Hierarchical Survivable Network Design Problems

Abstract

We address the problem of designing two-level networks protected against single edge failures. A set of nodes must be partitioned into terminals and hubs, hubs must be connected through a backbone network, and terminals must be assigned to hubs and connected to them through access networks, being the objective to minimize the total cost. We consider two survivable structures, two-edge connected (2EC) networks and rings, in both levels of the network. We present an integer programming formulation for these problems, solve them using a branch-and-cut algorithm, and show some computational results.

Facility Location with Tree Topology and Radial Distance Constraints

“…eir examples include distribution systems where transshipment among stocking points are 2 Complexity of significant size, locating emergency facilities such as ambulance stations and fire fighting units with respect to population centers, gasoline stations, fast food restaurants, and spacing between wireless radio base stations, construction of nuclear power plants or missile silos nearby, and dump sites for chemical waste or collected refuse, to name a few. For a more general and deep review related with facility location topic, the reader is referred to [1][2][3][4][5][6][30][31][32] and references therein. In particular, Farahani et al [3] present a recent survey related with distance covering location problems together with a comprehensive review of models, solution approaches, and applications where it also highlights the importance of the distance factor required when designing facility networks.…”

“…We note that the authors also highlight the importance of considering connectivity among facilities in this reference. Finally, in the domain of telecommunications, some related works, although not so similar, can be consulted for instance in references [30][31][32].…”

“…Constraints (28) are valid cuts obtained from constraints (7) and adapted for the spanning tree polytope [10,22]. Finally, constraints (29) and (30) are valid cuts for the constraints (11) [11].…”