線性規(guī)劃的靈敏度分析實驗報告

1、真誠為您提供優(yōu)質(zhì)參考資料，若有不當之處，請指正。運籌學/線性規(guī)劃實驗報告實驗室： 實驗日期：實驗項目線性規(guī)劃的靈敏度分析系 別數(shù)學系姓 名學 號班 級指導教師成 績一 實驗目的掌握用Lingo/Lindo對線性規(guī)劃問題進行靈敏度分析的方法，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)學模型，并利用計算機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)學模型、上機程序、實驗結果、結果分析與問題解答等）例題2-10MODEL: _1 MAX= 2 * X_1 + 3 * X_2 ; _2 X_1 + 2 * X_2 + X_3 = 8 ; _3 4 * X_1 + X_4

2、 = 16 ; _4 4 * X_2 + X_5 = 12 ; END編程sets:is/1.3/:b;js/1.5/:c,x;links(is,js):a;endsetsmax=sum(js(J):c(J)*x(J);for(is(I):sum(js(J):a(I,J)*x(J)=b(I);data:c=2 3 0 0 0;b=8 16 12;a=1 2 1 0 0 4 0 0 1 0 0 4 0 0 1;end dataend靈敏度分析 Ranges in which the basis is unchanged: Objective Coefficient Ranges Current

3、Allowable Allowable Variable Coefficient Increase Decrease X( 1) 2.000000 INFINITY 0.5000000 X( 2) 3.000000 1.000000 3.000000 X( 3) 0.0 1.500000 INFINITY X( 4) 0.0 0.1250000 INFINITY X( 5) 0.0 0.7500000 0.2500000Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease 2 8.000000 2

4、.000000 4.000000 3 16.00000 16.00000 8.000000 4 12.00000 INFINITY 4.000000當b2在8,32之間變化時 最優(yōu)基不變最優(yōu)解 Global optimal solution found at iteration: 0 Objective value: 14.00000Variable Value Reduced Cost B( 1) 8.000000 0.000000 B( 2) 16.00000 0.000000 B( 3) 12.00000 0.000000 C( 1) 2.000000 0.000000 C( 2) 3.

5、000000 0.000000 C( 3) 0.000000 0.000000 C( 4) 0.000000 0.000000 C( 5) 0.000000 0.000000 X( 1) 4.000000 0.000000 X( 2) 2.000000 0.000000 X( 3) 0.000000 1.500000 X( 4) 0.000000 0.1250000X( 5) 4.000000 0.000000A( 1, 1) 1.000000 0.000000A( 1, 2) 2.000000 0.000000 A( 1, 3) 1.000000 0.000000 A( 1, 4) 0.00

6、0000 0.000000 A( 1, 5) 0.000000 0.000000 A( 2, 1) 4.000000 0.000000 A( 2, 2) 0.000000 0.000000 A( 2, 3) 0.000000 0.000000 A( 2, 4) 1.000000 0.000000 A( 2, 5) 0.000000 0.000000 A( 3, 1) 0.000000 0.000000 A( 3, 2) 4.000000 0.000000 A( 3, 3) 0.000000 0.000000 A( 3, 4) 0.000000 0.000000 A( 3, 5) 1.00000

7、0 0.000000Row Slack or Surplus Dual Price 1 14.00000 1.000000 2 0.000000 1.500000 3 0.000000 0.1250000 4 0.000000 0.000000例題2-11模型MAX 2 X( 1) + 3 X( 2) SUBJECT TO 2 X( 1) + 2 X( 2) + X( 3) = 12 3 4 X( 1) + X( 4) = 16 4 4 X( 2) + X( 5) = 12 END編程sets:is/1.3/:b;js/1.5/:c,x;links(is,js):a;endsetsmax=su

8、m(js(J):c(J)*x(J);for(is(I):sum(js(J):a(I,J)*x(J)=b(I);data:c=2 3 0 0 0;b=12 16 12;a=1 2 1 0 0 4 0 0 1 0 0 4 0 0 1;end dataend最優(yōu)解 Global optimal solution found at iteration: 2 Objective value: 17.00000Variable Value Reduced Cost B( 1) 12.00000 0.000000 B( 2) 16.00000 0.000000 B( 3) 12.00000 0.000000

9、 C( 1) 2.000000 0.000000 C( 2) 3.000000 0.000000 C( 3) 0.000000 0.000000 C( 4) 0.000000 0.000000 C( 5) 0.000000 0.000000 X( 1) 4.000000 0.000000 X( 2) 3.000000 0.000000 X( 3) 2.000000 0.000000 X( 4) 0.000000 0.5000000 X( 5) 0.000000 0.7500000 A( 1, 1) 1.000000 0.000000A( 1, 2) 2.000000 0.000000 A( 1

