Cluster tools are closed mini production environments that are especially used in the semiconductor industry. They consist of multiple processing chambers. In contrast to single processing tools they can handle multiple lots with different process characteristics at the same time. The major challenge for scheduling cluster tools is the hard to predict process times of even comparable lots as they strongly depend on a changing product mix over the tool. In this paper a mathematical model for the external scheduling of a cluster tool workstation is presented. The goal is to minimize the weighted cycle time by accounting for the changing cycle times of each lot. A MIP model assigns lots to tools of a workstation and determines for each lot the chambers, which are used during the processing steps inside the cluster tool. Finally the developed method is compared with a simulation that uses dispatching strategies.