摘要
本文报导了线性规划最优对偶解的如下一个性质,即以最优对偶解按本文所述方式变换原问题的系数,并组成新的线性规划问题时,新的最优对偶解值全为1。本文对此现象作了经济意义上的解释。
An interesting property of the optimal dual solution of LP,that was not
mentioned in textbooks or research reports in the past,may be described as
following:
Suppose a LP problem is expressed as
max C·X
s.t.A·X≤B(1)
x≥0
where,C=(c_1,c_2,…,c_n),X=(x_1,x_2,…,x_n)~r,B=(b_1,b_2,…,b_n)~T,and A=(a_i)_(m×n)
Let D=(d_1,d_2,…,d_n)~T be the optimal dual solution,and all components of
which are assumed to be nonzero.Then if the components of matrices C,B and
A in(1)are replaced by:
c'_i=c_i·1/d_i,b'i=b_j·1/d_j,
a'_(ij)=a_(ij)·d_i/d,(2)
the components of the new optimal dual solution would all be unity,i.e.D′=
(1,1,1…,1)~T.This property would be useful in explaining the economic meaning
of the optimal dual solution of LP in some special cases.
出处
《系统工程》
CSCD
1990年第4期71-72,F003,共3页
Systems Engineering
