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

Exponentially better than brute force: solving the jobshop scheduling problem optimally by dynamic programming

Contents:

Author Info

  • Gromicho, J.A.S.

    (Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics)

  • Hoorn, J.J. van
  • Timmer, G.T.
Registered author(s):

    Abstract

    Scheduling problems received substantial attention during the last decennia. The job-shop problem is a very important scheduling problem, which is NP-hard in the strong sense and with well-known benchmark instances of relatively small size which attest the practical difficulty in solving it. The literature on job-shop scheduling problem includes several approximation and optimal algorithms. So far, no algorithm is known which solves the job-shop scheduling problem optimally with a lower complexity than the exhaustive enumeration of all feasible solutions. We propose such an algorithm, based on the well-known Bellman equation designed by Held and Karp to find optimal sequences and which offers the best complexity to solve the Traveling Salesman Problem known to this date. For the TSP this means O(n22n) which is exponentially better than O(n!) required to evaluate all feasible solutions. We reach similar results by first recovering the principle of optimality, which is not obtained for free in the case of the job-shop scheduling problem, and by performing a complexity analysis of the resulting algorithm. Our analysis is conservative but nevertheless exponentially better than brute force. We also show very promising results obtained from our implementation of this algorithm, which seem to indicate two things: firstly that there is room for improvement in the complexity analysis (we observe the generation of a number of solutions per state for the benchmark instances considered which is orders of magnitude lower than the bound we could devise) and secondly that the potential practical implications of this approach are at least as exciting as the theoretical ones, since we manage to solve some celebrated benchmark instances in processing times ranging from seconds to minutes.

    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://degree.ubvu.vu.nl/repec/vua/wpaper/pdf/20090056.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics in its series Serie Research Memoranda with number 0056.

    as in new window
    Length:
    Date of creation: 2009
    Date of revision:
    Handle: RePEc:vua:wpaper:2009-56

    Contact details of provider:
    Email:
    Web page: http://www.feweb.vu.nl
    More information through EDIRC

    Related research

    Keywords: Job-shop scheduling; dynamic programming; complexity analysis;

    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:vua:wpaper:2009-56. 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: (R. Dam).

    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.