10、, 3) 1.000000 0.000000 A( 1, 4) 0.000000 0.000000 A( 1, 5) 0.000000 0.000000 A( 2, 1) 4.000000 0.000000 A( 2, 2) 0.000000 0.000000A( 2, 3) 0.000000 0.000000 A( 2, 4) 1.000000 0.000000 A( 2, 5) 0.000000 0.000000 A( 3, 1) 0.000000 0.000000 A( 3, 2) 4.000000 0.000000 A( 3, 3) 0.000000 0.000000 A( 3, 4)

11、 0.000000 0.000000 A( 3, 5) 1.000000 0.000000 Row Slack or Surplus Dual Price 1 17.00000 1.000000 2 0.000000 0.000000 3 0.000000 0.5000000 4 0.000000 0.7500000最優(yōu)解（4,3,2,0,0）最優(yōu)值z=17分析 Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient

12、 Increase Decrease X( 1) 2.000000 INFINITY 2.000000 X( 2) 3.000000 INFINITY 3.000000 X( 3) 0.0 1.500000 INFINITY X( 4) 0.0 0.5000000 INFINITY X( 5) 0.0 0.7500000 INFINITY Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease 2 12.00000 INFINITY 2.000000 3 16.00000 8.000000 16.0

13、0000 4 12.00000 4.000000 12.00000例題2-12模型MAX 2 X( 1) + 3 X( 2) SUBJECT TO 2 X( 1) + 2 X( 2) + X( 3) = 8 3 4 X( 1) + X( 4) = 16 4 4 X( 2) + X( 5) = 12 END編程sets:is/1.3/:b;js/1.5/:c,x;links(is,js):a;endsetsmax=sum(js(J):c(J)*x(J);for(is(I):sum(js(J):a(I,J)*x(J)=b(I);data:c=2 3 0 0 0;b=8 16 12;a=1 2 1

14、0 0 4 0 0 1 0 0 4 0 0 1;end dataend靈敏度分析Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease X( 1) 2.000000 INFINITY 0.5000000 X( 2) 3.000000 1.000000 3.000000 X( 3) 0.0 1.500000 INFINITY X( 4) 0.0 0.1250000 INFINITY

15、X( 5) 0.0 0.7500000 0.2500000Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease 2 8.000000 2.000000 4.000000 3 16.00000 16.00000 8.000000 4 12.00000 INFINITY 4.000000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 MAX= 3 * X_1 + X_2 + 4 * X_3 ; _2 6 * X_1 + 3 * X_2 + 5 * X_3 = 4

16、50 ; _3 3 * X_1 + 4 * X_2 + 5 * X_3 = 300 ; END編程sets:is/1.2/:b;js/1.3/:c,x;links(is,js):a;endsetsmax=sum(js(J):c(J)*x(J);for(is(I):sum(js(J):a(I,J)*x(J)=b(I);data:c=3 1 4;b=450 300;a=6 3 5 3 4 5;end dataEnd最優(yōu)解 Global optimal solution found. Objective value: 270.0000 Infeasibilities: 0.000000 Total

17、solver iterations: 2Variable Value Reduced Cost B( 1) 450.0000 0.000000 B( 2) 300.0000 0.000000 C( 1) 3.000000 0.000000 C( 2) 1.000000 0.000000 C( 3) 4.000000 0.000000 X( 1) 50.00000 0.000000 X( 2) 0.000000 2.000000 X( 3) 30.00000 0.000000 A( 1, 1) 6.000000 0.000000 A( 1, 2) 3.000000 0.000000 A( 1,

18、3) 5.000000 0.000000 A( 2, 1) 3.000000 0.000000 A( 2, 2) 4.000000 0.000000 A( 2, 3) 5.000000 0.000000 Row Slack or Surplus Dual Price 1 270.0000 1.000000 2 0.000000 0.2000000 3 0.000000 0.6000000第一問：A生產(chǎn)50 B生產(chǎn)0 C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果Ranges in which the basis is unchanged: Objecti

19、ve Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease X( 1) 3.000000 1.800000 0.6000000 X( 2) 1.000000 2.000000 INFINITY X( 3) 4.000000 1.000000 1.500000 Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease 2 450.0000 150.0000 150.0000 3 300.

