  The dynamic vehicle dispatching problem corresponds to deciding which
vehicles to assign to requests that arise stochastically over time and space.
It emerges in diverse areas, such as in the assignment of trucks to loads to be
transported; in emergency systems; and in ride-hailing services. In this paper,
we model the problem as a semi-Markov decision process, which allows us to
treat time as continuous. In this setting, decision epochs coincide with
discrete events whose time intervals are random. We argue that an event-based
approach substantially reduces the combinatorial complexity of the decision
space and overcomes other limitations of discrete-time models often proposed in
the literature. In order to test our approach, we develop a new discrete-event
simulator and use double deep q-learning to train our decision agents.
Numerical experiments are carried out in realistic scenarios using data from
New York City. We compare the policies obtained through our approach with
heuristic policies often used in practice. Results show that our policies
exhibit better average waiting times, cancellation rates and total service
times, with reduction in average waiting times of up to 50% relative to the
other tested heuristic policies.
