Tang et al. (Eur J Oper Res 263:401–411, 2017) have recently introduced a parallel-batching machine scheduling problem with linearly deteriorating jobs of two agents and presented a computational complexity classification of various special cases of this problem, including a number of NP-hardness proofs. We refine these results by demonstrating strong NP-hardness of several special cases, which are proved NP-hard in the ordinary sense in Tang et al. (Eur J Oper Res 263:401–411, 2017). Our reduction employs the problem studied in the first issue of Journal of Scheduling.

中文翻译：

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单个并行批处理机上作业恶化的双代理调度：优化计算复杂度

唐等人。(Eur J Oper Res 263:401–411, 2017) 最近引入了一个并行批处理机器调度问题，其中两个代理的作业线性恶化，并提出了这个问题的各种特殊情况的计算复杂性分类，包括许多 NP-硬度证明。我们通过证明几个特殊情况的强 NP-hardness 来改进这些结果，这些特殊情况在 Tang 等人的普通意义上被证明是 NP-hard。(Eur J Oper Res 263:401–411, 2017)。我们的缩减采用了在第一期《调度杂志》中研究的问题。