Abstract
The rim multiparametric linear programming problem (RMPLP) is a parametric problem with a vector-parameter in both the right-hand side and objective function (i.e., in the “rim”). The RMPLP determines the region K* ⊂ E* such that the problem, maximize z(λ) = cT(λ)x, subject to Ax = b(λ), x ≧ 0, has a finite optimal solution for all λ ∈ K*. Let Bi be an optimal basis to the given problem, and let Ri*, be a region assigned to Bi such that for all λ ∈ Ri* the basis Bi is optimal. The goal of the RMPLP problem is to cover K* by the Ri* such that the various Ri* do not overlap. The purpose of this paper is to present a solution method for finding all regions Ri* that cover K* and do not overlap. This method is based upon an algorithm for a multiparametric problem described in an earlier paper by Gal and Nedoma.
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