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An effective problem decomposition method for scheduling of diffusion processes based on mixed integer linear programming

机译:基于混合整数线性规划的扩散过程调度问题有效分解方法

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Diffusion processes in semiconductor fabrication facilities (Fabs) usually refer to the series of processes from wafer cleaning processes to furnace processes. Most furnace tools are batch tools with large batch sizes and have relatively long process times when compared to the other processes. Strict time window constraints link cleaning processes with furnace processes for quality control. Those operational requirements for diffusion processes make their scheduling very difficult. This paper proposes an advanced scheduling approach based on a rolling horizon scheduling concept. Due to the combinatorial nature of the scheduling problem, the complexity of the problem increases exponentially when the number of jobs and tools increase. However, the computation time allowed for the scheduler is limited in practice, because the variability in most fabs requires schedulers to update the schedule in short intervals. We suggest an MILP (Mixed Integer Linear Programming) model for diffusion processes and propose an effective decomposition method to deal with this complexity problem. The decomposition method repeats multiple scheduling iterations as it gradually extends the number of runs on tools enabling the scheduler to generate near-optimal schedules in limited time intervals. The scheduler could make large improvements on KPIs such as queue time violation rates, batch sizes, throughput, etc. The software architecture of the scheduler implementation is also addressed in this paper.
机译:半导体制造设施(Fabs)中的扩散过程通常是指从晶片清洗过程到熔炉过程的一系列过程。大多数熔炉工具是批量较大的批处理工具,与其他方法相比,处理时间相对较长。严格的时间窗口约束将清洁过程与熔炉过程联系在一起,以进行质量控制。扩散过程的那些操作要求使其调度变得非常困难。本文提出了一种基于滚动地平线调度概念的高级调度方法。由于调度问题的组合性质,随着作业和工具数量的增加,问题的复杂性呈指数增长。但是,由于大多数工厂的可变性要求调度程序在较短的间隔内更新调度程序,因此调度程序所允许的计算时间实际上是有限的。我们建议用于扩散过程的MILP(混合整数线性规划)模型,并提出一种有效的分解方法来处理此复杂性问题。分解方法在逐步扩展工具上的运行次数时会重复多次调度迭代,从而使调度程序可以在有限的时间间隔内生成接近最佳的调度。调度程序可以对KPI进行重大改进,例如队列时间违规率,批处理大小,吞吐量等。本文还讨论了调度程序实现的软件体系结构。

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