The semiconductor manufacturing industry is significantly expensive both in equipment and materials. Cluster tools, a type of automated manufacturing system integrating processing modules and transport modules, are commonly used in this industry. Nowadays, multi-cluster tools, which are composed of several cluster tools connected by joint buffer modules, are often used for wafer production. This paper deals with K-unit cycle scheduling problems in single-armed two-cluster tools for processing identical wafers in deterministic settings. In a K-unit cycle, K wafers are exactly inserted into the two-cluster tool, and K completed wafers leave the two-cluster tool, usually not the same K wafers. Residency constraints and general moving times by the robot are both considered. The objective is to obtain optimal K-unit cycle schedules, which minimize cycle times. To analyze this scheduling problem in detail, a mixed integer linear programming (MILP) model is formulated and solved. Numerical examples are used to explain how the solution can be obtained from the MILP model in a K-unit cycle.