The pq-median problem: Location and districting of hierarchical facilities

To achieve an efficient and effective hierarchical location system, it is necessary to obtain not only an efficient set of facility locations, but also an efficient districting of the catchment areas, since these areas will be the ones to benefit from the services provided by the located facilities. In seeking an effective relation among the different levels in a hierarchy of facilities, all the cells assigned to a particular facility at one hierarchical level should belong to one and the same district in the next level of the hierarchy. This property leads to a ‘coherent’ districting structure. The research presented here concerns the optimal location and districting of hierarchical facilities in a network. A linear integer model that locates facilities in a two-level hierarchical system is presented in this paper; the pq-median model minimizes average distance to the closest facility in each hierarchy, while coherence among the levels of the hierarchy is enforced. Solution methods and computer times are provided.