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Cluster tools (also referred to as robotic cells) are extensively used in semiconductor wafer fabrication. We consider the problem of scheduling operations in an m -machine cluster tool that produces identical parts (wafers). Each machine is equipped with a unit-capacity input buffer and a unit-capacity output buffer. The machines and buffers are served by a dual-gripper robot. Each wafer is processed on each of the m machines, and the objective is to find a cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes the throughput. We first obtain a tight upper bound on the optimal throughput and then use this bound to obtain an asymptotically optimal sequence under conditions that are common in practice. Next, we quantify the improvement in productivity that can be realized from the use of unit-capacity input and output buffers at the machines. Finally, we illustrate our analysis on cluster tools with realistic parameters, based on our work with a Dallas-based semiconductor equipment manufacturer.