90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
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In this paper we study the cost-optimal deployment of optical access networks considering variants of the problem such as fiber to the home (FTTH), fiber to the building (FTTB), fiber to the curb (FTTC), or fiber to the neighborhood (FTTN). We identify the combinatorial structures of the most important sub-problems arising in this area and model these, e.g., as capacitated facility location, concentrator location, or Steiner tree problems. We discuss modeling alternatives as well. We finally construct a “unified” integer programming model that combines all sub-models and provides a global view of all these FTTx problems. We also summarize computational studies of various special cases.
In this paper, we study the hop constrained chain polytope, that is, the convex hull of the incidence vectors of (s,t)-chains using at most k arcs of a given digraph, and its dominant. We use extended formulations (implied by the inherent structure of the Moore-Bellman-Ford algorithm) to derive facet defining inequalities for these polyhedra via projection. Our findings result into characterizations of all facet defining {0,+1,-1}-inequalities for the hop constrained chain polytope and all facet defining {0,1}-inequalities
for its dominant. Although the derived inequalities are already known, such classifications were not previously given to the best of our knowledge. Moreover, we use this approach to generalize so called jump inequalities, which have been introduced in a paper of Dahl and Gouveia in 2004.