Abstract In this study, we investigate the lower bound and dominance conditions of the N-job and M-machine permutation flowshop scheduling problem to minimize the makespan based on machine idle times. We have developed and validated three dominance conditions and a lower bound based on a new approach that minimizes the machine idle times in a flowshop to facilitate the efficiency of the branch and bound approach. Most importantly, we have developed a dominance condition that is independent of the preceding and subsequent partial schedules, which has been considered critical but has not previously been developed in flowshop scheduling research. Finally, the efficiency of our developed branch and bound approach based on machine idle times is compared with the efficiencies of some previous branch and bound algorithms from the literature. We show that the dominance conditions that we developed can significantly improve the efficiency of the branch and bound approach.

中文翻译：

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基于机器空闲时间的置换流水车间调度问题的优势条件确定

摘要 在这项研究中，我们研究了 N-job 和 M-machine 置换流水车间调度问题的下界和优势条件，以最小化基于机器空闲时间的 makespan。我们已经开发并验证了三个优势条件和一个基于新方法的下限，该方法可以最大限度地减少流水车间的机器空闲时间，以提高分支定界方法的效率。最重要的是，我们开发了一个独立于前后部分调度的支配条件，这被认为是关键的，但以前在流水车间调度研究中尚未开发。最后，将我们开发的基于机器空闲时间的分支定界方法的效率与文献中一些以前的分支定界算法的效率进行比较。