Advanced Search
MyIDEAS: Login

Two row mixed integer cuts via lifting

Contents:

Author Info

  • SANTANU, Dey

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • WOLSEY, Laurence A.

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

Registered author(s):

    Abstract

    Recently, Andersen et al. [1], Borozan and Cornuéjols [6] and Cornuéjols and Margot [9] characterized extreme inequalities of a system of two rows with two free integer variables and nonnegative continuous variables. These inequalities are either split cuts or intersection cuts derived using maximal lattice-free convex sets. In order to use these inequalities to obtain cuts from two rows of a general simplex tableau, one approach is to extend the system to include all possible nonnegative integer variables (giving the two-row mixed integer infinite-group problem), and to develop lifting functions giving the coefficients of the integer variables in the corresponding inequalities. In this paper, we study the characteristics of these lifting functions. We begin by observing that functions giving valid coefficients for the nonnegative integer variables can be constructed by lifting a subset of the integer variables and then applying the fill-in procedure presented in Johnson [23]. We present conditions for these 'general fill-in functions" to be extreme for the two-row mixed integer infinite-group problem. We then show that there exists a unique 'trivial' lifting function that yields extreme inequalities when starting from a maximal lattice-free triangle with multiple integer points in the relative interior of one of its sides, or a maximal lattice-free triangle with integral vertices and one integer point in the relative interior of each side. In all other cases (maximal lattice-free triangle with one integer point in the relative interior of each side and non-integral vertices, and maximal lattice-free quadrilaterals), non-unique lifting functions may yield distinct extreme inequalities. For the case of a triangle with one integer point in the relative interior of each side and non-integral vertices, we present sufficient conditions to yield an extreme inequality for the two-row mixed integer infinite-group problem.

    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://www.uclouvain.be/cps/ucl/doc/core/documents/dp2008_30.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2008030.

    as in new window
    Length:
    Date of creation: 01 May 2008
    Date of revision:
    Handle: RePEc:cor:louvco:2008030

    Contact details of provider:
    Postal: Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium)
    Phone: 32(10)474321
    Fax: +32 10474304
    Email:
    Web page: http://www.uclouvain.be/core
    More information through EDIRC

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    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:cor:louvco:2008030. 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: (Alain GILLIS).

    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.