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We consider a generalization of the connected facility location problem where the clients must be connected to the open facilities via shared capacitated (tree) networks instead of independent shortest paths. This problem arises in the planning of ber optic telecommunication access networks, for example. Given a set of clients with positive demands, a set of potential facilities with opening costs, a set of capacitated access cable types, and a core cable type of innite capacity, one has to decide which facilities to open, how to interconnect them using a Steiner tree of innite capacity core cables, and which access cable types to install on which potential edges such that these edges form a forest and the installed capacities suce to simultaneously route the client demands to the open facilities via single paths. The objective is to minimize the total cost of opening facilities, building the core Steiner tree among them, and installing the access cables. In this paper, we devise a constant-factor approximation algorithm for problem instances where the access cable types obey economies of scale. In the special case where only multiples of a single cable type can be installed on the access edges, a variant of our algorithm achieves a performance guarantee of 6.72.
We consider a generalized version of the rooted connected facility location problem which occurs in planning of telecommunication networks with both survivability and hop-length constraints. Given a set of client nodes, a set of potential facility nodes including one predetermined root facility, a set of optional Steiner nodes, and the set of the potential connections among these nodes, that task is to decide which facilities to open, how to assign the clients to the open facilities, and how to interconnect the open facilities in such a way, that the resulting network contains at least edge-disjoint paths, each containing at most H edges, between the root and each open facility and that the total cost for opening facilities and installing connections is minimal. We study two IP models for this problem and present a branch-and-cut algorithm based on Benders decomposition for nding its solution. Finally, we report computational results.