線性規(guī)劃的靈敏度分析實驗報告

-.z."運籌學(xué)/線性規(guī)劃"實驗報告實驗室：實驗日期：實驗工程線性規(guī)劃的靈敏度分析系別數(shù)學(xué)系姓名學(xué)號班級指導(dǎo)教師成績一實驗?zāi)康恼莆沼肔ingo/Lindo對線性規(guī)劃問題進(jìn)展靈敏度分析的方法，理解解報告的內(nèi)容。初步掌握對實際的線性規(guī)劃問題建立數(shù)學(xué)模型，并利用計算機(jī)求解分析的一般方法。二實驗環(huán)境Lingo軟件三實驗內(nèi)容〔包括數(shù)學(xué)模型、上機(jī)程序、實驗結(jié)果、結(jié)果分析與問題解答等〕例題2-10MODEL:[_1]MA*=2**_1+3**_2;[_2]*_1+2**_2+*_3=8;[_3]4**_1+*_4=16;[_4]4**_2+*_5=12;END編程sets:is/1..3/:b;js/1..5/:c,*;links(is,js):a;endsetsma*=sum(js(J):c(J)**(J));for(is(I):sum(js(J):a(I,J)**(J))=b(I));data:c=23000;b=81612;a=121004001004001;enddataend靈敏度分析Rangesinwhichthebasisisunchanged:ObjectiveCoefficientRangesCurrentAllowableAllowableVariableCoefficientIncreaseDecrease*(1)2.000000INFINITY0.5000000*(2)3.0000001.0000003.000000*(3)0.01.500000INFINITY*(4)0.00.1250000INFINITY*(5)0.00.75000000.2500000RighthandSideRangesRowCurrentAllowableAllowableRHSIncreaseDecrease28.0000002.0000004.000000316.0000016.000008.000000412.00000INFINITY4.000000當(dāng)b2在 [8,32]之間變化時最優(yōu)基不變最優(yōu)解Globaloptimalsolutionfoundatiteration:0Objectivevalue:14.00000VariableValueReducedCostB(1)8.0000000.000000B(2)16.000000.000000B(3)12.000000.000000C(1)2.0000000.000000C(2)3.0000000.000000C(3)0.0000000.000000C(4)0.0000000.000000C(5)0.0000000.000000*(1)4.0000000.000000*(2)2.0000000.000000*(3)0.0000001.500000*(4)0.0000000.1250000*(5)4.0000000.000000A(1,1)1.0000000.000000A(1,2)2.0000000.000000A(1,3)1.0000000.000000A(1,4)0.0000000.000000A(1,5)0.0000000.000000A(2,1)4.0000000.000000A(2,2)0.0000000.000000A(2,3)0.0000000.000000A(2,4)1.0000000.000000A(2,5)0.0000000.000000A(3,1)0.0000000.000000A(3,2)4.0000000.000000A(3,3)0.0000000.000000A(3,4)0.0000000.000000A(3,5)1.0000000.000000RowSlackorSurplusDualPrice114.000001.00000020.0000001.50000030.0000000.125000040.0000000.000000例題2-11模型MA*2*(1)+3*(2)SUBJECTTO2]*(1)+2*(2)+*(3)=123]4*(1)+*(4)=164]4*(2)+*(5)=12END編程sets:is/1..3/:b;js/1..5/:c,*;links(is,js):a;endsetsma*=sum(js(J):c(J)**(J));for(is(I):sum(js(J):a(I,J)**(J))=b(I));data:c=23000;b=121612;a=121004001004001;enddataend最優(yōu)解Globaloptimalsolutionfoundatiteration:2Objectivevalue:17.00000VariableValueReducedCostB(1)12.000000.000000B(2)16.000000.000000B(3)12.000000.000000C(1)2.0000000.000000C(2)3.0000000.000000C(3)0.0000000.000000C(4)0.0000000.000000C(5)0.0000000.000000*(1)4.0000000.000000*(2)3.0000000.000000*(3)2.0000000.000000*(4)0.0000000.5000000*(5)0.0000000.7500000A(1,1)1.0000000.000000A(1,2)2.0000000.000000A(1,3)1.0000000.000000A(1,4)0.0000000.000000A(1,5)0.0000000.000000A(2,1)4.0000000.000000A(2,2)0.0000000.000000A(2,3)0.0000000.000000A(2,4)1.0000000.000000A(2,5)0.0000000.000000A(3,