Scheduling single-arm multi-cluster tools connected by one-space buffer modules beyond the schedulability assumption

Multi-cluster tools are increasingly being adopted for wafer production in semiconductor fabrications. The current paper deals with single-armed linear multi-cluster tools connected by one-space buffer modules with residency time constraints. Due to the complexity of operations, previous research has primarily focused on scenarios with the schedulability assumption-where there is always a wafer in processing at each step-using the backward strategy or its extensions for single-arm tools. However, it is open and more challenging to schedule such tools under general conditions beyond the schedulability assumption. The current paper deals with these general conditions. Furthermore, an innovative K-unit cyclic scheduling approach is applied to achieve higher productivity. Based on detailed analysis of the operations in these tools, a mixed integer linear programming model is formulated. Both illustrative examples and randomly generated instances are used to test and validate the proposed model. The results demonstrate that the proposed approach is valid and effective. Additionally, the K-unit cyclic schedules significantly improve productivity, which is of great importance for a company's profitability.