In this paper we study a proportionate flow shop of batching machines with release dates and a fixed number $m \geq 2$ of machines. The scheduling problem has so far barely received any attention in the literature, but recently its importance has increased significantly, due to applications in the industrial scaling of modern bio-medicine production processes. We show that for any fixed number of machines, the makespan and the sum of completion times can be minimized in polynomial time. Furthermore, we show that the obtained algorithm can also be used to minimize the weighted total completion time, maximum lateness, total tardiness and (weighted) number of late jobs in polynomial time if all release dates are $0$. Previously, polynomial time algorithms have only been known for two machines.

中文翻译：

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调度配料机的成比例流水车间

在本文中，我们研究了具有发布日期和固定数量 $m\geq 2$ 的配料机的成比例流水车间。到目前为止，调度问题在文献中几乎没有受到任何关注，但由于在现代生物医药生产过程的工业规模化中的应用，它的重要性最近显着增加。我们表明，对于任何固定数量的机器，可以在多项式时间内最小化完工时间和完成时间的总和。此外，我们表明，如果所有发布日期都是 0 美元，则所获得的算法还可用于在多项式时间内最小化加权总完成时间、最大延迟时间、总延迟时间和（加权）延迟作业数。以前，多项式时间算法仅适用于两台机器。