1)0.0000000.000000A(3,2)4.0000000.000000A(3,3)0.0000000.000000A(3,4)0.0000000.000000A(3,5)1.0000000.000000RowSlackorSurplusDualPrice117.000001.00000020.0000000.00000030.0000000.500000040.0000000.7500000最優(yōu)解〔4,3,2,0,0〕最優(yōu)值z=17分析Rangesinwhichthebasisisunchanged:ObjectiveCoefficientRangesCurrentAllowableAllowableVariableCoefficientIncreaseDecrease*(1)2.000000INFINITY2.000000*(2)3.000000INFINITY3.000000*(3)0.01.500000INFINITY*(4)0.00.5000000INFINITY*(5)0.00.7500000INFINITYRighthandSideRangesRowCurrentAllowableAllowableRHSIncreaseDecrease212.00000INFINITY2.000000316.000008.00000016.00000412.000004.00000012.00000例題2-12模型MA*2*(1)+3*(2)SUBJECTTO2]*(1)+2*(2)+*(3)=83]4*(1)+*(4)=164]4*(2)+*(5)=12END編程sets:is/1..3/:b;js/1..5/:c,*;links(is,js):a;endsetsma*=sum(js(J):c(J)**(J));for(is(I):sum(js(J):a(I,J)**(J))=b(I));data:c=23000;b=81612;a=121004001004001;enddataend靈敏度分析Rangesinwhichthebasisisunchanged:ObjectiveCoefficientRangesCurrentAllowableAllowableVariableCoefficientIncreaseDecrease*(1)2.000000INFINITY0.5000000*(2)3.0000001.0000003.000000*(3)0.01.500000INFINITY*(4)0.00.1250000INFINITY*(5)0.00.75000000.2500000RighthandSideRangesRowCurrentAllowableAllowableRHSIncreaseDecrease28.0000002.0000004.000000316.0000016.000008.000000412.00000INFINITY4.000000由靈敏度分析表知道C2在【0,4】之間變化時，最優(yōu)基不變。第六題模型MODEL:[_1]MA*=3**_1+*_2+4**_3;[_2]6**_1+3**_2+5**_3<=450;[_3]3**_1+4**_2+5**_3<=300;END編程sets:is/1..2/:b;js/1..3/:c,*;links(is,js):a;endsetsma*=sum(js(J):c(J)**(J));for(is(I):sum(js(J):a(I,J)**(J))<=b(I));data:c=314;b=450300;a=635345;enddataEnd最優(yōu)解Globaloptimalsolutionfound.Objectivevalue:270.0000Infeasibilities:0.000000Totalsolveriterations:2VariableValueReducedCostB(1)450.00000.000000B(2)300.00000.000000C(1)3.0000000.000000C(2)1.0000000.000000C(3)4.0000000.000000*(1)50.000000.000000*(2)0.0000002.000000*(3)30.000000.000000A(1,1)6.0000000.000000A(1,2)3.0000000.000000A(1,3)5.0000000.000000A(2,1)3.0000000.000000A(2,2)4.0000000.000000A(2,3)5.0000000.000000RowSlackorSurplusDualPrice1270.00001.00000020.0000000.200000030.0000000.6000000第一問：A生產(chǎn)50B生產(chǎn)0C生產(chǎn)30有最高利潤270元；第二問：單個價值系數(shù)和右端系數(shù)變化范圍的靈敏度分析結(jié)果Rangesinwhichthebasisisunchanged:ObjectiveCoefficientRangesCurrentAllowableAllowableVariableCoefficientIncreaseDecrease*(1)3.0000001.8000000.6000000*(2)1.0000002.000000INFINITY*(3)4.0000001.0000001.500000RighthandSideRangesRowCurrentAllowableAllowableRHSIncreaseDecrease2450.0000150.0000150.00003300.0000150.000075.00000當(dāng)A的利潤在【2.4，4.8】之間變化時，原最優(yōu)生產(chǎn)方案不變。