Decomposition of the Location Problem in a Hybrid Clustering-Location Model

Operations research is usually employed to solve the facility location problem, mainly using mixed integer linear programming (MILP). Meanwhile, some MILP models were not originally designed to solve a large class of location problems, corresponding to those where customers are served in a routing operation. In this case location and routing decisions are strongly interrelated. Moreover, this modeling approach has the difficult of facing a NP-hard problem situation, which means a very high algorithm complexity. Therefore, for large-scale problems the computational times are practically infeasible. This paper has developed an alternative method using a hybrid approach to solve the location problem, taking into account these two aspects: the NP- hard situation and the routing operation. The suggestion is to decompose the problem through a clustering procedure applied to the demand points, followed by the application of an optimization model to each cluster. The proposal appeared to be effective when applied to a set of test problems used on a conducted experiment designed to validate the method.