Traffic grooming has become an increasingly important area in optical networking research in recent years. Very recently, a min-max approach to network cost optimization has emerged as a new focus area. In this cost model, it is assumed that different network nodes will be provisioned with similar Opto-Electro-Optic (OEO) equipment; hence an objective seeking to minimize the maximum OEO capability needed at any node is appropriate. In this paper, we propose heuristics for traffic grooming with this objective in ring networks, which are practically important. We advance two approaches, both based on the concept of partitioning the traffic matrix, but in different ways. The approaches are of complementary strength, being useful for different traffic patterns. We present numerical results validating the performance of the algorithms.