The multiparametric linear programming (MLP) problem for the right-hand sides (RHS) is to maximize z = cTx subject to Ax = b(λ), x ≧ 0, where b(λ) be expressed in the form [Formula: see text] where F is a matrix of constant coefficients, and λ is a vector-parameter. The multiparametric linear programming (MLP) problem for the prices or objective function coefficients (OFC) is to maximize z = cT(v)x subject to Ax = b, x ≧ 0, where c(I) can be expressed in the form c(v) = c* + Hv, and where H is a matrix of constant coefficients, and v a vector-parameter. Let Bi be an optimal basis to the MLP-RHS problem and Ri be a region assigned to Bi such that for all λ ϵ Ri the basis Bi is optimal. Let K denote a region such that K = UiRi provided that the Ri for various I do not overlap. The purpose of this paper is to present an effective method for finding all regions Ri that cover K and do not overlap. This method uses an algorithm that finds all nodes of a finite connected graph. This method uses an algorithm that finds all nodes of a finite connected graph. An analogus method is presented for the MLP-OFC problem.
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Gál et al. (1972) studied this question.