The maximal covering location problem with accessibility indicators

Abstract Maximal covering location problems have been widely studied, due to the practical applications of their solutions in real-life scenarios where it is not possible to fulfill the total demand. For example, these solutions can be used to provide humanitarian relief or to allocate fire stations, hospitals, and commercial services. However, coverage is commonly based on the ability of clients to reach the facilities or on the ability of facilities to serve clients within a reasonable area (or radius) or in a limited service time. In this study, we assume that facilities have a limited service area, while people in demand centroids have a degree of mobility encompassing a reasonable travel distance to look for their demand. Based on the latter assumption, we define a maximum covering location problem that optimizes an accessibility measure. This is a weighted sum of accessibility indicators based on the coverage of demand centroids, the number of demand centroids with access to opportunities within their mobility radius, the number and location of opportunities, a travel cost function, and spatial disaggregation. We formulate our optimization problem through a mixed-integer linear program; an experimental stage on randomly-generated instances shows that a commercial solver is capable of obtaining near-optimal solutions in reasonable computational times for large instances. In addition, we use data from an economically-deprived region in Mexico to perform a sensitivity analysis for different service and mobility radii. Finally, we implement the Linear Best Worst Method to obtain the value of weights parameters representing subjective preferences for different indicators of accessibility.

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