Abstract The block in-process permutation flow shop with total completion time criterion is known to be NP-hard for m ⩾ 2 . Since the literature is scarce in this theme, this article aims to fill this gap. It presents an improvement of the branch and bound algorithm to solve this problem through the development of a new machine-based lower bound which exploits the machine idleness and the occurrence of blocking. The computational experiments point out that the algorithm can handle n ⩽ 20 test problems in less than 2 min. Therefore, this work can support the scheduling of many applications in manufacturing systems with limited buffers.

中文翻译：

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具有总完成时间准则的阻塞置换流水车间的改进下界

摘要 对于 m ⩾ 2 ，已知具有总完成时间标准的块中置换流水车间是 NP-hard 的。由于该主题的文献稀缺，本文旨在填补这一空白。它提出了分支定界算法的改进，通过开发一个新的基于机器的下界来解决这个问题，该下界利用了机器空闲和阻塞的发生。计算实验表明，该算法可以在不到 2 分钟的时间内处理 n ⩽ 20 个测试问题。因此，这项工作可以支持在缓冲区有限的制造系统中调度许多应用程序。