The Nested Hierarchical Median Facility Location Problem

A median model for the location of nested hierarchical facilities is presented. In hierarchical facility systems, there are multiple levels of service facilities such that each facility level provides different but related services. The specific hierarchical location system modeled is a nested facility hierarchy such that the location of a higher level facility at a site requires that the 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 no referrals exist. The nested hierarchical median problem is formulated as a binary linear program (BLP). 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. The computational experience for 2-level and 3-level locational systems on moderately sized networks is reported.