In this paper we study a simple extension of the total weighted flowtime minimization problem for single and identical parallel machines. While the standard problem simply defines a set of jobs with their processing times and weights and assumes that all jobs have release date 0 and have no deadline, we assume that the release date of each job is a decision variable that is only constrained by a single global latest arrival deadline. To our knowledge, this simple yet practically highly relevant extension has never been studied. Our main contribution is that we show the NP- completeness of the problem even for the single machine case and provide an exhaustive empirical study of different typical approaches including genetic algorithms, tree search, and constraint programming.
翻译：在本文中,我们研究的是单一和相同的平行机器总加权流时最小化问题的简单延伸。标准问题只是界定了一组有处理时间和重量的工作,并假定所有工作都有释放日期0,没有最后期限,我们假设每个工作的释放日期是一个决定变量,仅受一个全球最新到达期限的限制。据我们所知,这一简单但实际上高度相关的扩展从未研究过。我们的主要贡献是,我们展示了NP——问题的完整性,即使是单一机器案件也是如此,并且提供了对遗传算法、树搜索和制约程序制定等不同典型方法的详尽经验研究。
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