The ring/k-rings network design problem : model and branch-and-cut algorithm

Rodriguez-Martin, Inmaculada and Salazar-Gonzalez, Juan-Jose and Yaman, Hande (2016) The ring/k-rings network design problem : model and branch-and-cut algorithm. Networks, 68 (2). pp. 130-140. ISSN 0028-3045

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 urn:x-wiley:00283045:media:net21687:net21687-math-0001, thus resulting in a ring/ urn:x-wiley:00283045:media:net21687:net21687-math-0002‐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.