How to locate services optimizing redundancy: A comparative analysis of K-Covering Facility Location models

Redundancy aspects related to covering facility location problems are of extreme importance for many applications, in particular those regarding critical services. For example, in the healthcare sector, facilities such as ambulances or first-aid centers must be located robustly against unpredictable events causing disruption or congestion. In this paper, we propose different modeling tools that explicitly address coverage redundancy for the underlying service. We also evaluate, both theoretically and experimentally, the properties and behavior of the models, and compare them from a computational and managerial point of view. More precisely, by starting from three classical double-covering models from the literature (BACOP1, BACOP2, and DSM), we define three parametric families of models (namely, K-BACOP1, K-BACOP2, and K-DSM) which generalize the former to any possible Kth coverage level of interest. The study of such generalizations allows us to derive interesting managerial insights on location decisions at the strategic level. The CPU performance and the quality of the solutions returned are assessed through ad-hoc KPIs collected over many representative instances with different sizes and topological characteristics, and also by dynamically simulating scenarios involving possible disruption for the located facilities. Finally, a real case study concerning ambulance service in Morocco is analyzed. The results show that, in general, K-BACOP1 performs very well, even if intrinsic feasibility issues limit its broad applicability. Instead, K-DSM achieves the best coverage and equity performances for lower levels of redundancy, while K-BACOP2 seems the most robust choice when high redundancy is required, showing smoother and more predictable trends.