Abstract
This article traces the evolution of ambulance location and relocation models proposed over the past 30years. The models are classified in two main categories. Deterministic models are used at the planning stage and ignore stochastic considerations regarding the availability of ambulances. Probabilistic models reflect the fact that ambulances operate as servers in a queueing system and cannot always answer a call. In addition, dynamic models have been developed to repeatedly relocate ambulances throughout the day.
1. Introduction
This review article traces the evolution of ambulance location and relocation models proposed over the past 30years. This period was marked by an unprecedented growth not only in computer technology, but also in modeling and algorithmic sophistication, in the performance of mathematical programming solvers, and in the widespread adoption of computer software at several levels of decision making. The literature on ambulance positioning systems truly reflects this evolution. The first models proposed were unsophisticated integer linear programming formulations, but over time more realistic features were gradually introduced, and solution techniques also evolved.
7. Summary and conclusions
There has been an important evolution in the development of ambulance location and relocation models over the past thirty years. The first models were very basic and did not take into account the fact that some coverage is lost when an ambulance is dispatched to a call. Nevertheless, these early models served as a sound basis for the development of all subsequent models. The question of ambulance non-availability was addressed in two main ways. Deterministic models yield solutions in which demand points are overcovered, but the actual availability of ambulances is not considered. Probabilistic models work with the busy fraction of vehicles, which can be estimated in a number of ways, including sophisticated queueing calculations. Dynamic models have just started to emerge. They can be used to periodically update ambulance positions throughout the day. Tests have shown that such models can work in practice provided that fast heuristics exist and sufficient computing power are available. We summarize in Tables 1 and 2 the main available deterministic and probabilistic models for ambulance location and relocation.
