IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v47y2025i2d10.1007_s00291-024-00782-y.html
   My bibliography  Save this article

A branch and cut algorithm to optimize a weighted sum-of-ratios in multiobjective mixed-integer fractional programming

Author

Listed:
  • João Paulo Costa

    (CeBER, Faculty of Economics
    INESC Coimbra)

  • Maria João Alves

    (CeBER, Faculty of Economics
    INESC Coimbra)

Abstract

Multiobjective linear fractional programming is useful to model multiobjective problems where all or some of the objective functions are a ratio or proportion of one linear/affine function to another linear/affine function. In practice, many of such problems include integer variables. If the weighted-sum scalarization is used to compute efficient solutions to the multiobjective problem, then the scalar problem to be solved for each weight vector turns out to be a weighted sum-of-ratios. There are several algorithms reported in the literature to optimize weighted sum-of-ratios, but almost all of them cannot deal with integer variables. In this paper we propose a Branch & Cut algorithm to optimize weighted-sums of the objective functions in multiobjective mixed integer fractional programming (MOMIFP). Several theoretical properties that support the algorithm are presented and proved. Computational experiments with randomly generated general problems are presented and discussed, which show that the algorithm is able to deal with practical MOMIFP problems.

Suggested Citation

  • João Paulo Costa & Maria João Alves, 2025. "A branch and cut algorithm to optimize a weighted sum-of-ratios in multiobjective mixed-integer fractional programming," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(2), pages 667-695, June.
    • Handle: RePEc:spr:orspec:v:47:y:2025:i:2:d:10.1007_s00291-024-00782-y
    DOI: 10.1007/s00291-024-00782-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-024-00782-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00291-024-00782-y?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:spr:orspec:v:47:y:2025:i:2:d:10.1007_s00291-024-00782-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.