MC3-3 - Exact Approaches to the Single Source Network...

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Exact Approaches to the Single Source Network Loading Problem Ivana Ljubić * Peter Putz * Juan-José Salazar González ? * Department of Statistics and Decision Support Systems, University of Vienna Brünnerstr. 72, 1210 Vienna, Austria ? DEIOC, Universidad de La Laguna Av. Astrofísico Francisco Sánchez, s/n, 38271 La Laguna, Tenerife, Spain Abstract We consider the problem of deploying a broadband telecommunications system that lays optical fiber cable from a central office to a number of end-customers. We are dealing with a capacitated network design problem that requires an installation of fiber optic cables with sufficient capacity to carry the traffic from the central office to the end-customers. This is the single-source variant of the network loading problem . In this paper we propose a new compact disaggregated mixed integer programming (MIP) formulation for the problem. We project out flow variables by introducing Benders’ cuts that are further strengthened by additional inequalities. The whole procedure is incorporated into a branch-and-cut framework. In our computational experiments we do see improved gaps, when deploying Benders’ inequalities, at least in some cases. Reducing the computational cost for separating the Benders’ cuts and improving our primal heuristic to help closing the gap faster is the main focus of our ongoing effort. Keywords : Network Loading Problem, Branch-and-Cut, Benders Inequalities 1 Introduction We consider the problem of deploying a broadband telecommunications system that lays optical fiber cable from a central office to a number of end-customers . In case of the fiber to the home technology, the end- customers represent houses, whereas when deploying fiber to the curb technology, the end-customers are usually multiplexor devices. In both cases, we are dealing with a capacitated network design problem that requires an installation of fiber optic cables with sufficient capacity to carry the traffic from the central office to the end-customers. We start with a network without capacities, or with some pre-installed capacities, and search for the installation of at most one cable type per link at minimum total cost. In this paper we provide a theoretical and computational comparison of several mixed integer program- ming (MIP) formulations for the problem. We also propose a branch-and-cut approach based on the cut-set inequalities, extended with strengthening Benders’ inequalities. In our computational experiments we do see improved gaps, when deploying Benders’ inequalities, at least in some cases. Reducing the computational cost for separating the Benders’ cuts and improving our primal heuristic to help closing the gap faster is the main focus of our ongoing effort.
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