The Multiple Gradual Maximal Covering Location Problem

This article describes a new spatial optimization model, the Multiple Gradual Maximal Covering Location Problem (MG-MCLP). This model is useful when coverage from multiple facilities or sensors is necessary to consider a demand to be covered, and when the quality of that coverage varies with the number of located facilities within the service distance, and the distance from the demand itself. The motivating example for this model uses a coupled GIS and optimization framework to determine the optimal locations for acoustic sensors-typically used in police applications for gunshot detection-in Tuscaloosa, AL. The results identify the optimal facility locations for allocating multiple facilities, at different locations, to cover multiple demands and evaluate those optimal locations with distance-decay. Solving the MG-MCLP over a range of values allows for comparing the performance of varying numbers of available resources, which could be used by public safety operations to demonstrate the number of resources that would be required to meet policy goals. The results illustrate the flexibility in designing alternative spatial allocation strategies and provide a tractable covering model that is solved with standard linear programming and GIS software, which in turn can improve spatial data analysis across many operational contexts.