  In this paper, we study uni-parametric linear optimization problems, in which
simultaneously the right-hand-side and the left-hand-side of constraints are
linearly perturbed with identical parameter.
  In addition to the concept of change point, the induced optimal partition is
introduced, and its relation to the well-known optimal partition is
investigated. Further, the concept of free variables in each invariancy
intervals is described. A modified generalized computational method is provided
with the capability of identifying the intervals for the parameter value where
induced optimal partitions are invariant. The behavior of the optimal value
function is described in its domain. Some concrete examples depict the results.
We further implement the methodology on some test problems to observe its
behavior on large scale problems.
