菜籃子工程模板

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某市的菜籃子工程某市是一個人口不到15萬的小城市,根據(jù)該市的蔬菜種植情況,分別在A、B、C三地設(shè)三個收購點,再由收購點分別送到全市8個蔬菜市場。按照常年情況,A、B、C三個收購點每天收購量分別為200、170和160(單位:100kg),各個菜市場每天需求量及發(fā)生供應(yīng)短缺時的損失見表1。從收購點到個菜市場的距離見表2,設(shè)從收購點到各菜市場蔬菜調(diào)運費用為1元/(100kg·100m)。表1各菜市場每天需求量及短缺損失菜市場每天需求量(100kg)短缺損失(元/100kg)175102608380547010510010655879058808表2收購點到各菜市場的距離距離(單位:100m)菜市場12345678收購點A488191162216B14771612162317C20191114615510為該市設(shè)計一個從收購點到菜市場的定點供應(yīng)方案,使蔬菜調(diào)運費用與預(yù)期的短缺損失之和最小。若規(guī)定各菜市場短缺量一律不超過需求量的20%,重新設(shè)計定點供應(yīng)方案。為了滿足城市居民的蔬菜供應(yīng),該市的領(lǐng)導(dǎo)規(guī)劃增加蔬菜種植面積,試問增產(chǎn)的蔬菜每天應(yīng)分別向A、B、C三個收購點各供應(yīng)多少最為經(jīng)濟合理。參考答案:調(diào)運總費用3890,短缺總損失720,總費用為4610(方案略).調(diào)運總費用4208,短缺總費用598,總費用為4806(方案略)。增產(chǎn)蔬菜80,每天都向C這個收購點供應(yīng)最經(jīng)濟。基本假設(shè)設(shè)xij為第i個集散點向第j個菜市場供應(yīng)蔬菜的數(shù)量,lij為第i個集散點到第j個菜市場供應(yīng)蔬菜的距離,bj為第j個市場每天的需求量,dj為第j個市場每天的短缺損失,ai為第i個集散點每天的收購量,cij為第i個集散點向第j個菜市場的單位運費(i=123,j=1..8)約束條件、=(i=1,2,3)<=(j=1..8)>=0(i=1,2,3;j=1..8)(3)對各問求解分析第一問目標(biāo)函數(shù)minz= **+(-)(i=1,2,3;j=1..8)程序:Model:Sets:Jsd/1..3/:a;Csc/1..8/:b;dqss/1..8/:d;J_c(jsd,csc):x,c,l;EndsetsData:a=200,170,160;b=75,60,80,70,100,55,90,80;d=10,8,5,10,10,8,5,8;l=4,8,8,19,11,6,22,16,14,7,7,16,12,16,23,17,20,19,11,14,6,15,5,10;c=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;Enddata@for(jsd(i):[st1]@sum(csc(j):x(i,j))=a(i));@for(csc(j):[st2]@sum(jsd(i):x(i,j))<=b(j));[obj]min=@sum(jsd(i):@sum(csc(j):c(i,j)*x(i,j)*l(i,j)))+@sum(csc(j):d(j)*(b(j)-@sum(jsd(i):x(i,j))));End運行結(jié)果:Globaloptimalsolutionfound.Objectivevalue:4610.000Infeasibilities:0.000000Totalsolveriterations:9ModelClass:LPTotalvariables:24Nonlinearvariables:0Integervariables:0Totalconstraints:12Nonlinearconstraints:0Totalnonzeros:70Nonlinearnonzeros:0VariableValueReducedCostA(1)200.00000.000000A(2)170.00000.000000A(3)160.00000.000000B(1)75.000000.000000B(2)60.000000.000000B(3)80.000000.000000B(4)70.000000.000000B(5)100.00000.000000B(6)55.000000.000000B(7)90.000000.000000B(8)80.000000.000000D(1)10.000000.000000D(2)8.0000000.000000D(3)5.0000000.000000D(4)10.000000.000000D(5)10.000000.000000D(6)8.0000000.000000D(7)5.0000000.000000D(8)8.0000000.000000X(1,1)75.000000.000000X(1,2)0.0000000.000000X(1,3)40.000000.000000X(1,4)0.0000002.000000X(1,5)30.000000.000000X(1,6)55.000000.000000X(1,7)0.00000012.00000X(1,8)0.0000001.000000X(2,1)0.00000011.00000X(2,2)60.000000.000000X(2,3)40.000000.000000X(2,4)70.000000.000000X(2,5)0.0000002.000000X(2,6)0.00000011