串行批调度以最小化总加权延迟工作量

中文摘要 AI 辅助

我们研究了在串行批处理机器上调度作业以最小化总加权延迟工作量的问题。在串行批处理设置中，批次内的作业按顺序处理，并且直到批次中最后一个作业完成其处理之前，没有任何作业从机器上移除。一个批次的处理时间是该批次内作业处理时间之和，并且批次中每个作业的完成时间等于该批次中作业的制造跨度。当新批次开始时，机器需要恒定的设置时间。我们证明，即使所有作业具有共同的到期日和单位权重，在此环境中最小化总加权延迟工作量也是$NP$-难的。对于一般问题，我们提出了一种伪多项式时间动态规划算法。此外，我们探讨了两个特例，即具有共同到期日的情况以及到期日、处理时间和权重之间具有一致性条件的情况。对于这两个特例，我们开发了专门的伪多项式时间动态规划算法。所提出的方法配备了专门的加速技术以增强其计算性能。扩展实验表明，动态规划算法在时间效率上优于Gurobi。

英文摘要

We study the problem of scheduling jobs on a serial-batch machine with the aim of minimising the total weighted late work. In a serial-batch setting, jobs within a batch are processed sequentially, and none are removed from the machine until the last job in the batch completes its processing. The processing time of a batch is the sum of the processing times of the jobs within it, and the completion time for each job in the batch is equal to the makespan of the jobs in the batch. When a new batch begins, a constant setup time is required for the machine. We show that minimising the total weighted late work in this environment is $NP$-hard even if all jobs have a common due date and unit weight. For the general problem, we present a pseudo-polynomial time dynamic programming algorithm. Additionally, we explore two special cases, i.e., one with a common due date and another with an agreeable condition among due dates, processing times and weights. For both special cases, we develop specialised pseudo-polynomial time dynamic programming algorithms. The proposed approaches are equipped with specialised acceleration techniques to enhance their computational performance. The extended experiments demonstrate that the dynamic programming algorithms outperform Gurobi in time efficiency.

发表机构

• College of Economics and Management, Nanjing University of Aeronautics and Astronautics（南京航空航天大学经济与管理学院）
• Institute of Computing Science, Poznan University of Technology（波兹南理工大学计算科学研究所）

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