The Capacitated m-Ring-Star Problem R. Baldacci Dipartimento di Elettronica, Informatica e Sistemistica, University of Bologna, Via Venezia, 52, 47023 Cesena, Italy, rbaldacci@deis.unibo.it M. Dell’Amico 1 Dipartimeto di Scienze e Metodi dell’Ingegneria, University of Modena and Reggio Emilia Via Allende 2, 42100 Reggio Emilia, Italy, dellamico@unimore.it J. Salazar Gonz´alez DEIOC, Facultad de Matem´ aticas, Universidad de La Laguna 38271 La Laguna, Tenerife, Spain, jjsalaza@ull.es Received June 2004; revised August 2005; accepted January 2007 Abstract The Capacitated m-Ring-Star Problem (CmRSP) is the problem of design- ing a set of rings that pass through a central depot and through some transi- tion points and/or customers, and then assigning each non-visited customer to a visited point or customer. The number of customers visited and assigned to a ring is bounded by an upper limit: the capacity of the ring. The objec- tive is to minimize the total routing cost plus assignment costs. The problem has practical applications in the design of urban optical telecommunication networks. This paper presents and discusses two integer programming for- mulations for the CmRSP. Valid inequalities are proposed to strengthen the linear programming relaxation, and are used as cutting planes in a branch- and-cut approach. The procedure is implemented and tested on a large family of instances, including real-world instances, and the good performance of the proposed approach is demonstrated. Subject classifications : Networks/graphs: optical network design. Programming, integer, cutting plane: Branch-and-cut algorithm. Area of review : Telecommunications and Networking. 1 Corresponding author: Mauro Dell’Amico, University of Modena and Reggio Emilia, via Allende, 2, 42100 Reggio Emilia, Italy, Tel. +39-0522-522-228, Fax +39-0522-522-230, e-mail dellamico@unimore.it. 1