Stochastic wafer fabrication scheduling

Abstract

To meet the challenge of integrating uncertainty analysis into wafer fabrication scheduling, this paper proposes a stochastic dynamic programming model for scheduling new releases and bottleneck processing by stage. Based on the paradigm of stochastic linear quadratic control (SLQ), the fab scheduling model incorporates considerable analysis of uncertainties in yields and demands. The SLQ scheduling model explicitly captures the reentrant flow structure characteristic of wafer fabrication. Moreover, the SLQ scheduling model removes a major weakness in applying dynamic programming to production control by accommodating noninteger values for lead times. Embedded in the SLQ scheduling model is what the authors term a degree-2 yield distribution that subsumes most popular yield distributions in the literature. As long as the underlying system dynamics behave in a degree-2 fashion, the corresponding optimal scheduling policy turns out to be a linear control rule that is easy to compute and implement. Industrial data are used to test the effectiveness and robustness of the SLQ machinery versus the LP rolling horizon and pull heuristic methodologies. Encouraging results and valuable insights are obtained from extensive numerical experiments that show promise for successfully managing uncertainties surrounding fab scheduling.