Scheduling of Single-Arm Cluster Tools with Residency Time Constraints and Chamber Cleaning Operations

To ensure wafer quality, engineers have to impose wafer residency time constraints and chamber cleaning operations on cluster tools; this has been widely used in semiconductor manufacturing. Wafer residency time constraints and chamber cleaning operations make the scheduling problem of cluster tools more challenging. This work aims to solve such a scheduling problem for single-arm cluster tools and presents a novel method based on the use of virtual wafers. Under a one-cyclic schedule obtained for single-arm cluster tools without chamber cleaning requirements, virtual wafers are loaded into the tool such that when a process module (PM) processes virtual wafers, a chamber cleaning operation is performed in practice. The key to solve this scheduling problem is to find a wafer loading sequence with the highest performance in terms of cycle time. With this idea, this work constructs a genetic algorithm to search for such a solution. Since the obtained solution is a periodical wafer loading sequence based on a one-wafer cyclic schedule, it can be easily implemented. Therefore, this work has high practical value to numerous semiconductor manufacturers. Experiments were performed to show the efficiency and effectiveness of the proposed method.

Cyclic exit strategies to suppress COVID-19 and allow economic activity

Many countries have applied lockdown that helped suppress COVID-19, but with devastating economic consequences. Here we propose exit strategies from lockdown that provide sustainable, albeit reduced, economic activity. We use mathematical models to show that a cyclic schedule of 4-day work and 10-day lockdown, or similar variants, can prevent resurgence of the epidemic while providing part-time employment. The cycle pushes the reproduction number R below one by reduced exposure time and by exploiting the virus latent period: those infected during work days reach peak infectiousness during lockdown days. The number of work days can be adapted in response to observations. Throughout, full epidemiological measures need to continue including hygiene, physical distancing, compartmentalization, testing and contact tracing. This conceptual framework, when combined with other interventions to control the epidemic, can offer the beginnings of predictability to many economic sectors.