Multiparametric Linear Programming

The multiparametric linear programming (MLP) problem for the right-hand sides (RHS) is to maximize z = c^Tx subject to Ax = b(λ), x ≧ 0, where b(λ) be expressed in the form

The multiparametric linear programming (MLP) problem for the prices or objective function coefficients (OFC) is to maximize z = c^T(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 B_i be an optimal basis to the MLP-RHS problem and R_i be a region assigned to B_i such that for all λ ϵ R_i the basis B_i is optimal. Let K denote a region such that K = U_iR_i provided that the R_i for various I do not overlap.

The purpose of this paper is to present an effective method for finding all regions R_i 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.