The hierarchical network design problem

Abstract

In this paper the authors introduce the hierarchical network design problem (HNDP). The object of the HNDP is to identify the least cost, two-level hierarchical network. The network must include a primary path from a predetermined starting node to a predetermined terminus node. In addition, each node not on the primary path must be connected to some node on that path by means of a secondary path. The problem is initially formulated as an integer linear program. An heuristic is then presented which employs a K shortest path algorithm, and a minimum spanning tree algorithm. Heuristic results of two sample problems are presented and compared to the results obtained by solving the integer LP formulation. Potential applications of the formulation are also discussed.