1+11*x2+(x2+x1-15-20)*0.1+x3*11.5+(x3+x2+x1-15-20-25)*0.1+x4*12.5;x2+x1>=35;x3+x2+x1>=60;x4+x3+x2+x1=80;x1>=15;x2<=35;x3<=30;x4<=20;@gin(x1);@gin(x2);@gin(x3);@gin(x4);End程序運(yùn)行結(jié)果：Globaloptimalsolutionfound.Objectivevalue:913.5000Objectivebound:913.5000Infeasibilities:0.000000Extendedsolversteps:0Totalsolveriterations:0VariableValueReducedCostX115.0000012.30000X235.0000011.20000X330.0000011.60000X40.00000012.50000RowSlackorSurplusDualPrice1913.5000-1.00000020.0000000.000000315.000000.000000420.000000.00000050.0000000.00000060.0000000.00000070.0000000.000000820.000000.000000建模結(jié)果：第一季度生產(chǎn)15臺(tái)，第二季度生產(chǎn)35臺(tái)，第三季度生產(chǎn)30臺(tái)，第四季度生產(chǎn)0臺(tái)，最小值913.5萬(wàn)元。3．五名選手的百米成績(jī)?nèi)缟纤?；如何選拔隊(duì)員組成4′100米混合泳接力隊(duì)?討論:丁的蛙泳成績(jī)退步到1’15”2；戊的自由泳成績(jī)進(jìn)步到57”5,組成接力隊(duì)的方案是否應(yīng)該調(diào)整？變量定義：設(shè)表示第個(gè)人參加第個(gè)項(xiàng)目，表示第個(gè)人沒(méi)有參加第個(gè)項(xiàng)目，為第個(gè)人的第個(gè)項(xiàng)目的成績(jī)（）。目標(biāo)函數(shù)：。約束條件：每個(gè)人最多參加一個(gè)項(xiàng)目，所以，每個(gè)項(xiàng)目必須有且最多有一個(gè)人選擇，所以，同時(shí)有。Lingo程序Model:sets:person/1..5/;position/1..4/;link(person,position):x,a;endsetsdata:a=66.8,75.6,87,58.6,57.2,66,66.4,53,78,67.8,84.6,59.4,70,74.2,69.6,57.2,67.4,71,83.8,62.4;enddatamin=@sum(link:x*a);@for(person(i):@sum(position(j):x(i,j))<=1;);@for(position(j):@sum(person(i):x(i,j))=1;);@for(link:@bin(x));end程序運(yùn)行結(jié)果Globaloptimalsolutionfound.Objectivevalue:253.2000Objectivebound:253.2000Infeasibilities:0.000000Extendedsolversteps:0Totalsolveriterations:0VariableValueReducedCostX(1,1)0.00000066.80000X(1,2)0.00000075.60000X(1,3)0.00000087.00000X(1,4)1.00000058.60000X(2,1)1.00000057.20000X(2,2)0.00000066.00000X(2,3)0.00000066.40000X(2,4)0.00000053.00000X(3,1)0.00000078.00000X(3,2)1.00000067.80000X(3,3)0.00000084.60000X(3,4)0.00000059.40000X(4,1)0.00000070.00000X(4,2)0.00000074.20000X(4,3)1.00000069.60000X(4,4)0.00000057.20000X(5,1)0.00000067.40000X(5,2)0.00000071.00000X(5,3)0.00000083.80000X(5,4)0.00000062.40000A(1,1)66.800000.000000A(1,2)75.600000.000000A(1,3)87.000000.000000A(1,4)58.600000.000000A(2,1)57.200000.000000A(2,2)66.000000.000000A(2,3)66.400000.000000A(2,4)53.000000.000000A(3,1)78.000000.000000A(3,2)67.800000.000000A(3,3)84.600000.000000A(3,4)59.400000.000000A(4,1)70.000000.000000A(4,2)74.200000.000000A(4,3)69.600000.000000A(4,4)57.200000.000000A(5,1)67.400000.000000A(5,2)71.000000.000000A(5,3)83.800000.000000A(5,4)62.400000.000000RowSlackorSurplusDualPrice1253.2000-1.00000020.0000000.00000030.0000000.00000040.0000000.00000050.0000000.00000061.0000000.00000070.0000000.00000080.0000000.00000090.0000000.000000100.0000000.000000模型結(jié)論甲乙丙丁4人組隊(duì)分別參加自由泳、蝶泳、仰泳、蛙泳的比賽，成績(jī)?yōu)?53.2s=4’13”2。