Noncyclic Scheduling of Multi-cluster Tools with Multi-type Wafers Based on Pareto Optimization

In semiconductor manufacturing, multi-cluster tools are widely used. Recently, the variety of wafer types has attracted increasing interests due to the demand of diversification and efficiency in industrial production. In this paper, we focus on the noncyclic scheduling problem of multi-type wafers in multi-cluster tools. Firstly, a universal model is constructed to describe such problem for both single-armed and dual-armed robots. Correspondingly, an improved dynamic programming algorithm is proposed based on Pareto optimization, in which a renumber rule and a normalization rule are introduced to merge redundant states and further increase the searching efficiency. Theoretical analysis of computational efficiency is also discussed. Numerical experiments verify the effectiveness of the proposed algorithm in minimizing makespan on the noncyclic scheduling with multi-type wafers.