Generalized Optimal Scheduling of Cluster Tools With Reentrance and Residency Time Constraints

Cluster tools have been widely used in the semiconductor industry. In previous work, singe-arm and dual-arm cluster tools are dealt with separately. When considering residency time constraints, algorithms for scheduling robot moving sequences are mainly developed based on backward and swap strategies, respectively. How about the performance of other robot moving sequences is still an open problem. The present work addresses general conditions by considering all feasible robot moving sequences—beyond backward- and swap-based strategies. In addition, both dual-arm and single-arm cluster tools with reentrance are handled simultaneously. To solve this, the problem is first divided into two parts—the basic one without reentrance and reentrant operations. Based on detailed analysis of all available robot operations in a cluster tool, mixed-integer programming formulations are developed for both parts. Subsequently, both illustrative examples and randomly generated instances are tested to validate the efficiency of the proposed approach. Results of one example show improvement comparing to previous work. Another two examples—not scheduled previously—are scheduled well by the proposed approach. Meanwhile, the flexibility of operations obtained by the proposed model is demonstrated by an example with six processing modules and 12 stages in a dual-arm cluster tool. Additionally, more randomly generated instances are tested more to validate the proposed approach and analyze computation time.