Optimal Control of a Manufacturing Process That Involves Trial Runs
研究半导体晶圆制造中常见的试运行过程，通过随机凸性理论，给出最多进行k*次单件试运行的最优控制策略。
We study a manufacturing process that is quite common in semiconductor wafer fabrication. In generic terms, the job to be processed consists of J units. To process the job, a “setup” is required, followed by routine processing and testing. In principle, the entirety of the job can be set up and processed in a single batch. However, the setup is prone to failure, leading to loss of units. Hence, in practice trial runs are often conducted, with each trial involving a small batch of units. Here we identify an optimal control of such processes. The policy prescribes a maximum of k* (≤J) single-unit trial runs. To establish optimality, we use the recently developed notion of stochastic convexity/concavity and related machinery.