IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v21y1975i5p567-575.html
   My bibliography  Save this article

Rim Multiparametric Linear Programming

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.21.5.567
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.21.5.567?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:21:y:1975:i:5:p:567-575. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.