An Integer Linear Programming Formulation and Branch-and-Cut Algorithm for the Capacitated m-Ring-Star Problem Hern´ an Berinsky 1 Department of Computer Science University of Buenos Aires Buenos Aires, Argentina Paula Zabala 1 Department of Computer Science University of Buenos Aires Consejo Nacional de Investigaciones Cient´ ıficas y T´ ecnicas Buenos Aires, Argentina Abstract We study the capacitated m-ring-star problem (CmRSP ) that faces the design of minimum cost network structure that connects customers with m rings using a set of ring connections that share a distinguished node (depot ), and optionally star connections that connect customers to ring nodes. Ring and star connections have some associated costs. Also, rings can include transit nodes, named Steiner nodes, to reduce the total network cost if possible. The number of customers in each ring- star (ring’s customers and customer connected to it through star connections) have an upper bound (capacity ). These kind of networks are appropriate in optical fiber urban environments. CmRSP is know to be NP-Hard. In this paper we propose an integer linear pro- gramming formulation and a branch-and-cut algorithm. Keywords: network design, m-ring-star, branch-and-cut, integer programming. 1 Email: {hberins,pzabala}@dc.uba.ar Electronic Notes in Discrete Mathematics 37 (2011) 273–278 1571-0653/$ – see front matter © 2011 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm doi:10.1016/j.endm.2011.05.047