Stochastic Modeling for Serial-Batching Workstations with Heterogeneous Machines

The bottleneck workstation in semiconductor manufacturing is lithography. Lithography is a complex manufacturing system (CMS) and consists of multiple products, serial-batching operations, re-entrant process flows, and parallel non-identical machines. Existing stochastic models for such a CMS focus on simple extensions of the classical queueing theory. These models fail to question the applicability of the theory but try to modify model inputs on the first moment (average) and the second moment (variation). The implementation of these models has been unsatisfactory. In this paper, we provide a stochastic model of such a CMS. We model the arrival process of CMS by Poisson process and the service process by Markov decision process. We propose a geometric-distribution based probabilistic dispatching model. The model is verified using a lithography workstation in a high-volume wafer fabrication facility. This study provides a theoretic framework and promising results for serial-batching operation modeling in semiconductor manufacturing and other industries as well.