In a recent paper (He et al. in J Comb Optim 33(2):626–644, 2017), the authors considered single machine resource allocation scheduling with general truncated job-dependent learning effect. For the convex resource consumption function and limited resource cost, the problem is to minimize the weighted sum of makespan, total completion time, the total absolute deviation in completion time and resource consumption cost. They conjectured that this problem is NP-hard. In this note we show that this problem can be solved in \(O(n^3)\) time. It is also shown that Lemma 4 in He et al. (2017) is incorrect by a counter-example.

中文翻译：

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注意具有一般截断的作业相关学习效果的资源受限调度的时间复杂性

在最近的一篇论文中（He等人，J Comb Optim 33（2）：626–644，2017年），作者考虑了具有一般截断的作业相关学习效果的单机资源分配调度。对于凸的资源消耗函数和有限的资源成本，问题在于最小化制造期的加权总和，总完成时间，完成时间的总绝对偏差和资源消耗成本。他们认为这个问题是NP难题。在此注释中，我们证明了可以在\（O（n ^ 3）\）时间内解决此问题。还显示He等人的引理4。（2017）通过反例是不正确的。