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In our work we consider the cost optimal optical ring design problem. Given a set of wavelength demands between nodes which are arranged in a fiber ring topology, the problem is one of designing multiple optical rings stacked on the topology to carry the nodal demands with three different ring-interworking constraints. This design is to be carried out in a manner to minimize the overall equipment cost which includes two major components: a nodal optical ring switch cost and a fixed per ring cost. The ring-interworking schemes dealt with in this work are single-node ring interworking (SRI), basic dual-node ring interworking (DRI) and DRI with protection access. We have proposed an LP column generation based heuristic and a cost lower bound for each of the three constrained design cases. In numerical studies, the heuristic was observed to produce designs within 10 - 15% of the cost lower bound in the worst cases and within 1% on average.