Optimal Ambulance Dispatching

Abstract

This chapter considers the ambulance dispatch problem, in which one must decide which ambulance to send to an incident in real time. In practice as well as in literature, it is commonly believed that the closest idle ambulance is the best choice. This chapter describes alternatives to the classical closest idle ambulance rule. Our first method is based on a Markov decision problem (MDP), which constitutes the first known MDP model for ambulance dispatching. Moreover, in the broader field of dynamic ambulance management, this is the first MDP that captures more than just the number of idle vehicles, while remaining computationally tractable for reasonably-sized ambulance fleets. We analyze the policy obtained from this MDP, and transform it to a heuristic for ambulance dispatching that can handle the real-time situation more accurately than our MDP states can describe. We evaluate our policies by simulating a realistic emergency medical services region in the Netherlands. For this region, we show that our heuristic reduces the fraction of late arrivals by 13% compared to the “closest idle” benchmark policy. This result sheds new light on the popular belief that deviating from the closest idle dispatch policy cannot greatly improve the objective.

Appendix: Notation

Notation in this chapter	Common notation
$\mathcal{A}_{s}$	A(s)
R(s, a)	r a(s)
p a(s, s′)	p(s | s′, a)
V i (s)	V t (s)