We address a two-machine no-wait flowshop scheduling problem with respect to the performance measure of total completion time. Minimizing total completion time is important when inventory cost is of concern. Setup times are treated separately from processing times. Furthermore, setup times are uncertain with unknown distributions and are within some lower and upper bounds. We develop a dominance relation and propose eight algorithms to solve the problem. The proposed algorithms, which assign different weights to the processing and setup times on both machines, convert the two-machine problem into a single-machine one for which an optimal solution is known. We conduct computational experiments to evaluate the proposed algorithms. Computational experiments reveal that one of the proposed algorithms, which assigns the same weight to setup and processing times, is superior to the rest of the algorithms. The results are statistically verified by constructing confidence intervals and test of hypothesis.

中文翻译：

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在不确定的和有限制的设置时间的情况下，最大程度地减少两台机器的无等待流水车间的总完成时间

关于总完成时间的性能指标，我们解决了两机无等待流水车间调度问题。当需要考虑存货成本时，尽量缩短总完成时间非常重要。设置时间与处理时间分开处理。此外，在未知分布的情况下，建立时间是不确定的，并且处于一定的上下限内。我们建立了优势关系，并提出了八种算法来解决该问题。所提出的算法为两台机器的处理和设置时间分配了不同的权重，将两台机器的问题转换为单台机器的问题，为此已知了最佳解决方案。我们进行计算实验以评估所提出的算法。计算实验表明，提出的算法之一，它将相同的权重分配给设置和处理时间，优于其他算法。通过建立置信区间和检验假设对结果进行统计验证。