1、The Computer Package of LP,2 LINGO,1 LINDO,3 MATLAB - LINPROG,- To Solve LP, IP and QP,- To Solve LP and NLP,- To Solve LP, IP, QP, Multi-Goal Programming and NLP,Using LINDO to Solve LP,Input Given Data Solution Press Button Output,The Computer Package of LP-LINDO,！This is a LP for max max 3 x1+5 x

2、2+4 x3 subject to 2 x1+3 x21500 2 x2+4 x3800 3 x1+2 x2 +5 x32000 end,1 Input Given Data,max z=3x1+5x2+4x3 s. t. 2x1+3x2 1500 2x2+4x3 800 3x1+2x2+5x3 2000 x1, x2, x3 0.,The Computer Package of LP-LINDO,變量以字母開頭，下標寫在后面，系數(shù)與變量之間加空格； 約束條件以 subject to (或ST) 開始； 要輸入 = 約束，也可用 代替； 變量的非負約束條件可省略； 不能接受括號 “（）”,逗號

3、 “ ，” 和運算符“ * ”; 不區(qū)分變量的大小寫； 結束時以end 標示。,Remarks：,The Computer Package of LP-LINDO,2 Output,LP OPTIMUM FOUND AT STEP 3 OBJECTIVE FUNCTION VALUE 1) 2675.000 VARIABLE VALUE REDUCED COST X1 375.000000 0.000000 X2 250.000000 0.000000 X3 75.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 1.05

4、0000 3) 0.000000 0.625000 4) 0.000000 0.300000,The Computer Package of LP-LINDO,Input Given Data LINDO Model LINGO Model Solution Press Button Output,Using LINGO to Solve LP,The Computer Package of LP-LINGO,1 LINDO Model Input Given Data,max z=3x1+5x2+4x3 s. t. 2x1+3x2 1500 2x2+4x3 800 3x1+2x2+5x3 2

5、000 x1, x2, x3 0.,model: max=3*x1+5*x2+4*x3; 2*x1+3*x2=1500; 2*x2+4*x3=800; 3*x1+2*x2+5*x3=2000; end,The Computer Package of LP-LINGO,Remarks (與LINDO區(qū)別)：,目標函數(shù)中加等號； 變量與系數(shù)之間用“*”； model: end可省略； 每個語句后面必須以分號結束.,The Computer Package of LP-LINGO,model: sets: endsets data: enddata Transferring Function and

6、 Computation end,! Define Set,！Define Data,The Computer Package of LP-LINGO,2 LINGO Model Input Given Data,model: ！Beginning sets: ！Definition of Set ve/1.3/:c,x; co/1.3/:b; ma(co,ve):a; endsets ！注：集表達式：名稱/成員/：屬性 名稱（初始集）：屬性,Set,The Computer Package of LP-LINGO,Data:,data:！Definition of Data c=3 5 4;

7、 b=1500 800 2000; a=2 3 0 0 2 4 3 2 5; enddata ！注：數(shù)據(jù)的大小與集合定義中一致，分量中間用空格或逗號分開，數(shù)據(jù)結束后用分號；,The Computer Package of LP-LINGO,Transferring Function,max=sum(ve(j):c(j)*x(j); for(co(i):sum(ve(j):a(i,j)*x(j)=b(i); Main Function： for(set(set_index_list)|condition:expression) sum(set(set_index_list)|condition:

8、expression) min(max)(set(set_index_list)|condition:expression),The Computer Package of LP-LINGO,3 Output,Global optimal solution found at iteration: 3 Objective value: 2675.000 Variable Value Reduced Cost C( 1) 3.000000 0.000000 C( 2) 5.000000 0.000000 C( 3) 4.000000 0.000000 X( 1) 375.0000 0.000000

9、 X( 2) 250.0000 0.000000 X( 3) 75.00000 0.000000,The Computer Package of LP-LINGO,B( 1) 1500.000 0.000000 B( 2) 800.0000 0.000000 B( 3) 2000.000 0.000000 A( 1, 1) 2.000000 0.000000 A( 1, 2) 3.000000 0.000000 A( 1, 3) 0.000000 0.000000 A( 2, 1) 0.000000 0.000000 A( 2, 2) 2.000000 0.000000 A( 2, 3) 4.

10、000000 0.000000 A( 3, 1) 3.000000 0.000000 A( 3, 2) 2.000000 0.000000 A( 3, 3) 5.000000 0.000000,The Computer Package of LP-LINGO,Row Slack or Surplus Dual Price 1 2675.000 1.000000 2 0.000000 1.050000 3 0.000000 0.6250000 4 0.000000 0.3000000,The Computer Package of LP-LINGO,The Computer Package of

11、 LP-MATLAB,If we want to get the value of the objective function at X: FVAL = CTX, then use X, fval=linprog( ).,Example 1,C=-5; -4; -6 A= 1 -1 1;3 2 4;3 2 0 b=20; 42; 30 lb=zeros(3,1),First, enter the coefficients,The Computer Package of LP-MATLAB,Next, call a linear programming routine. x, fval = linprog(C, A, b, , , lb); x = 0.0000 15.0000 3.0000 fval = -78.0000,The Computer Package of LP-MATLAB,Example 2,First, enter the coefficients,C=-2; -3; 5 A= -2 5 -