Designing radio-mobile access networks based on synchronous digital hierarchy rings

In this paper, we address the SDH network design problem (SDHNDP) which arises while designing the fixed part of global system for mobile communications access networks using synchronous digital hierarchy (SDH) rings. An SDH ring is a simple cycle that physically links a subset of antennae to a single concentrator. Inside a ring, a concentrator handles the total traffic induced by antennae. Technological considerations limit the number of antennae and the total length of a ring. The SDHNDP is a new problem. It belongs to a class of location-routing problems that introduce location into the multi-depot vehicle routing problem. In this paper, we precisely describe the SDHNDP and propose a mixed integer programming-based model for it. Furthermore, we devise a heuristic algorithm that computes a feasible solution. We report the results of our computational experiments using the CPLEX software, on instances comprising up to 70 antennae or six concentrator sites. An analysis provides insight into the behavior of the lower bound obtained by the LP relaxation of the model, in response to the network density. This lower bound can be improved by adding some valid inequalities. We show that an interesting cut can be obtained by approximating the minimum number of rings in any feasible solution. This can be achieved by solving a "minimum capacitated partition problem". Finally, we compare the lower bound to the heuristic solution value for a set of instances.