Robust production capacity planning of a wafer fabrication system with uncertain wafer lots transfer probabilities

Production capacity planning is an important problem in the design of a semiconductor wafer fabrication system, which means to optimize the number of tools in the system so that expected production rate, work-in-process level can be satisfied and the cost of building the wafer fab can be minimized. However, a wafer fab usually produces multiple types of wafers, different types of wafers have different and complicated processing routes, and the work-in-process quantities of different types of wafers changes frequently due to the fluctuation of demands. Therefore, the transfer probabilities of wafer lots among tools, material handle devices and bays in the wafer fab are uncertain. To deal with this uncertainty, it is necessary to improve the robustness of he production capacity planning of a wafer fab. In this paper, we construct an open queueing network-based model of a wafer fab and developed a mathematical model of the robust production capacity planning problem with the objective of maximizing the probability of satisfying expected performance requirements. To solve this problem, a heuristic algorithm is proposed and numerical experiments are conducted to evaluate the robustness of the solution.