Modular capacitated maximal covering location problem for the optimal siting of emergency vehicles

Abstract

To improve the application of the maximal covering location problem (MCLP), several capacitated MCLP models were proposed to consider the capacity limits of facilities. However, most of these models assume only one fixed capacity level for the facility at each potential site. This assumption may limit the application of the capacitated MCLP. In this article, a modular capacitated maximal covering location problem (MCMCLP) is proposed and formulated to allow several possible capacity levels for the facility at each potential site. To optimally site emergency vehicles, this new model also considers allocations of the demands beyond the service covering standard. Two situations of the model are discussed: the MCMCLP-facility-constraint (FC), which fixes the total number of facilities to be located, and the MCMCLP-non-facility-constraint (NFC), which does not. In addition to the model formulations, one important aspect of location modeling—spatial demand representation—is included in the analysis and discussion. As an example, the MCMCLP is applied with Geographic Information System (GIS) and optimization software packages to optimally site ambulances for the Emergency Medical Services (EMS) Region 10 in the State of Georgia. The limitations of the model are also discussed.