We examine the possibilities of concurrently processing multiple wafer types in a cluster tool. In this paper, we propose a way of cyclically mixing two wafer types for a single-armed cluster tool and scheduling the tool operation. For a given cycle plan, we also develop a method of optimally scheduling the tool so as to minimize the cycle time. We wish to compare cycle plans that optimize different performance measures such as tool utilization, throughput rate, etc. To do this, for a given cycle plan, we develop a Petri net model for the tool's operational behavior. We also develop a necessary and sufficient condition for which the conventional simple optimal backward sequence for a single wafer case is still optimal; that is, it minimizes the tool cycle time for concurrent processing. Moreover, for some identified conditions, all wafer types can achieve their maximum throughput rates in a concurrent schedule by the backward sequence, over all possible schedules. For the case where the backward sequence is not optimal, we develop a mixed integer programming (MIP) for determining an optimal robot task sequence and schedule, which can be efficiently solved by various algorithms or commercial solvers. Finally, through illustrative examples, we compute the optimal cycle times and schedules for various cycle plans and operational strategies.