Integrating expected coverage and local reliability for emergency medical services location problems

Daskin's MEXCLP model [Daskin M. A maximum expected covering location model: formulation, properties, and heuristic solution. Transportation Science 1983;17:48–70] was one of the first efforts to capture the stochastic nature of emergency medical services (EMS) location problems within a mixed-integer formulation. With their subsequent introduction of MALP, ReVelle and Hogan [The maximum availability location problem. Transportation Science 1989;23:192–200] offered two key advances, local vehicle busyness estimates and the α-reliability objective. While these constructs have influenced many subsequent EMS location models, they have been subjected to relatively little empirical analysis. To address this, we introduce the LR-MEXCLP, a hybrid model combining the local busyness estimates of MALP with the maximum coverage objective of MEXCLP. We then solve a series of problems with all three models and employ simulation to estimate aggregate service levels. We find that LR-MEXCLP leads to modest but consistent service gains over both MALP and MEXCLP. These results support the merits of local busyness estimates, but they also suggest that the α-reliability objective may be inappropriate when seeking to maximize aggregate system response capabilities. More generally, our research underscores the utility of (a) linking modeling assumptions and goals with real-world application contexts, and (b) employing simulation or other techniques to validate theoretical results.