Advanced Search
MyIDEAS: Login to save this paper or follow this series

Robust Counterparts of Inequalities Containing Sums of Maxima of Linear Functions

Contents:

Author Info

  • Gorissen, B.L.
  • Hertog, D. den

    (Tilburg University, Center for Economic Research)

Registered author(s):

    Abstract

    This paper adresses the robust counterparts of optimization problems containing sums of maxima of linear functions and proposes several reformulations. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables, affine in a parameter with box uncertainty, and affine in a parameter with general uncertainty. In the literature, often the reformulation that is exact when there is no uncertainty is used. However, in robust optimization this reformulation gives an inferior solution and provides a pessimistic view. We observe that in many papers this conservatism is not mentioned. Some papers have recognized this problem, but existing solutions are either too conservative or their performance for different uncertainty regions is not known, a comparison between them is not available, and they are restricted to specific problems. We provide techniques for general problems and compare them with numerical examples in inventory management, regression and brachytherapy. Based on these examples, we give tractable recommendations for reducing the conservatism.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://arno.uvt.nl/show.cgi?fid=120682
    Our checks indicate that this address may not be valid because: 404 Not Found. If this is indeed the case, please notify (Richard Broekman)
    Download Restriction: no

    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-115.

    as in new window
    Length:
    Date of creation: 2011
    Date of revision:
    Handle: RePEc:dgr:kubcen:2011115

    Contact details of provider:
    Web page: http://center.uvt.nl

    Related research

    Keywords: robust optimization; sum of maxima of linear functions; biaffine uncertainty; robust conic quadratic constraints;

    Find related papers by JEL classification:

    This paper has been announced in the following NEP Reports:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Ng, Tsan Sheng & Sun, Yang & Fowler, John, 2010. "Semiconductor lot allocation using robust optimization," European Journal of Operational Research, Elsevier, vol. 205(3), pages 557-570, September.
    2. Aharon, Ben-Tal & Boaz, Golany & Shimrit, Shtern, 2009. "Robust multi-echelon multi-period inventory control," European Journal of Operational Research, Elsevier, vol. 199(3), pages 922-935, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:dgr:kubcen:2011115. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).

    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.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 profile, as there may be some citations waiting for confirmation.

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