A Clustering‐Based Approach to the Capacitated Facility Location Problem 1

This research develops a clustering-based location-allocation method to the Capacitated Facility Location Problem (CFLP), which provides an approximate optimal solution to determine the location and coverage of a set of facilities to serve the demands of a large number of locations. The allocation is constrained by facility capacities - different facilities may have different capacities and the overall capacity may be inadequate to satisfy the total demands. This research transforms this special location-allocation problem into a clustering model. The proposed approach has two parts: (1) the allocation of demands to facilities considering capacity constraints while minimizing the cost; and (2) the iterative optimization of facility locations using an adapted K-means clustering method. The quality of a location-allocation solution is measured using an objective function, which is the demand-weighted distance from demand locations to their assigned facilities. The clustering-based method is evaluated against an adapted Genetic Algorithm (GA) alternative, which integrates the allocation component as described above but uses GA operations to search for 'optimal' facility locations. Experiments and evaluations are carried out with various data sets (including both synthetic and real data).