IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v347y2025i3d10.1007_s10479-025-06545-4.html
   My bibliography  Save this article

Sampling methods for multi-stage robust optimization problems

Author

Listed:
  • Francesca Maggioni

    (University of Bergamo)

  • Fabrizio Dabbene

    (Politecnico di Torino)

  • Georg Ch. Pflug

    (University of Vienna and International Institute for Applied Systems Analysis (IIASA))

Abstract

In this paper, we consider multi-stage robust optimization problems of the minimax type. We assume that the total uncertainty set is the cartesian product of stagewise compact uncertainty sets and approximate the given problem by a sampled subproblem. Instead of looking for the worst case among the infinite and typically uncountable set of uncertain parameters, we consider only the worst case among a randomly selected subset of parameters. By adopting such a strategy, two main questions arise: (1) Can we quantify the error committed by the random approximation, especially as a function of the sample size? (2) If the sample size tends to infinity, does the optimal value converge to the “true” optimal value? Both questions will be answered in this paper. An explicit bound on the probability of violation is given and chain of lower bounds on the original multi-stage robust optimization problem provided. Numerical results dealing with a multi-stage inventory management problem show that the proposed approach works well for problems with two or three time periods while for larger ones the number of required samples is prohibitively large for computational tractability. Despite this, we believe that our results can be useful for problems with such small number of time periods, and it sheds some light on the challenge for problems with more time periods.

Suggested Citation

  • Francesca Maggioni & Fabrizio Dabbene & Georg Ch. Pflug, 2025. "Sampling methods for multi-stage robust optimization problems," Annals of Operations Research, Springer, vol. 347(3), pages 1385-1423, April.
  • Handle: RePEc:spr:annopr:v:347:y:2025:i:3:d:10.1007_s10479-025-06545-4
    DOI: 10.1007/s10479-025-06545-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-025-06545-4
    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/s10479-025-06545-4?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:annopr:v:347:y:2025:i:3:d:10.1007_s10479-025-06545-4. 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.