IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v41y1993i1p60-76.html
   My bibliography  Save this article

Stochastic and Dynamic Vehicle Routing in the Euclidean Plane with Multiple Capacitated Vehicles

Author

Listed:
  • Dimitris J. Bertsimas

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Garrett van Ryzin

    (Columbia University, New York, New York)

Abstract

In 1991, D. J. Bertsimas and G. van Ryzin introduced and analyzed a model for stochastic and dynamic vehicle routing in which a single, uncapacitated vehicle traveling at a constant velocity in a Euclidean region must service demands whose time of arrival, location and on-site service are stochastic. The objective is to find a policy to service demands over an infinite horizon that minimizes the expected system time (wait plus service) of the demands. This paper extends our analysis in several directions. First, we analyze the problem of m identical vehicles with unlimited capacity and show that in heavy traffic the system time is reduced by a factor of 1/ m 2 over the single-server case. One of these policies improves by a factor of two on the best known system time for the single-server case. We then consider the case in which each vehicle can serve at most q customers before returning to a depot. We show that the stability condition in this case depends strongly on the geometry of the region. Several policies that have system times within a constant factor of the optimum in heavy traffic are proposed. Finally, we discuss extensions to mixed travel cost and system time objectives.

Suggested Citation

  • Dimitris J. Bertsimas & Garrett van Ryzin, 1993. "Stochastic and Dynamic Vehicle Routing in the Euclidean Plane with Multiple Capacitated Vehicles," Operations Research, INFORMS, vol. 41(1), pages 60-76, February.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:1:p:60-76
    DOI: 10.1287/opre.41.1.60
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.41.1.60
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.41.1.60?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:1:p:60-76. 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.