Robust production capacity planning under uncertain wafer lots transfer probabilities for semiconductor automated material handling systems

In this paper, wafer lots transfer probability (WLTP) is introduced to capture the flowing rate of wafer lots among production bays, which is uncertain due to various wafer types and quantities. We study a new production capacity planning problem for wafer fabrication systems with uncertain WLTP. Based on an open queueing network model, the average work-in-process (WIP) level of the system is evaluated. Because of the uncertain WLTP, the average WIP level fluctuates significantly and sometimes exceeds its upper bound. Therefore, we develop a robust production capacity planning model with two layers: the bottom layer for finding the maximum WIP fluctuation under a given vehicle quantity, and the upper layer for determining the vehicle quantities to minimize the WIP fluctuation and the probability of the average WIP exceeding the upper bound. A method based on the monotonicity of the objective functions is developed to solve such a bi-objective optimization problem.