Tool sequence optimization based on three logical modes of robot control via CPLEX optimization

Cluster tools have advantages of shorter cycle times, faster process development, and better yield for less contamination. The sequence of dual-arm cluster tools is a complex logistics process during the semiconductor production. Efficient use of cluster tools is naturally very significant to competitive fab operations. Generating an optimized sequence in a computationally efficient manner and assessing the quality of the requirements to improve the fab production are the key factors for semiconductor manufacturing productivity. The Petri net modeling is introduced to minimize the makespan of the process for the three different logical modes and select a better mode after comparing the makespan among the three logical modes. The tool sequence optimization problem is formulated as optimization firing transition sequences based on the Petri net and then the formulation is converted to be linearly solved by the branch-and-cut method in the standard commercial solver CPLEX. Special methods for the linear conversion are highlighted. Due to the limited calculation time requirement for the real production and the large scale of the problem, special methods for the efficiency tuning are applied according to the characteristics of the problem. Numerical testing is supported by one of the most advanced semiconductor enterprises and the computational results show significant improvement compared with the traditional manual sequence results.