A sequential solution methodology for capacity allocation and lot scheduling problems for photolithography

In this paper, we study the shift scheduling problem for photolithography workcenters, which involves specifying the start and finish times for individual lots over the duration of the shift. For the schedule to be accurate, the operational policies (such as set-up control policies) and auxiliary resources of the workcenter (such as reticles) must be considered, which further complicates the problem. We present a sequential procedure that separates the problem into capacity allocation and lot sequencing sub-problems. Although solving these problems sequentially is not a new idea, the lack of empirical evidence of the benefits and insight into implementation issues motivate this research. We use a simulation model of a wafer fabrication facility to examine the effects of using this procedure for scheduling of the photolithography operations. We show that the procedure is a viable method to schedule photolithography workcenter. The choice of the time horizon over which the capacity allocation problem is solved affects cycle time metrics and the number of set-ups significantly. However, varying reticle and set-up constraints has little impact. Finally, we show that the procedure is sensitive to the structure of the operation-stepper matrix and suggest a remedy to overcome the problem