An Integer Linear Programming based heuristic for the Capacitated m-Ring-Star Problem

We address the Capacitated m-Ring-Star Problem in which the aim is to find m rings (simple cycles) visiting a central depot, a subset of customers and a subset of potential (Steiner) nodes, while customers not belonging to any ring must be “allocated” to a visited (customer or Steiner) node. Moreover, the rings must be node-disjoint and the number of customers allocated or visited in a ring cannot be greater than a given capacity Q. The objective is to minimize the total visiting and allocation costs. The Capacitated m-Ring-Star Problem is NP-hard, since it generalizes the Traveling Salesman Problem.