Unlike siting a high school or a library, in which the criterion for a good location is the least aggregate travel of the people who use the facility, emergency services are best sited by using a distance or time standard. The measure wasn't invented by me and my students, but we were the first to show how to use it in mathematical equations that find best locations.

If we can get as many people as possible within a community covered (say 95 percent) within the time standard (say 15 minutes) by an available ambulance, given the total ambulance resources available, then we have an effective deployment pattern for ambulances.

Of course, it's not unusual for ambulances to be out on the road, and not at the position at which they were initially stationed. That's an important situation to deal with for two reasons. First, if the nearest stationed ambulance isn't actually available (even though it was stationed initially within the time standard), the responding ambulance will have to come from further away--maybe from outside the time standard, which defeats the initial deployment plan. Second, if the ambulance nominally stationed at some position is nearly always running, the emergency medical crews run the risk of being overworked.

Using a tool known as integer programming (it's a form of optimization of resource utilization), we can deploy the total ambulance resources in such a way that for each demand area, the probability of an ambulance actually being available within the time standard is at least 90 percent or 95 percent, depending on the specification of those in charge--assuming there are sufficient ambulance resources in the system. It turns out that when we accomplish such a deployment, we also limit the workload to manageable levels.

Housing ambulances within hospitals makes most sense in small urban areas with low ambulance demand because the trained personnel can help out at the hospital when they are not out on calls. If, on the other hand, the ambulances are on the street a significant proportion of the time, placing them at the hospital makes less sense. What's more, if the hospital or hospitals are centrally located, this makes for longer response times to people who live on the periphery.

Fire stations, conversely, are probably dispersed across the city--as they should be--and this makes them a better choice if the ambulances keep busy.

Consider the case of a two-hospital system (1, 7) with seven ambulances deployed optimally (3,5,11,13,14,16,21).

Notice that the best ambulance locations are not at the hospitals. The ambulances face a time standard that includes going to the scene and transporting from the scene back to the hospital. If the ambulances were located at the hospitals, in order to meet calls at the periphery of the region, they would have to travel from hospital to distant demand and back to hospital--a long time on the road. On the other hand, if the ambulances are sited at outer nodes (perhaps these are fire stations), the ambulances can pick up calls at those outer nodes and dash directly in to the hospitals. So in this situation deploying ambulances at the hospitals looks quite inefficient.

The county council members in Paradise, Florida, might also do well to consider basing their ambulances at independent stations- -even if it means building new structures. With independent stations, ambulances can be deployed nearest the high demands-- near the high-risk bars with the knife fights, nearer the curving expressway with the bad merge and blind spots. And the additional cost isn't as much as you might think: the largest, most significant cost of an ambulance system is the 24-hour-a-day personnel, not the building.

I'm not saying that hospitals and fire stations should never be chosen for ambulance depots. If the use of existing hospital and fire stations is efficient from a location standpoint, it makes sense to choose them, but if it is not, other alternatives should be considered.

RETURN TO APRIL 1997 TABLE OF CONTENTS.