.00000X(2,7)0.00000014.00000X(2,8)0.0000003.000000X(3,1)0.00000021.00000X(3,2)0.00000016.00000X(3,3)0.0000008.000000X(3,4)0.0000002.000000X(3,5)70.000000.000000X(3,6)0.00000014.00000X(3,7)90.000000.000000X(3,8)0.0000000.000000C(1,1)1.0000000.000000C(1,2)1.0000000.000000C(1,3)1.0000000.000000C(1,4)1.0000000.000000C(1,5)1.0000000.000000C(1,6)1.0000000.000000C(1,7)1.0000000.000000C(1,8)1.0000000.000000C(2,1)1.0000000.000000C(2,2)1.0000000.000000C(2,3)1.0000000.000000C(2,4)1.0000000.000000C(2,5)1.0000000.000000C(2,6)1.0000000.000000C(2,7)1.0000000.000000C(2,8)1.0000000.000000C(3,1)1.0000000.000000C(3,2)1.0000000.000000C(3,3)1.0000000.000000C(3,4)1.0000000.000000C(3,5)1.0000000.000000C(3,6)1.0000000.000000C(3,7)1.0000000.000000C(3,8)1.0000000.000000L(1,1)4.0000000.000000L(1,2)8.0000000.000000L(1,3)8.0000000.000000L(1,4)19.000000.000000L(1,5)11.000000.000000L(1,6)6.0000000.000000L(1,7)22.000000.000000L(1,8)16.000000.000000L(2,1)14.000000.000000L(2,2)7.0000000.000000L(2,3)7.0000000.000000L(2,4)16.000000.000000L(2,5)12.000000.000000L(2,6)16.000000.000000L(2,7)23.000000.000000L(2,8)17.000000.000000L(3,1)20.000000.000000L(3,2)19.000000.000000L(3,3)11.000000.000000L(3,4)14.000000.000000L(3,5)6.0000000.000000L(3,6)15.000000.000000L(3,7)5.0000000.000000L(3,8)10.000000.000000RowSlackorSurplusDualPriceST1(1)0.000000-7.000000ST1(2)0.000000-6.000000ST1(3)0.000000-2.000000ST2(1)0.00000013.00000ST2(2)0.0000007.000000ST2(3)0.0000004.000000ST2(4)0.0000000.000000ST2(5)0.0000006.000000ST2(6)0.0000009.000000ST2(7)0.0000002.000000ST2(8)80.000000.000000OBJ4610.000-1.000000結(jié)果分析最優(yōu)運輸方案為A運往菜市場1蔬菜數(shù)量為75公斤,運往菜市場3蔬菜數(shù)量為40公斤,運往菜市場5蔬菜數(shù)量為30公斤,運往菜市場6蔬菜數(shù)量為55公斤;B運往菜市場2蔬菜數(shù)量為60公斤,運往菜市場3蔬菜數(shù)量為40公斤,運往菜市場4蔬菜數(shù)量為70公斤;C運往菜市場5蔬菜數(shù)量為7第二問目標(biāo)函數(shù)minz= **+(-)(i=1,2,3;j=1..8)新增一個約束條件:=(j=1..8)程序Model:Sets:Jsd/1..3/:a;Csc/1..8/:b;dqss/1..8/:d;J_c(jsd,csc):x,c,l;EndsetsData:a=200,170,160;b=75,60,80,70,100,55,90,80;d=10,8,5,10,10,8,5,8;l=4,8,8,19,11,6,22,16,14,7,7,16,12,16,23,17,20,19,11,14,6,15,5,10;c=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;Enddata@for(jsd(i):[st1]@sum(csc(j):x(i,j))=a(i));@for(csc(j):[st2]@sum(jsd(i):x(i,j))<=b(j));@for(csc(j):[st3]@sum(jsd(i):x(i,j))>=0.8*b(j));[obj]min=@sum(jsd(i):@sum(csc(j):c(i,j)*x(i,j)*l(i,j)))+@sum(csc(j):d(j)*(b(j)-@sum(jsd(i):x(i,j))));End運行結(jié)果:Globaloptimalsolutionfound.Objectivevalue:4806.000Infeasibilities:0.000000Totalsolveriterations:11ModelClass:LPTotalvariables:24Nonlinearvariables:0Integervariables:0Totalconstraints:20Nonlinearconstraints:0Totalnonzeros:94Nonlinearnonzeros:0VariableValueReducedCostA(1)200.00000.000000A(2)170.00000.000000A(3)160.00000.000000B(1)75.000000.000000B(2)60.000000.000000B(3)80.000000.000000B(4)70.000000.000000B(5)100.00000.000000B(6)55.000000.000000B(7)90.000000.000000B(8)80.000000.000000D(1)10.000000.000000D(2)8.0000000.000000D(3)5.0000000.000000D(4)10.000000.000000D(5)10.000000.000000D(6)8.0000000.000000D(7)5.0000000.000000D(8)8.0000000.000000X(1,1)75.000000.000000X(1,2)0.0000000.000000X(1,3)10.000000.000000X(1,4)0.0000002.000000X(1,5)60.000000.000000X(1,6)55.000000.000000X(1,7)0.00000012.00000X(1,8)0.0000001.000000X(2,1)0.00000011.00000X(2,2)60.000000.000000X(2,3)54.000000.000000X(2,4)56.000000.000000X(2,5)0.0000002.000000X(2,6)0.00000011.00000X(2,7)0.00000014.00000X(2,8)0.0000003.000000X(3,1)0.00000021.00000X(3,2)0.00000016.00000X(3,3)0.0000008.000000X(3,4)0.0000002.000000X(3,5)24.000000.000000X(3,6)0.00000014.00000X(3,7)72.000000.000000X(3,8)64.000000.000000C(1,1)1.0000000.000000C(1,2)1.0000000.000000C(1,3)1.0000000.000000C(1,4)1.0000000.000000C(1,5)1.0000000.000000C(1,6)1.0000000.000000C(1,7)1.0000000.000000C(1,8)1.0000000.000000C(2,1)1.0000000.000000C(2,2)1.0000000.000000C(2,3)1.0000000.000000C(2,4)1.0000000.000000C(2,5)1.0000000.000000C(2,6)1.0000000.000000C(2,7)1.0000000.000000C(2,8)1.0000000.000000C(3,1)1.0000000.000000C(3,2)1.0000000.000000C(3,3)1.0000000.000000C(3,4)1.0000000.000000C(3,5)1.0000000.000000C(3,6)1.0000000.000000C(3,7)1.0000000.000000C(3,8)1.0000000.000000L(1,1)4.0000000.000000L(1,2)8.0000000.000000L(1,3)8.0000000.000000L(1,4)19.000000.000000L(1,5)11.000000.000000L(1,6)6.0000000.000000L(1,7)22.000000.000000L(1,8)16.000000.000000L(2,1)14.000000.000000L(2,2)7.0000000.000000L(2,3)7.0000000.000000L(2,4)16.000000.000000L(2,5)12.000000.000000L(2,6)16.000000.000000L(2,7)23.000000.000000L(2,8)17.000000.000000L(3,1)20.000000.000000L(3,2)19.000000.000000L(3,3)11.000000.000000L(3,4)14.000000.000000L(3,5)6.0000000.000000L(3,6)15.000000.000000L(3,7)5.0000000.000000L(3,8)10.000000.000000RowSlackorSurplusDualPriceST1(1)0.000000-1.000000ST1(2)0.0000000.000000ST1(3)0.0000004.000000ST2(1)0.0000007.000000ST2(2)0.0000001.000000ST2(3)16.000000.000000ST2(4)14.000000.000000ST2(5)16.000000.000000ST2(6)0.0000003.000000ST2(7)18.000000.000000ST2(8)16.000000.000000ST3(1)15.000000.000000ST3(2)12.000000.000000ST3(3)0.000000-2.000000ST3(4)0.000000-6.000000ST3(5)4.0000000.000000ST3(6)11.000000.000000ST3(7)0.000000-4.000000ST3(8)0.000000-6.000000OBJ4806.000-1.000000結(jié)果:最優(yōu)運輸方案為A運往菜市場1蔬菜數(shù)量為75公斤,運往菜市場3蔬菜數(shù)量為10公斤,運往菜市場5蔬菜數(shù)量為60公斤,運往菜市場6蔬菜數(shù)量為55公斤;B運往菜市場2蔬菜數(shù)量為60公斤,運往菜市場3蔬菜數(shù)量為54公斤,運往菜市場4蔬菜數(shù)量為56公斤;C運往菜市場5蔬菜數(shù)量為24公斤,運往菜市場7蔬菜數(shù)量為72公斤,運往菜市場8蔬菜數(shù)量為第三問因為根據(jù)題意,各菜市場的需求量大于各收購點的收購量,因此要增大收購量來滿足短缺的需求。