A Clustering - Based Approach to a Special Capacitated Facility Location Problem

This paper presents a clustering-based approach to address a special case of the Capacitated Facility Location Problem (CFLP). The goal is to find the optimal locations of a finite set of facilities to satisfy the demands of a large set of fixed locations, while the sum of the demands at the point locations associated with the same facility cannot exceed its capacity. We develop a clustering-based approach to this special CFLP instance and evaluate this approach with various experiments. The overall performance is evaluated using the average distance from the point locations to their assigned facilities. The experiments on data sets of random distribution and clustered distribution show that the clustering-based approach can lead to near-optimal configurations of facility locations with fast converges, no matter whether the capacity of facilities is sufficient or insufficient for the total demands. We also test the method with a real data set (i.e., allocating emergency shelters to serve people on a Caribbean island), where demands at point locations are not equal and the capacities of facilities are not the same.