Designing Robust Coverage Systems: A Maximal Covering Model with Geographically Varying Failure Probabilities

Covering models have been used in a wide range of modeling and geospatial analysis applications ranging from planning emergency services to natural reserve design. One topic in coverage modeling that has received considerable research attention is addressing uncertainty due to facility unavailability and service disruptions. In this article, we propose a covering model that maximizes the expected coverage of demand by considering the possibility of facility failures. Unlike existing models that assume a uniform failure probability across all sites in an area, the proposed model can account for spatially varying failure probabilities and describes better the underlying geographic processes that cause facility failures. The model is posed as a spatial optimization problem using integer linear programming. We compare two different formulations of the covering model and discuss their properties. The proposed model formulations have been tested computationally using a warning sirens data set that has been widely used in assessing covering models. We conclude with a summary of findings as well as possible directions of future research.