第三問：模型MODEL:[_1]MA*=3**_1+*_2+4**_3+3**_4;[_2]6**_1+3**_2+5**_3+8**_4<=450;[_3]3**_1+4**_2+5**_3+2**_4<=300;END編程sets:is/1..2/:b;js/1..4/:c,*;links(is,js):a;endsetsma*=sum(js(J):c(J)**(J));for(is(I):sum(js(J):a(I,J)**(J))<=b(I));data:c=3143;b=450300;a=63583452;enddataEnd最優(yōu)解Globaloptimalsolutionfound.Objectivevalue:275.0000Infeasibilities:0.000000Totalsolveriterations:2VariableValueReducedCostB(1)450.00000.000000B(2)300.00000.000000C(1)3.0000000.000000C(2)1.0000000.000000C(3)4.0000000.000000C(4)3.0000000.000000*(1)0.0000000.1000000*(2)0.0000001.966667*(3)50.000000.000000*(4)25.000000.000000A(1,1)6.0000000.000000A(1,2)3.0000000.000000A(1,3)5.0000000.000000A(1,4)8.0000000.000000A(2,1)3.0000000.000000A(2,2)4.0000000.000000A(2,3)5.0000000.000000A(2,4)2.0000000.000000RowSlackorSurplusDualPrice1275.00001.00000020.0000000.233333330.0000000.5666667利潤275元值得生產(chǎn)。第四問由單個價值系數(shù)和右端系數(shù)變化范圍的靈敏度分析結(jié)果Rangesinwhichthebasisisunchanged:ObjectiveCoefficientRangesCurrentAllowableAllowableVariableCoefficientIncreaseDecrease*(1)3.0000001.8000000.6000000*(2)1.0000002.000000INFINITY*(3)4.0000001.0000001.500000RighthandSideRangesRowCurrentAllowableAllowableRHSIncreaseDecrease2450.0000150.0000150.00003300.0000150.000075.00000當(dāng)購置150噸時此時可買360元在減去購置150噸的進(jìn)價60元此時可獲利300超過了原方案，應(yīng)該購置。第七題模型MODEL:[_1]MA*=30**_1+20**_2+50**_3;[_2]*_1+2**_2+*_3<=430;[_3]3**_1+2**_3<=410;[_4]*_1+4**_2<=420;[_5]*_1+*_2+*_3<=300;[_6]*_2>=70;[_7]*_3<=240;END編程sets:is/1..6/:b;js/1..3/:c,*;links(is,js):a;endsetsma*=sum(js(J):c(J)**(J));sum(js(J):a(1,J)**(J))<=b(1);sum(js(J):a(2,J)**(J))<=b(2);sum(js(J):a(3,J)**(J))<=b(3);sum(js(J):a(4,J)**(J))<=b(4);sum(js(J):a(5,J)**(J))>=B(5);sum(js(J):a(6,J)**(J))<=b(6);data:c=302050;b=43041042030070240;a=121302140111010001;enddataend最優(yōu)解Globaloptimalsolutionfound.Objectivevalue:12150.00Infeasibilities:0.000000Totalsolveriterations:4VariableValueReducedCostB(1)430.00000.000000B(2)410.00000.000000B(3)420.00000.000000B(4)300.00000.000000B(5)70.000000.000000B(6)240.00000.000000C(1)30.000000.000000C(2)20.000000.000000C(3)50.000000.000000*(1)0.00000035.00000*(2)95.000000.000000*(3)205.00000.000000A(1,1)1.0000000.000000A(1,2)2.0000000.000000A(1,3)1.0000000.000000A(2,1)3.0000000.000000A(2,2)0.0000000.000000A(2,3)2.0000000.000000A(3,1)1.0000000.000000A(3,2)4.0000000.000000A(3,3)0.0000000.000000A(4,1)1.0000000.000000A(4,2)1.0000000.000000A(4,3)1.0000000.000000A(5,1)0.0000000.000000A(5,2)1.0000000.000000A(5,3)0.0000000.000000A(6,1)0.0000000.000000A(6,2)0.0000000.000000A(6,3)1.0000000.000000RowSlackorSurplusDualPrice112150.001.000000235.000000.00000030.00000015.00000440.000000.00000050.00000020.00000625.000000.000000735.000000.000000最優(yōu)解〔095205〕最優(yōu)值12150第