The nested hierarchical median facility location model

In this paper the authors deal with the location of nested hierarchical facilities. In hierarchical facility systems there are multiple levels of service facilities such that each facility level provides different but related services. The specific hierarchical locational system which we model is a nested facility hierarchy such that the location of a higher level facility at a site requires that services of all lower levels also be located at that site. In addition, it is assumed that all demand is serviced directly by the closest facility of the appropriate level and that there are no referrals. The authors formulate the nested hierarchical median problem as a binary linear program. The resulting BLPs can be solved with a Lagrangian dual bounding approach based on a novel extension of the corresponding p-median solution procedure and a special relaxation of the BLP formulation. Computational experience for 2-level and 3-level locational systems on moderately sized networks are reported.