We investigate the scheduling problem on a single bounded parallel-batch machine where jobs belong to two non-disjoint agents (called agent A and agent B) and are of equal length but different size. Each job’s size can be arbitrarily split into two parts and processed in the consecutive batches. It is permitted to process the jobs from different agents in a common batch. We show that it is unary NP-hard for the problem of minimizing the total weighted completion time of the jobs of agent A subject to the maximum cost of the jobs of agent B being upper bounded by a given threshold. For the case of the jobs of agent A having identical weights, we study the version of Pareto problem, and give a polynomial-time algorithm to generate all Pareto optimal points and a Pareto optimal schedule corresponding to each Pareto optimal point.

中文翻译：

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具有两个不相干代理和可拆分作业的单机批处理调度

我们在一个有界并行批处理机器上研究调度问题，在该机器上，作业属于两个不相交的代理（称为代理A和代理B），并且长度相等，但大小不同。每个作业的大小可以任意分为两部分，并以连续的批次进行处理。允许在同一批中处理来自不同代理的作业。我们证明，在代理B的工作的最大成本受给定阈值上限的约束下，使代理A的工作的总加权完成时间最小化的问题是一元NP难题。对于具有相同权重的业务代表A的工作，我们研究了帕累托问题的版本，并给出了多项式时间算法来生成所有帕累托最优点和对应于每个帕累托最优点的帕累托最优计划。