Abstract
We describe an ambulance service in terms of its main operation parameters and strategic decision variables. Assisted by queuing theory, we calculate the key performance indicators (KPI) that concern the manager and the KPI that concern the patient. We use them to improve the operation of a private ambulance service in Chile. First, we evaluate whether the historical performance is consistent with the resources deployed. Then, we estimate the impact of some operational enhancements, such as reducing the cycle time or enlarging the fleet. Finally, we optimize the geographical coverage of the bases. We conclude that simple mathematical expressions are very useful to evaluate and improve the operation.
Keywords: ambulances, queuing theory, performance

Introduction

Ambulance services must send a vehicle to the site of a medical emergency as fast as possible. Since they deal with life and death situations, they have drawn extensive attention from Operations Research [1]. A critical aspect of the service quality is the waiting time due to the possibility that ambulances are all busy. In order to understand its determinants, Markov chain models define a set of states or scenarios and the rates of transition among them, and calculate the steady-state probability of the system. With this methodology, Taylor & Templeton [2] analyze an ambulance service that takes emergency and regular calls. They conclude that, in order to respond to emergencies with promptitude, regular calls must be served only if a minimum number of vehicles remain idle. Brandeau & Larson [3] study an ambulance system using the “hypercube” model, which consists of a multidimensional Markov chain of multiple queues, one at each base. Goldberg & Szidarovszky [4] propose a method for calculating the ambulance busyness probabilities within the model. Mendonça & Morabito [5] use the hypercube to estimate the expected performance of an ambulance service in a Brazilian highway. Takeda et al. [6] use it to evaluate how much to decentralize a urban ambulance service.

Queuing models are an abstraction of Markov chain models. Green & Kolesar [7] assess their empirical validity to assign patrols to New York City police stations. They conclude that queuing theory provides good approximations of the system behavior. Singer et al. [8] configure a fleet whose vehicles get calls while on the route. The objective is to minimize operating costs subject to several constraints, including a maximum waiting time for customers, modeled using queuing formulas.

Publicado en Computers and Operations Research 35, 2549-2560.