模型分析當(dāng)隊(duì)員丁的蛙泳成績(jī)有較大退步，只有1’15”2；而戊的自由泳成績(jī)進(jìn)步到57”5，對(duì)lingo程序進(jìn)行修改，重新建模。程序以及運(yùn)行結(jié)果為Model:sets:person/1..5/;position/1..4/;link(person,position):x,a;endsetsdata:a=66.8,75.6,87,58.6,57.2,66,66.4,53,78,67.8,84.6,59.4,70,74.2,75.2,57.2,67.4,71,83.8,57.5;enddatamin=@sum(link:x*a);@for(person(i):@sum(position(j):x(i,j))<=1;);@for(position(j):@sum(person(i):x(i,j))=1;);@for(link:@bin(x));endGlobaloptimalsolutionfound.Objectivevalue:257.7000Objectivebound:257.7000Infeasibilities:0.000000Extendedsolversteps:0Totalsolveriterations:0VariableValueReducedCostX(1,1)0.00000066.80000X(1,2)0.00000075.60000X(1,3)0.00000087.00000X(1,4)0.00000058.60000X(2,1)1.00000057.20000X(2,2)0.00000066.00000X(2,3)0.00000066.40000X(2,4)0.00000053.00000X(3,1)0.00000078.00000X(3,2)1.00000067.80000X(3,3)0.00000084.60000X(3,4)0.00000059.40000X(4,1)0.00000070.00000X(4,2)0.00000074.20000X(4,3)1.00000075.20000X(4,4)0.00000057.20000X(5,1)0.00000067.40000X(5,2)0.00000071.00000X(5,3)0.00000083.80000X(5,4)1.00000057.50000A(1,1)66.800000.000000A(1,2)75.600000.000000A(1,3)87.000000.000000A(1,4)58.600000.000000A(2,1)57.200000.000000A(2,2)66.000000.000000A(2,3)66.400000.000000A(2,4)53.000000.000000A(3,1)78.000000.000000A(3,2)67.800000.000000A(3,3)84.600000.000000A(3,4)59.400000.000000A(4,1)70.000000.000000A(4,2)74.200000.000000A(4,3)75.200000.000000A(4,4)57.200000.000000A(5,1)67.400000.000000A(5,2)71.000000.000000A(5,3)83.800000.000000A(5,4)57.500000.000000RowSlackorSurplusDualPrice1257.7000-1.00000021.0000000.00000030.0000000.00000040.0000000.00000050.0000000.00000060.0000000.00000070.0000000.00000080.0000000.00000090.0000000.000000100.0000000.000000模型結(jié)果:乙丙丁戊分別參加蝶泳、仰泳、蛙泳、自由泳的比賽，比賽成績(jī)?yōu)?57.7s=4’17”7。4.某卡車公司撥款8000000元用于購(gòu)買新的運(yùn)輸工具，可供選擇的運(yùn)輸工具有三種。運(yùn)輸工具A載重量為10t，平均時(shí)速為45km/h，價(jià)格為260000元；運(yùn)輸工具B載重為20t，平均時(shí)速為40km/h，價(jià)格為360000元；運(yùn)輸工具C是B的改進(jìn)，增加了可代一個(gè)司機(jī)使用的臥鋪，這一改變使載重量變?yōu)?8t，平均運(yùn)行速度仍然是40km/h，但價(jià)格為420000元。運(yùn)輸工具A需要一名司機(jī)，如果每天三班工作，每天平均可以運(yùn)行18h，當(dāng)?shù)胤梢?guī)定運(yùn)輸工具B和C需要兩名司機(jī)，每天三班工作時(shí)B平均可以運(yùn)行18h，而C可以運(yùn)行21h，該公司目前每天有150名司機(jī)可供使用，而且在短期內(nèi)無(wú)法招募到其他訓(xùn)練有素的司機(jī)。當(dāng)?shù)氐墓?huì)禁止任何一名司機(jī)每天工作超過(guò)一個(gè)班次。此外，維修設(shè)備有限，所以購(gòu)買的運(yùn)輸工具的數(shù)量不能超過(guò)30輛。建立數(shù)學(xué)模型，幫助公司確定購(gòu)買每種運(yùn)輸工具的數(shù)量，使工廠每天的總運(yùn)力（t.km）