Optimization on Multiple-time Reentrant Process of Robotic Cluster Tools with parallel process modules and chamber cleaning operations

In a cluster tool, for reentrant processes, wafers need to visit some process modules (PMs) multiple times and cleaning operations are required by PMs to eliminate the residual gases and chemicals, which complicates the scheduling problem of a cluster tool. This work aims to solve the challenging scheduling problem of dual-arm cluster tools with parallel PMs and chamber cleaning operations for reentrant processes. To do so, by analyzing the evolution processes of a tool, it is found that such a tool can operate under a periodical robot task sequence containing several local and global cycles. Furthermore, starting from different legal initial states, the tool can operate under different periodical schedules with different performance in terms of the cycle time. Also, the cycle time can be reduced by minimizing the maximal number of consecutive local cycles in a periodical schedule. With such findings, a mixed integer linear programming (MILP) model is established to minimize the maximum consecutive local cycles by ignoring the chamber cleaning operations. Compared with the existing MILP model to find a global optimal solution, the number of discrete variables in the established MILP is reduced by at least 99.08%, resulting in fast computation. Further, with the chamber cleaning operations considered, based on the established MILP, an efficient two-step method is presented to find the best periodical schedule among various possible robot task sequences. As demonstrated by experimental results, the proposed method is practically applicable since its solution time is less than 2 s in the tested cases.