Optimal Coverage Analysis of Existing Public Facility using the Capacitated P-Center Model

Abstract

The P-Center problem algorithm has been one of the most famous ways of providing solutions for locating facilities. Despite the frequent usage of this algorithm, research on the integration of Geographical Information Systems (GIS) and the P-Centre problem has not been much explored. This research uses the P-Centre problem approach in providing a solution to determining the optimal location of existing public facilities within the Shomolu Local Government Area, with the primary goal of minimizing the maximum travel distance from each demand node to the closest facility. Primary and secondary school's optimum and tolerable distances from the residential areas were determined. Spatial analysis was carried out on the sufficiency or otherwise of Primary and Secondary Schools within the Local Government Area. Multi-criteria queries were carried out, and results revealed that between 2011 and 2015, the Local Government Area did not have a sufficient number of schools to meet the demand, while from 2016 - 2020, schools will be grossly inadequate. Polynomials were derived for these deficiencies, which can be used to predict future deficiencies if relevant government agencies fail to provide more schools as the population increases.