IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Fixed-charge transportation on a path: optimization, LP formulations and separation

  • VAN VYVE, Mathieu

    ()

    (Université catholique de Louvain, CORE and Louvain School of Management, B-1348 Louvain-la-Neuve, Belgium)

Registered author(s):

    The fixed-charge transportation problem is an interesting problem in its own right. This paper further motivates its study by showing that it is both a special case and a strong relaxation of the big-bucket multi-item lot-sizing problem. We then provide a polyhedral analysis of the polynomially solvable special case in which the associated bipartite graph is a path. We give a O(n^3)-time optimization algorithm and two O(n^2)-size linear programming extended formulation. We describe a new class of inequalities that we call "path-modular" inequalities. We give two distinct proofs of their validity. The first one is direct and crucially relies on sub- and super- modularity of an associated set function. The second proof is by showing that the projection of one of the extended linear programming formulations onto the original variable space yields exactly the polyhedron described by the path- modular inequalities. Thus we also show that these inequalities suffice to describe the convex hull of the set of feasible solutions. We finally report on computational experiments comparing extended LP formulation, valid inequalities separation and a standard MIP solver.

    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/coredp2010_68web.pdf
    Download Restriction: no

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2010068.

    as
    in new window

    Length:
    Date of creation: 01 Oct 2010
    Date of revision:
    Handle: RePEc:cor:louvco:2010068
    Contact details of provider: Postal: Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium)
    Phone: 32(10)474321
    Fax: +32 10474304
    Web page: http://www.uclouvain.be/core
    Email:


    More information through EDIRC

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

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

    When requesting a correction, please mention this item's handle: RePEc:cor:louvco:2010068. 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.