In this paper, a qualification management problem arising in semiconductor wafer fabrication facilities (wafer fabs) is studied. The stepper machines, a common bottleneck in many wafer fabs, must be qualified to process lots of different families. A qualification time window is associated with each stepper and family. It can be reinitialized as needed and can be extended by on-time processing of lots from qualified families. Fast heuristic approaches, among them a Greedy Randomized Adaptive Search Procedure (GRASP), are proposed to solve large-sized problem instances using a small amount of computing time. The qualification decisions modeled by binary decision variables are made by heuristic procedures that exploit the problem structure while the real-valued quantities for each family and stepper are computed using linear programming. Computational experiments based on randomly generated problem instances are conducted. The results show that the proposed matheuristics are able to quickly provide high-quality solutions.

中文翻译：

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晶圆厂资格管理决策的数学

在本文中，研究了半导体晶圆制造设施（晶圆厂）中出现的资格管理问题。步进机是许多晶圆厂的常见瓶颈，必须有资格处理许多不同的系列。资格时间窗口与每个步进器和系列相关联。它可以根据需要重新初始化，并且可以通过按时处理合格系列的批次进行扩展。提出了快速启发式方法，其中包括贪婪随机自适应搜索程序 (GRASP)，以使用少量计算时间解决大型问题实例。由二元决策变量建模的资格决策是通过利用问题结构的启发式程序做出的，而每个系列和步进器的实数值是使用线性规划计算的。进行了基于随机生成的问题实例的计算实验。结果表明，所提出的数学算法能够快速提供高质量的解决方案。