Hierarchical concentrator location problem

Abstract

This paper addresses the problem of locating concentrators in a computer communications network where a concentrator could be connected to another concentrator in a hierarchy. A mathematical programming model is developed. The objective is to minimize the costs of setting up and operating the communications network subject to capacity constraints. A Lagrangian relaxation approach is used to develop a heuristic solution procedure which is both efficient and effective. Extensive computational experiments were conducted to test the performance of the solution procedure. Problems with up to 200 terminal and 10 potential concentrator locations were studied. The gap between the feasible solution value and the best lower bound was used to judge the quality of the procedure. The mean gaps were in the range of 3–12% across a wide range of problem structures.