In a recent paper, Jiang et al. (Eng Optim 52(1):37–52, 2020) considered proportionate flowshop scheduling with position-dependent weights. For common and slack due-date assignment problems, they proved that both of these two problems can be solved in \(O(n^{2} \log n)\) time, where \(n\) is the number of jobs. The contribution of this paper is that we show that these two problems can be optimally solved by a lower-order algorithm, i.e., in \(O(n\log n)\) time.

中文翻译：

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具有到期日期分配和位置相关权重的成比例Flowshop调度研究

在最近的一篇论文中，Jiang等人。（Eng Optim 52（1）：37–52，2020）考虑了比例流水作业调度与位置相关的权重。对于常见的和松弛的到期日分配问题，他们证明了这两个问题都可以在\（O（n ^ {2} \ log n）\）的时间内解决，其中\（n \）是作业数。本文的贡献在于，我们证明了这两个问题可以通过低阶算法（即\（O（n \ log n）\）时间内）得到最佳解决。