Dynamic Multi-Vehicle Routing with Multiple Classes of Demands

TL;DR

This paper addresses a complex dynamic vehicle routing problem with multiple vehicle classes and demand types, proposing a novel policy that nearly achieves the theoretical lower bound on delay performance under heavy load conditions.

Contribution

It introduces a new routing policy for multi-class, multi-vehicle demand environments and proves its near-optimality in heavy load scenarios, independent of many system parameters.

Findings

Policy performs within a constant factor of the lower bound.

Constant factor depends only on the number of classes.

Performance analysis under heavy load conditions shows near-optimality.

Abstract

In this paper we study a dynamic vehicle routing problem in which there are multiple vehicles and multiple classes of demands. Demands of each 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 (and thus the optimal), 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.