The ring/κ‐rings network design problem: Model and branch‐and‐cut algorithm

Abstract

This article considers the problem of designing a two‐level network where the upper level consists of a backbone ring network connecting the so‐called hub nodes, and the lower level is formed by access ring networks that connect the non‐hub nodes to the hub nodes. There is a fixed cost for each type of link, and a facility opening cost associated to each hub. The number of nodes in each access ring is bounded, and the number of access rings connected to a hub is limited to italicκ , thus resulting in a ring/ italicκ ‐rings topology. The aim is to decide the hubs to open and to design the backbone and access rings to minimize the installation cost. We propose a mathematical model, give valid inequalities, and describe a branch‐and‐cut algorithm to solve the problem. Computational results show the algorithm is able to find optimal solutions on instances involving up to 40 nodes within a reasonable time. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(2), 130–140 2016

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].…”

Um modelo estendido para o problema de roteamento em anéis de dois níveis

“…Variações do problema já foram estudadas na literatura, utilizando-se outros métodos para a sua solução, como em [Rodríguez-Martín et al 2016a] e [Rodríguez-Martín et al 2016b], que utilizam a abordagem branch-andcut.…”