與第一問比較分析,應(yīng)使收購量大于當(dāng)前的量,使需求量得到滿足,不再產(chǎn)生短缺損失,因此重新建立模型為:Minz=**(i=1,2,3;j=1..8)>=(i=1,2,3)=(i=1,2,3)>=0(i=1,2,3;j=1..8)程序:Model:Sets:Jsd/1..3/:a;Csc/1..8/:b;J_c(jsd,csc):x,c,l;EndsetsData:a=200,170,160;b=75,60,80,70,100,55,90,80;l=4,8,8,19,11,6,22,16,14,7,7,16,12,16,23,17,20,19,11,14,6,15,5,10;c=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;Enddata@for(jsd(i):[st1]@sum(csc(j):x(i,j))>=a(i));@for(csc(j):[st2]@sum(jsd(i):x(i,j))=b(j));[obj]min=@sum(jsd(i):@sum(csc(j):c(i,j)*x(i,j)*l(i,j)));End運行結(jié)果為:Globaloptimalsolutionfound.Objectivevalue:4770.000Infeasibilities:0.000000Totalsolveriterations:12ModelClass:LPTotalvariables:24Nonlinearvariables:0Integervariables:0Totalconstraints:12Nonlinearconstraints:0Totalnonzeros:72Nonlinearnonzeros:0VariableValueReducedCostA(1)200.00000.000000A(2)170.00000.000000A(3)160.00000.000000B(1)75.000000.000000B(2)60.000000.000000B(3)80.000000.000000B(4)70.000000.000000B(5)100.00000.000000B(6)55.000000.000000B(7)90.000000.000000B(8)80.000000.000000X(1,1)75.000000.000000X(1,2)40.000000.000000X(1,3)0.0000000.000000X(1,4)0.0000002.000000X(1,5)30.000000.000000X(1,6)55.000000.000000X(1,7)0.00000012.00000X(1,8)0.0000001.000000X(2,1)0.00000011.00000X(2,2)20.000000.000000X(2,3)80.000000.000000X(2,4)70.000000.000000X(2,5)0.0000002.000000X(2,6)0.00000011.00000X(2,7)0.00000014.00000X(2,8)0.0000003.000000X(3,1)0.00000021.00000X(3,2)0.00000016.00000X(3,3)0.0000008.000000X(3,4)0.0000002.000000X(3,5)70.000000.000000X(3,6)0.00000014.00000X(3,7)90.000000.000000X(3,8)80.000000.000000C(1,1)1.0000000.000000C(1,2)1.0000000.000000C(1,3)1.0000000.000000C(1,4)1.0000000.000000C(1,5)1.0000000.000000C(1,6)1.0000000.000000C(1,7)1.0000000.000000C(1,8)1.0000000.000000C(2,1)1.0000000.000000C(2,2)1.0000000.000000C(2,3)1.0000000.000000C(2,4)1.0000000.000000C(2,5)1.0000000.000000C(2,6)1.0000000.000000C(2,7)1.0000000.000000C(2,8)1.0000000.000000C(3,1)1.0000000.000000C(3,2)1.0000000.000000C(3,3)1.0000000.000000C(3,4)1.0000000.000000C(3,5)1.0000000.000000C(3,6)1.0000000.000000C(3,7)1.0000000.000000C(3,8)1.0000000.000000L(1,1)4.0000000.000000L(1,2)8.0000000.000000L(1,3)