Mathematics of Operations Research
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The Dynamic Assignment Problem
Transportation Science
Approximation Algorithms for Orienteering and Discounted-Reward TSP
SIAM Journal on Computing
Dynamic multi-vehicle routing with multiple classes of demands
ACC'09 Proceedings of the 2009 conference on American Control Conference
A Stochastic and Dynamic Vehicle Routing Problem with Time Windows and Customer Impatience
Mobile Networks and Applications
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In this paper we introduce a dynamic vehicle routing problem in which there are multiple vehicles and multiple priority classes of service demands. Service demands of each priority class arrive in the environment randomly over time and require a random amount of on-site service that is characteristic of the class. To service a demand, one of the vehicles must travel to the demand location and remain there for the required on-site service time. The quality of service provided to each class is given by the expected delay between the arrival of a demand in the class and that demand's service completion. The goal is to design a routing policy for the service vehicles which minimizes a convex combination of the delays for each class. First, we provide a lower bound on the achievable values of the convex combination of delays. Then, we propose a novel routing policy and analyze its performance under heavy-load conditions (i.e., when the fraction of time the service vehicles spend performing on-site service approaches one). The policy performs within a constant factor of the lower bound, where the constant depends only on the number of classes, and is independent of the number of vehicles, the arrival rates of demands, the on-site service times, and the convex combination coefficients.