A Decomposition Algorithm for Local Access Telecommunications Network Expansion Planning

Growing demand, increasing diversity of services, and advances in transmission and switching technologies are prompting telecommunication companies to rapidly expand and modernize their networks. This paper develops and tests a decomposition methodology to generate cost-effective expansion plans, with performance guarantees, for one major component of the network hierarchy-the local access network connecting customers to the local switching center. The model captures economies of scale in facility costs, and addresses the central tradeoff between installing concentrators and expanding cables to accommodate demand growth. By exploiting the special tree and routing structure of the expansion planning problem, our solution method integrates two major algorithmic strategies from mathematical programming-the use of valid inequalities, obtained by studying a problem's polyhedral structure, and dynamic programming, which can be used to solve an uncapacitated version of the local access network expansion planning problem. The computational results for three actual test networks demonstrate that this enhanced dynamic programming algorithm, when embedded in a Lagrangian relaxation scheme (with problem preprocessing and local improvement), is very effective in generating good upper and lower bounds: implemented on a personal computer, the method was able to generate solutions that are within 1.2 to 7.0% of optimality. In addition to developing a successful solution methodology for a practical problem, this paper illustrates the possibility of effectively combining decomposition methods and polyhedral approaches.