Controlled Wafer Release in Clustered Photolithography Tools: Flexible Flow Line Job Release Scheduling and an LMOLP Heuristic

As a clustered photolithography tool (CPT) in semiconductor wafer manufacturing can cost as much as US$100 million, it must be operated efficiently. To maximize throughput, wafers are generally admitted to a CPT opportunistically, that is, as soon as they are available and the tool can accept them. Here, our goal is to develop release methods that retain throughput but increase manufacturing agility. As Petri net methods prove intractable, we develop a heuristic based on the use of flexible flow line models for the CPT. Such models are appropriate when the tool throughput for each class of wafers is dictated by the bottleneck process time plus unavoidable robot handling overhead. The heart of the heuristic is a lexicographic multiple objective linear program (LMOLP). It first ensures that wafers exit the tool as early as possible and subsequently delays the wafer admission to minimize the mean residency time.