The capacitated m-ring-star problem

The Capacitated m-Ring-Star Problem (CmRSP) is the problem of designing a set of rings that pass through a central depot and through some transition points and/or customers, and then assigning each nonvisited 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 objective 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 formulations 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.