The two-stage assembly scheduling problem is widely used in industrial and service industries. This study focuses on the two-stage three-machine flow shop assembly problem mixed with a controllable number and sum-of-processing times-based learning effect, in which the job processing time is considered to be a function of the control of the truncation parameters and learning based on the sum of the processing time. However, the truncation function is very limited in the two-stage flow shop assembly scheduling settings. Thus, this study explores a two-stage three-machine flow shop assembly problem with truncated learning to minimize the makespan criterion. To solve the proposed model, we derive several dominance rules, lemmas, and lower bounds applied in the branch-and-bound method. On the other hand, three simulated annealing algorithms are proposed for finding approximate solutions. In both the small and large size number of job situations, the SA algorithm is better than the JS algorithm in this study. All the experimental results of the proposed algorithm are presented on small and large job sizes, respectively.

中文翻译：

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两阶段三机流水车间装配问题与可控制数量和总和基于处理时间的学习效果的模拟退火算法混合

两阶段装配调度问题已广泛应用于工业和服务业。这项研究的重点是两阶段三机流水车间装配问题，其中混合了可控制的数量和基于处理总和的学习效果，其中作业处理时间被认为是截断控制的函数参数和基于处理时间总和的学习。但是，截断功能在两阶段流水车间装配调度设置中非常有限。因此，本研究探索了具有截短学习的两阶段三机流水车间装配问题，以最大程度地缩短了制造期限标准。为了解决所提出的模型，我们导出了分支定界方法中应用的几个支配规则，引理和下界。另一方面，提出了三种模拟退火算法来寻找近似解。无论工作量大小，在本研究中，SA算法均优于JS算法。提出的算法的所有实验结果分别在较小和较大的作业规模上给出。