The LP Procedure |
Sensitivity analysis is a technique for examining the effects of changes in model parameters on the optimal solution. The analysis enables you to examine the size of a perturbation to the right-hand-side or objective vector by an arbitrary change vector for which the basis of the current optimal solution remains optimal.
Note: When sensitivity analysis is performed on integer-constrained problems, the integer variables are fixed at the value they obtained in the integer optimal solution. Therefore, care must be used when interpreting the results of such analyses. Care must also be taken when preprocessing is enabled, because preprocessing usually alters the original formulation.
Consider the problem :
where is a right-hand-side change vector.
Let denote an optimal basic
feasible solution to
.
PROC LP can be used to examine the effects of changes in
on the
solution
of problem
.
For the basic solution
, let
be the
matrix composed of the basic columns of
and
let
be the matrix composed of the nonbasic
columns of
.
For the basis matrix
, the basic components of
, written as
, can
be expressed as
For and
, PROC LP reports the following:
Consider the problem :
where is a price change vector.
Let denote an optimal basic
feasible solution to
.
PROC LP can be used to examine the effects of changes in
on the
solution
of problem
.
For the basic solution
,
let
be the matrix composed of the basic
columns of
and let
be the matrix
composed of the nonbasic columns of
.
For basis matrix
, the
reduced cost associated with the
th
variable can be written as
For each price coefficient change vector identified with
the keyword PRICESEN in the TYPE
variable, PROC LP finds an interval
such that for
,
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