20、0000 150.0000 75.00000當A的利潤在【2.4，4.8】之間變化時，原最優(yōu)生產(chǎn)計劃不變。第三問：模型MODEL: _1 MAX= 3 * X_1 + X_2 + 4 * X_3 + 3 * X_4 ; _2 6 * X_1 + 3 * X_2 + 5 * X_3 + 8 * X_4 = 450 ; _3 3 * X_1 + 4 * X_2 + 5 * X_3 + 2 * X_4 = 300 ; END編程sets:is/1.2/:b;js/1.4/:c,x;links(is,js):a;endsetsmax=sum(js(J):c(J)*x(J);for(is(I):sum(

21、js(J):a(I,J)*x(J)=b(I);data:c=3 1 4 3;b=450 300;a=6 3 5 8 3 4 5 2;end dataEnd最優(yōu)解 Global optimal solution found. Objective value: 275.0000 Infeasibilities: 0.000000 Total solver iterations: 2 Variable Value Reduced Cost B( 1) 450.0000 0.000000 B( 2) 300.0000 0.000000 C( 1) 3.000000 0.000000 C( 2) 1.0

22、00000 0.000000 C( 3) 4.000000 0.000000 C( 4) 3.000000 0.000000 X( 1) 0.000000 0.1000000 X( 2) 0.000000 1.966667 X( 3) 50.00000 0.000000 X( 4) 25.00000 0.000000 A( 1, 1) 6.000000 0.000000 A( 1, 2) 3.000000 0.000000 A( 1, 3) 5.000000 0.000000 A( 1, 4) 8.000000 0.000000 A( 2, 1) 3.000000 0.000000 A( 2,

23、 2) 4.000000 0.000000 A( 2, 3) 5.000000 0.000000 A( 2, 4) 2.000000 0.000000 Row Slack or Surplus Dual Price 1 275.0000 1.000000 2 0.000000 0.2333333 3 0.000000 0.5666667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果Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allow

24、able Variable Coefficient Increase Decrease X( 1) 3.000000 1.800000 0.6000000 X( 2) 1.000000 2.000000 INFINITY X( 3) 4.000000 1.000000 1.500000 Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease 2 450.0000 150.0000 150.0000 3 300.0000 150.0000 75.00000當購買150噸時 此時可買360元 在減去購買

25、150噸的進價60元 此時可獲利300超過了原計劃，應該購買。第七題模型MODEL: _1 MAX= 30 * X_1 + 20 * X_2 + 50 * X_3 ; _2 X_1 + 2 * X_2 + X_3 = 430 ; _3 3 * X_1 + 2 * X_3 = 410 ; _4 X_1 + 4 * X_2 = 420 ; _5 X_1 + X_2 + X_3 = 70 ; _7 X_3 = 240 ; END編程sets:is/1.6/:b;js/1.3/:c,x;links(is,js):a;endsetsmax=sum(js(J):c(J)*x(J);sum(js(J):a(

26、1,J)*x(J)=b(1);sum(js(J):a(2,J)*x(J)=b(2);sum(js(J):a(3,J)*x(J)=b(3);sum(js(J):a(4,J)*x(J)=B(5);sum(js(J):a(6,J)*x(J)=b(6);data:c=30 20 50;b=430 410 420 300 70 240;a=1 2 1 3 0 2 1 4 0 1 1 1 0 1 0 0 0 1;end dataend最優(yōu)解 Global optimal solution found. Objective value: 12150.00 Infeasibilities: 0.000000

27、Total solver iterations: 4 Variable Value Reduced Cost B( 1) 430.0000 0.000000 B( 2) 410.0000 0.000000 B( 3) 420.0000 0.000000 B( 4) 300.0000 0.000000 B( 5) 70.00000 0.000000 B( 6) 240.0000 0.000000 C( 1) 30.00000 0.000000 C( 2) 20.00000 0.000000 C( 3) 50.00000 0.000000 X( 1) 0.000000 35.00000 X( 2)

28、 95.00000 0.000000 X( 3) 205.0000 0.000000 A( 1, 1) 1.000000 0.000000 A( 1, 2) 2.000000 0.000000 A( 1, 3) 1.000000 0.000000 A( 2, 1) 3.000000 0.000000 A( 2, 2) 0.000000 0.000000 A( 2, 3) 2.000000 0.000000 A( 3, 1) 1.000000 0.000000 A( 3, 2) 4.000000 0.000000 A( 3, 3) 0.000000 0.000000 A( 4, 1) 1.000000 0.000000 A( 4, 2) 1.000000 0.000000 A( 4, 3) 1.000000 0.0