IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v4y2000i3d10.1023_a1009874227903.html
   My bibliography  Save this article

A Probabilistic Feasibility and Value Analysis of the Generalized Assignment Problem

Author

Listed:
  • H. Edwin Romeijn

    (University of Florida)

  • Nanda Piersma

    (Erasmus University Rotterdam)

Abstract

We study the generalized assignment problem, under a probabilistic model for its cost and requirement parameters. First we address the issue of feasibility by deriving a tight condition on the probabilistic model that ensures that the corresponding problem instances are feasible with probability one as the number of jobs goes to infinity. Then, under an additional condition on the parameters, we show that the optimal solution value, normalized by dividing by the number of jobs, converges with probability one to a constant, again as the number of jobs goes to infinity. Finally, we discuss various examples.

Suggested Citation

  • H. Edwin Romeijn & Nanda Piersma, 2000. "A Probabilistic Feasibility and Value Analysis of the Generalized Assignment Problem," Journal of Combinatorial Optimization, Springer, vol. 4(3), pages 325-355, September.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:3:d:10.1023_a:1009874227903
    DOI: 10.1023/A:1009874227903
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1009874227903
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1009874227903?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Richard Freling & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2003. "A Branch-and-Price Algorithm for the Multiperiod Single-Sourcing Problem," Operations Research, INFORMS, vol. 51(6), pages 922-939, December.
    2. H. Edwin Romeijn & Dolores Romero Morales, 2003. "An asymptotically optimal greedy heuristic for the multiperiod single‐sourcing problem: The cyclic case," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 412-437, August.
    3. H. Edwin Romeijn & Dolores Romero Morales, 2001. "Generating Experimental Data for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 49(6), pages 866-878, December.

    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:jcomop:v:4:y:2000:i:3:d:10.1023_a:1009874227903. 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.