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

Induced optimal partition invariancy in linear optimization: constraints perturbation