Protecting telecommunications networks : toward a minimum-cost solution

The problem of designing fibre-optic networks for telecommunications can be decomposed into (at least) three non-trivial subproblems. In the first of these subproblems one must determine how many fibre-optic cables (fibres) are required at either end of a street. In the next subproblem a minimumcost network must be designed to support the fibres. The network must also provide distinct paths from either end of the street to the central exchange(s). Finally, the fibre-optic cables must be placed in protective covers. These covers are available in a number of different sizes, allowing some flexibility when covering each section of the network. However, fibres placed within a single cover must always be covered together for maintenance reasons. In this paper we describe two formulations for finding a minimum-cost (protective) covering for the network (the third of these subproblems). This problem is a generalised set covering problem with side constraints and is further complicated by the introduction of fixed and variable welding costs. The first formulation uses dynamic programming (DP) to select covers along each arc (in the network). However, this formulation cannot accurately model the fixed costs and does not guarantee optimality. The second formulation, based on the DP formulation, uses integer programming (IP) to solve the problem and guarantees optimality, but is only tractable for smaller problems. The cost of the networks constructed by the IP model is less than those designed using the DP model, but the saving is not significant for the problems examined (less than 0.1%). This indicates that the DP model will generally give very good solutions despite its limitation. Furthermore, as the problem dimensions grow, DP gives significantly better solution times than IP.