实验3 线性规划图解法的灵敏性分析.doc

实验3 线性规划的灵敏性分析成绩专业班级 信息121 班 学号 201212030120 姓名 刘帅 报告日期 实验类型：验证性实验 综合性实验 设计性实验实验目的：熟练线性规划图解法的灵敏性分析。实验内容：线性规划的灵敏性分析4个（题目自选b,c灵敏性分析）实验原理 在线性规划图解法求出最优解的情况下，分析b,c分别变化对最优解的影响，确定最优解的变化范围，在变化的情况下能求出最优解。实验步骤1 要求上机实验前先编写出程序代码 2 编辑录入程序3 调试程序并记录调试过程中出现的问题及修改程序的过程4 经反复调试后，运行程序并验证程序运行是否正确。5 记录运行时的输入和输出。 预习编写程序代码：实验报告：根据实验情况和结果撰写并递交实验报告。(1) 唯一最优解：max z=x1+x2建立simplex.m文件function x,z,flg,sgma=simplex(A,A1,b,c,m,n,n1,cb,xx) % A,b are the matric in A*x=b % c is the matrix in max z=c*x % A1 is the matric in simplex table % m is the numbers of row in A and n is the column number in A % n1 is the nubers of artificial variables,and artificial variables are default at the last % n1 variables in x. % cb is the worth coefficient matrix for basic variables % xx is the index matrix for basic variables % B1 is the invers matrix for the basic matrix in simplex table.The initial % matrix is default as the last m con in the matrix A. x=zeros(n,1); z=0; B1=A1(:,n-m+1:n)sgma1=c-(cb*B1)*A; masg,kk=max(sgma1); k=kk(1); flg=0; ll=0; while (masg0)&(ll0 thita(i)=A1(i,k)b(i); end end r8,c8=find(thita999); if sum(c8)m mith,rr=min(thita); r=rr(1); aa=A1(r,k); for i=1:m if i=r b(r)=b(r)/aa; for j=1:n A1(r,j)=A1(r,j)/aa; end end end for i=1:m if i=r cc=A1(i,k) b(i)=b(i)-b(r)*cc; for j=1:n A1(i,j)=A1(i,j)-A1(r,j)*cc; end end end cb(r)=c(k); xx(r)=k; B1=A1(:,n-m+1:n); sgma1=c-(cb*B1)*A; masg,kk=max(sgma1); k=kk(1); thita=100+zeros(m,1); else flg=3; masg=-1; x=unbound solution; z=inf; end end if flg=3 if n1=0 sgma1=c-(cb*B1)*A rc,ccc=find(sgma1-0.0000000001); if sum(rc)=n-m flg=1; else flg=2; end x=zeros(n,1); for i=1:m x(xx(i)=b(i); end z=c*x; else x=zeros(n,1); for i=1:m x(xx(i)=b(i); end xa=x(n-n1+1):n,:); ra=find(xa); if sum(ra)=0 sgma1=c-(cb*B1)*A; rc,ccc=find(sgma1 A=1 4 2 0;2 3 0 1; A1=A; b=6;8; c=1 1 0 1; m=2; n=1; cb=0 0 ; xx=2,4; x,z,flg,sgma=simplex(A,A1,b,c,m,n,3,cb,xx)B1 = 1 0 0 1cc = 3cc = 0.34763cc = 0x =nothingz =nothingflg = 4sgma =0.0000 0.0000 -0.1000 -0.1000建立lingbo.m文件function a1,b1=lingbo(B1,b,r) m=length(b); aa=-10000*ones(m,1); bb=10000*ones(m,1); for i=1:m if B1(i,r)0 aa(i)=-b(i)/B1(i,r); end if B1(i,r) B1=0 1 ;1 1; a1,b1=lingbo(B1,b,1)a1 = -4b1 = 4000 a1,b1=lingbo(B1,b,2)a1 = -4b1 = 4000（2）无穷多个最优解max z=2x1+3x2运行过程及结果： A=6 4 1 0;2 1 0 1; A1=A; b=4;6; c=3 2 0 0; m=2; n=4; cb=0 0; xx=3,2; x,z,flg,sgma=simplex(A,A1,b,c,m,n,3,cb,xx)B1 = 1 0 0 1cc = 2x =nothingz =nothingflg = 4sgma = 0 0 -0.5000 0取r=1,2，运行结果为 a1,b1=lingbo(B1,b,r) B1=1 0 ;1 0; a1,b1=lingbo(B1,b,1)a1 = -4b1 = 1000 a1,b1=lingbo(B1,b,2)a1 = -4b1 = 1000（3）无可行解max z=3x1+2x2运行过程及结果： A=2 1 1 0;3 4 0 1; A1=A; b=2;12; c=3 2 0 0; m=2; n=4; cb=0 0; xx=3,4; x,z,flg,sgma=simplex(A,A1,b,c,m,n,3,cb,xx)B1 = 1 0 0 1cc = 3cc = 2.5000x =unbound solutionz =nothingflg = 4sgma =-1 0 -2 0取r=1,2，运行结果为 a1,b1=lingbo(B1,b,r) B1=1 0 ;0 1; a1,b1=lingbo(B1,b,1)a1 = -6b1 = 10000 a1,b1=lingbo(B1,b,2)a1 = -6b1 = 10000（4）无界解max z=5x1+6x2运行过程及结果： A=2 -1 1 0;-2 2 0 3; A1=A; b=2;2; c=4 5 0 0; m=2; n=4; cb=0 0; xx=4,6; x,z,flg,sgma=simplex(A,A1,b,c,m,n,3,cb,xx)B1 = 1 0 0 1cc = -1cc = -0.6667cc = 0x =unbound solutionz =nothingflg = 4sgma =0.0000 0.0000 -6.7500 -4.2500取r=1,2，运行结果为 a1,b1=lingbo(B1,b,r) B1=1 0 ;0 1; a1,b1=lingbo(B1,b,1)a1 = -6b1 = 10000 a1,b1=lingbo(B1,b,2)a1 = -6b1 = 10000实验总结：通过这次的实验，我初步了解了在线性规划图解法