Multiparametric Linear Programming

Tomas Gal and Josef Nedoma
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Tomas Gal: Technische Hochschule, Aachen, West Germany
Josef Nedoma: Czechoslovak Academy of Sciences, Prague, Czechoslovakia

Management Science, 1972, vol. 18, issue 7, 406-422

Abstract: The multiparametric linear programming (MLP) problem for the right-hand sides (RHS) is to maximize z = c T x subject to Ax = b(\lambda), x \geqq 0, where b(\lambda) be expressed in the form where F is a matrix of constant coefficients, and \lambda is a vector-parameter. 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 \geqq 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 \lambda \epsilon R i the basis B i is optimal. Let K denote a region such that K = U i R 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.

Date: 1972
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