Optimising batch operations under energy constraint with truncated position-based learning effect and ageing effect
研究了半导体晶圆制造中，在能源消耗约束下，考虑操作员学习效应和设备老化效应的批次调度问题，提出了近似算法并分析了最坏情况性能比。
Motivated by applications in semiconductor wafer manufacturing, we study a scheduling model with truncation-based batch position learning effects and ageing effects under energy consumption constraints. In production, semiconductor batch processing equipment has a fixed energy consumption constraint. If the energy consumption required for a single batch in semiconductor wafer processing exceeds the equipment’s allowable energy constraint, it may lead to instability in the dimensional accuracy of the semiconductor wafers. In semiconductor manufacturing equipment, material deposition in the reaction chamber leads to the ageing effect, resulting in inevitable degradation of equipment performance. However, when the deposition uniformity is maintained at the process specification limit, the performance deterioration keeps steady. On the other hand, operators exhibit learning effects. After the learning phase, operators reach their best capability and it keeps steady. We consider two batch operation models. In the first model, semiconductor wafers have identical processing times. We prove that this model is strongly NP-hard problem. When ageing effects dominate, the absolute and asymptotic worst-case ratios of the algorithm are 2 and 1.493. When learning effects dominate, the absolute and asymptotic worst-case ratios are 2 and 1.714. In the second model, the energy consumption of the semiconductor products is proportional to the processing time. This model is also strongly NP-hard. We propose approximation algorithms that have absolute and asymptotic worst-case ratios less than 2.