Cyclic scheduling of multi-type wafers concurrent processing in single-arm cluster tools with residency time constraints

With the recent trend towards larger wafer sizes and smaller demand lots recently, there is a growing need for simultaneous production of multiple wafer types in a cluster tool. This presents a more complex scheduling challenge compared to identical types. Previous research primarily focuses on specific scenarios limited to the backward sequence, leaving a gap in the handling of more generalized scenarios without sequence restrictions. This paper proposes an approach towards the generalized cyclic scheduling of multiple wafer types in single-arm cluster tools, considering residency time constraints. A comprehensive operational scenario is described, using distinct symbols differentiate processing stages of wafers and their associated process modules. These elements are interconnected through shared process module sets. Based on detailed analysis of operations, a mixed integer linear programming model is proposed to handle the generalized scheduling problem. In the model, precedent relationships of robot operations are well defined, effectively preventing conflicts among them. Additionally, this model ensures the proper sequencing of processing stages in process modules – shared or not – to avoid overlap. Finally, the proposed approach is tested by both illustrative examples, especially including those previously considered unschedulable, and randomly generated instances. Testing results conduct the efficiency and validity of the proposed model. Copyright © 2025 Published by Elsevier Ltd.