Author
Listed:
- Dimitris J. Bertsimas
(Massachusetts Institute of Technology, Cambridge, Massachusetts)
- Garrett van Ryzin
(Massachusetts Institute of Technology, Cambridge, Massachusetts)
Abstract
We propose and analyze a generic mathematical model for dynamic, stochastic vehicle routing problems, the dynamic traveling repairman problem (DTRP). The model is motivated by applications in which the objective is to minimize the wait for service in a stochastic and dynamically changing environment. This is a departure from classical vehicle routing problems where one seeks to minimize total travel time in a static, deterministic environment. Potential areas of application include repair, inventory, emergency service and scheduling problems. The DTRP is defined as follows: Demands for service arrive in time according to a Poisson process, are independent and uniformly distributed in a Euclidean service region, and require an independent and identically distributed amount of on-site service by a vehicle. The problem is to find a policy for routing the service vehicle that minimizes the average time demands spent in the system. We propose and analyze several policies for the DTRP. We find a provably optimal policy in light traffic and several policies with system times within a constant factor of the optimal policy in heavy traffic. We also show that the waiting time grows much faster than in traditional queues as the traffic intensity increases, yet the stability condition does not depend on the system geometry.
Suggested Citation
Dimitris J. Bertsimas & Garrett van Ryzin, 1991.
"A Stochastic and Dynamic Vehicle Routing Problem in the Euclidean Plane,"
Operations Research, INFORMS, vol. 39(4), pages 601-615, August.
Handle:
RePEc:inm:oropre:v:39:y:1991:i:4:p:601-615
DOI: 10.1287/opre.39.4.601
Download full text from publisher
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:39:y:1991:i:4:p:601-615. 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.