一問模型MODEL:[_1]MA*=30**_1+20**_2+60**_3;[_2]*_1+2**_2+*_3<=430;[_3]3**_1+2**_3<=410;[_4]*_1+4**_2<=420;[_5]*_1+*_2+*_3<=300;[_6]*_2>=70;[_7]*_3<=190;END編程sets:is/1..6/:b;js/1..3/:c,*;links(is,js):a;endsetsma*=sum(js(J):c(J)**(J));sum(js(J):a(1,J)**(J))<=b(1);sum(js(J):a(2,J)**(J))<=b(2);sum(js(J):a(3,J)**(J))<=b(3);sum(js(J):a(4,J)**(J))<=b(4);sum(js(J):a(5,J)**(J))>=B(5);sum(js(J):a(6,J)**(J))<=b(6);data:c=302060;b=43041042030070190;a=121302140111010001;enddataend最優(yōu)解Globaloptimalsolutionfound.Objectivevalue:13700.00Infeasibilities:0.000000Totalsolveriterations:4VariableValueReducedCostB(1)430.00000.000000B(2)410.00000.000000B(3)420.00000.000000B(4)300.00000.000000B(5)70.000000.000000B(6)190.00000.000000C(1)30.000000.000000C(2)20.000000.000000C(3)60.000000.000000*(1)10.000000.000000*(2)100.00000.000000*(3)190.00000.000000A(1,1)1.0000000.000000A(1,2)2.0000000.000000A(1,3)1.0000000.000000A(2,1)3.0000000.000000A(2,2)0.0000000.000000A(2,3)2.0000000.000000A(3,1)1.0000000.000000A(3,2)4.0000000.000000A(3,3)0.0000000.000000A(4,1)1.0000000.000000A(4,2)1.0000000.000000A(4,3)1.0000000.000000A(5,1)0.0000000.000000A(5,2)1.0000000.000000A(5,3)0.0000000.000000A(6,1)0.0000000.000000A(6,2)0.0000000.000000A(6,3)1.0000000.000000RowSlackorSurplusDualPrice113700.001.000000230.000000.00000030.0000003.333333410.000000.00000050.00000020.00000630.000000.00000070.00000033.33333最優(yōu)解〔10，100,190〕最優(yōu)值13700；可行。第二問由原問題的單個價值系數(shù)和右端系數(shù)變化范圍的靈敏度分析結(jié)果得Rangesinwhichthebasisisunchanged:ObjectiveCoefficientRangesCurrentAllowableAllowableVariableCoefficientIncreaseDecrease*(1)30.0000035.00000INFINITY*(2)20.0000030.0000020.00000*(3)50.00000INFINITY23.33333RighthandSideRangesRowCurrentAllowableAllowableRHSIncreaseDecrease2430.0000INFINITY35.000003410.000050.0000020.000004420.0000INFINITY40.000005300.000010.0000025.00000670.0000025.00000INFINITY7240.0000INFINITY35.00000當(dāng)C2增加到310時此時模型MODEL:[_1]MA*=30**_1+20**_2+50**_3;[_2]*_1+2**_2+*_3<=430;[_3]3**_1+2**_3<=410;[_4]*_1+4**_2<=420;[_5]*_1+*_2+*_3<=310;[_6]*_2>=70;[_7]*_3<=240;END編程sets:is/1..6/:b;js/1..3/:c,*;links(is,js):a;endsetsma*=sum(js(J):c(J)**(J));sum(js(J):a(1,J)**(J))<=b(1);sum(js(J):a(2,J)**(J))<=b(2);sum(js(J):a(3,J)**(J))<=b(3);sum(js(J):a(4,J)**(J))<=b(4);sum(js(J):a(5,J)**(J))>=B(5);sum(js(J):a(6,J)**(J))<=b(6);data:c=302050;b=43041042031070240;a=121302140111010001;enddataend此時最優(yōu)解Globaloptimalsolutionfound.Objectivevalue:12350.00Infeasibilities:0.000000Totalsolveriterations:4VariableValueReducedCostB(1)430.00000.000000B(2)410.00000.000000B(3)420.00000.000000B(4)310.00000.000000B(5)70.000000.000000B(6)240.0000