Vehicle routing problem

The vehicle routing problem (VRP) is a combinatorial optimization and nonlinear programming problem seeking to service a number of customers with a fleet of vehicles. Proposed by Dantzig and Ramser in 1959, VRP is an important problem in the fields of transportation, distribution and logistics. [cite journal
author = Dantzig, G.B.
coauthors = Ramser, J.H.
year = 1959
title = The Truck Dispatching Problem
journal = Management Science
volume = 6
issue = 1
pages = 80-91
url = http://links.jstor.org/sici?sici=0025-1909(195910)6%3A1%3C80%3ATTDP%3E2.0.CO%3B2-A
accessdate = 2008-04-17] Often the context is that of delivering goods located at a central depot to customers who have placed orders for such goods. Implicit is the goal of minimizing the cost of distributing the goods. Many methods have been developed for searching for good solutions to the problem, but for all but the smallest problems, finding global minimum for the cost function is computationally complex.

Overview

Several variations and specializations of the vehicle routing problem exist:
* Vehicle Routing Problem with Pickup and Delivery (VRPPD): A number of goods need to be moved from certain pickup locations to other delivery locations. The goal is to find optimal routes for a fleet of vehicles to visit the pickup and drop-off locations.
* Vehicle Routing Problem with LIFO: Similar to the VRPPD, except an additional restriction is placed on the loading of the vehicles: at any delivery location, the item being delivered must be the item most recently picked up. This scheme reduces the loading and unloading times at delivery locations because there is no need to temporarily unload items other than the ones that should be dropped off.
* Vehicle Routing Problem with Time Windows (VRPTW): The delivery locations have time windows within which the deliveries (or visits) must be made.
* Capacitated Vehicle Routing Problem (with or without Time Windows): CVRP or CVRPTW. The vehicles have limited carrying capacity of the goods that must be delivered.

Although VRP is related to the Job Shop Scheduling Problem, the two problems are typically solved using different techniques. cite conference | author = Beck, J.C. | coauthors = Prosser, P.; Selensky, E. | year = 2003 | title = Vehicle routing and job shop scheduling: What’s the difference | conference = | booktitle = Proceedings of the 13th International Conference on Artificial Intelligence Planning and Scheduling | publisher =
url = http://www.dcs.gla.ac.uk/pras/pubs/Icaps03.pdf | conferenceurl = ]

ee also

* Travelling salesman problem

References

Further reading

*
* cite journal | author = Psaraftis, H.N. | year = 1988 | title = Dynamic vehicle routing problems
journal = Vehicle Routing: Methods and Studies | volume = 16 | pages = 223-248
* cite journal | author = Bertsimas, D.J. | coauthors = Van Ryzin, G. | year = 1991 | title = A Stochastic and Dynamic Vehicle Routing Problem in the Euclidean Plane | journal = Operations Research | volume = 39 | issue = 4
pages = 601-615 | url = http://links.jstor.org/sici?sici=0030-364X(199107%2F08)39%3A4%3C601%3AASADVR%3E2.0.CO%3B2-P | accessdate = 2008-04-17
*

External links

* [http://www.dna-evolutions.com/dnaappletsample.html Demo applet of a evolutionary algorithm for solving TSP's and VRPTW problems]
* [http://neo.lcc.uma.es/radi-aeb/WebVRP/ WebVRP]