A Separable Programming Approach to Expected Coverage: An Application to Ambulance Location

A separable programming approach is developed for the maximum expected covering location problem (MEXCLP), which is encountered often in emergency medical services applications. Ambulances must be located to ensure efficient response time, subject to the constraint that ambulances will be available for service only when they are not out on other calls. With separable programming, the problem is formulated as a nonlinear MEXCLP. The nonlinear formulation can be extended to guarantee minimum coverage (and optimality) through the incorporation of specifications for the satisfaction of expected coverage criteria such that each node be covered a minimum number of times. In addition, the formulation can be extended to allow simultaneous consideration of different types of expected coverage criteria through construction of a coverage matrix. In application to sample problems, the nonlinear MEXCLP is shown to yield optimal solutions very quickly.