Computational Optimization and Applications, 29, 127–146, 2004 c  2004 Kluwer Academic Publishers. Manufactured in The Netherlands. Telecommunication Network Capacity Design for Uncertain Demand * R. ANDRADE A. LISSER Abdel.Lisser@lri.fr Universit´ e de Paris Sud, Laboratoire de Recherche en Informatique, Bˆ at 490, Universit´ e de Paris Sud, 91405 Orsay, Cedex, France N. MACULAN Universidade Federal do Rio de Janeiro, COPPE-Sistemas, C.P. 68511, 21945-970, Rio de Janeiro, Brasil G. PLATEAU Universit´ e de Paris Nord, LIPN, Institut Galil´ ee, Avenue J.-B. Cl´ ement 93430, Villetaneuse, France Received March 22, 2002; Revised February 25, 2004 Abstract. The expansion of telecommunication services has increased the number of users sharing network resources. When a given service is highly demanded, some demands may be unmet due to the limited capacity of the network links. Moreover, for such demands, telecommunication operators should pay penalty costs. To avoid rejecting demands, we can install more capacities in the existing network. In this paper we report experiments on the network capacity design for uncertain demand in telecommunication networks with integer link capacities. We use Poisson demands with bandwidths given by normal or log-normal distribution functions. The expectation function is evaluated using a predetermined set of realizations of the random parameter. We model this problem as a two-stage mixed integer program, which is solved using a stochastic subgradient procedure, the Barahona’s volume approach and the Benders decomposition. Keywords: Benders decomposition, stochastic subgradient procedures, network design 1. Introduction The current progress in transmission technology allowed a considerable evolution in telecommunication systems. High speed networks improved traffic transmission rates and thus new services requiring more link capacities can be provided. Telecom companies need to reduce unmet requests for an increasing and unknown de- mand of services. For this, we can install additional capacity in the network links. The problem consists in minimizing total costs composed of investment and penalty costs. Concerning the uncertain parameters, we assume that the number of traffic scenarios is limited and discrete. The number of demands is given by a Poisson random variable and their bandwidths are given by normal or log-normal distribution functions. We consider these ∗ This work was supported by France Telecom R&D.