Optimal Fleet Mix and Ambulance Dispatching in

Emergency Medical Service Systems


Kenneth C. Chong

Shane G. Henderson

Mark E. Lewis

Cornell University
School of Operations Research and Information Engineering
Ithaca, New York 14853


We consider the problem of selecting the number of Advanced Life Support (ALS) and Basic Life Support

(BLS) ambulances— the fleet mix— to deploy in an emergency medical service system. ALS units can treat

a wider range of emergencies, while BLS units are less expensive to operate. Because the choice of fleet mix

can affect how ambulances are dispatched to incoming emergency calls, we construct a two-tiered model

incorporating both types of decisions. We model the dispatching problem as one of control of a two-class

queueing system with two types of servers, which we analyze using Markov decision process theory. We

show that the optimal policy takes the form of a monotone switching curve, but demonstrate that the

corresponding value function is, in general, not concave. From the value function induced by the optimal

policy, we obtain a measure by which system performance under a given fleet mix can be evaluated. We then

use this measure to solve a single-variate optimization problem to identify the optimal fleet mix, subject

to a budget constraint. Our numerical experiments indicate that, within the context of our model, all-ALS

fleets do not significantly outperform well-chosen mixed fleets.