Integrating Expected Coverage and Local Reliability for Emergency Medical Services Location Problems

Daskin's, The Maximum Expected Covering Location Problem (MEXCLP) model 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, Maximum Availability Location Problem, offered two key advances, local vehicle busyness estimates and the x-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 x-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.