Rim Multiparametric Linear Programming

Tomas Gal
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Tomas Gal: Rhein.-Westf. Technische Hochschule, Aachen, West Germany

Management Science, 1975, vol. 21, issue 5, 567-575

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* \subset E* such that the problem, maximize z(\lambda) = c T (\lambda)x, subject to Ax = b(\lambda), x \geqq 0, has a finite optimal solution for all \lambda \in K*. Let B i be an optimal basis to the given problem, and let R i *, be a region assigned to B i such that for all \lambda \in R i * the basis B i is optimal. The goal of the RMPLP problem is to cover K* by the R i * such that the various R i * do not overlap. The purpose of this paper is to present a solution method for finding all regions R i * 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.

Date: 1975
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:21:y:1975:i:5:p:567-575

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