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Rim Multiparametric Linear Programming

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  • Tomas Gal

    (Rhein.-Westf. Technische Hochschule, Aachen, West Germany)

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.

Suggested Citation

  • Tomas Gal, 1975. "Rim Multiparametric Linear Programming," Management Science, INFORMS, vol. 21(5), pages 567-575, January.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:5:p:567-575
    DOI: 10.1287/mnsc.21.5.567
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    Cited by:

    1. Efstratios Pistikopoulos & Luis Dominguez & Christos Panos & Konstantinos Kouramas & Altannar Chinchuluun, 2012. "Theoretical and algorithmic advances in multi-parametric programming and control," Computational Management Science, Springer, vol. 9(2), pages 183-203, May.
    2. Richard Oberdieck & Martina Wittmann-Hohlbein & Efstratios Pistikopoulos, 2014. "A branch and bound method for the solution of multiparametric mixed integer linear programming problems," Journal of Global Optimization, Springer, vol. 59(2), pages 527-543, July.
    3. Ilbin Lee & Stewart Curry & Nicoleta Serban, 2019. "Solving Large Batches of Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 302-317, April.
    4. Curry, Stewart & Lee, Ilbin & Ma, Simin & Serban, Nicoleta, 2022. "Global sensitivity analysis via a statistical tolerance approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 44-59.
    5. Iosif Pappas & Nikolaos A. Diangelakis & Efstratios N. Pistikopoulos, 2021. "The exact solution of multiparametric quadratically constrained quadratic programming problems," Journal of Global Optimization, Springer, vol. 79(1), pages 59-85, January.
    6. Martina Wittmann-Hohlbein & Efstratios Pistikopoulos, 2013. "On the global solution of multi-parametric mixed integer linear programming problems," Journal of Global Optimization, Springer, vol. 57(1), pages 51-73, September.

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