A Polyhedral Approach for Solving Two Facility Network Design Problem

Abstract

The paper studies the problem of designing telecommunication networks using transmission facilities of two different capacities. The point-to-point communication demands are met by installing a mix of facilities of both capacities on the edges to minimize total cost. We consider 3-partitions of the original graph which results in smaller 3-node subproblems. The extreme points of this subproblem polyhedron are enumerated using a set of proposed theorems. We introduce a new approach for computing the facets of the 3-node problem based on polarity theory after obtaining the extreme points. The facets of the subproblem are then translated back to those of the original problem using an extended version of a previously known theorem. We have tested our approach on several randomly generated and real life networks. The computational results show that 3-partition facets reduce the integrality gap by approximately 30-50% compared to that provided by 2-partition facets. Also there is a substantial reduction in the size of the branch-and-bound tree if these facets are used.