IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v41y1993i6p1055-1064.html
   My bibliography  Save this article

The Delivery Man Problem and Cumulative Matroids

Author

Listed:
  • Matteo Fischetti

    (University of Padova, Padova, Italy)

  • Gilbert Laporte

    (University of Torino, Torino, Italy)

  • Silvano Martello

    (University of Bologna, Bologna, Italy)

Abstract

Given a complete directed graph G = ( V , A ), the delivery man problem (DMP) consists of determining a Hamiltonian circuit minimizing the sum of distances (along the circuit) from a given vertex v 1 , to every vertex of V , including v 1 itself. There exists a number of applications of the DMP in the fields of distribution and machine scheduling. The DMP is NP-hard. The objective of this paper is to develop new theoretical results and an exact algorithm for the problem. A new, integer linear programming formulation is provided, and results on the matroidal structure of a class of combinatorial problems are developed. These are used to derive lower bounds for the DMP. These bounds are embedded into an enumerative algorithm. The largest problems solved to optimality with the proposed algorithm involve 60 vertices. This compares favorably with previously published methods.

Suggested Citation

  • Matteo Fischetti & Gilbert Laporte & Silvano Martello, 1993. "The Delivery Man Problem and Cumulative Matroids," Operations Research, INFORMS, vol. 41(6), pages 1055-1064, December.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:6:p:1055-1064
    DOI: 10.1287/opre.41.6.1055
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.41.6.1055
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.41.6.1055?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
    ---><---

    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:inm:oropre:v:41:y:1993:i:6:p:1055-1064. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.