In this paper, we investigate the single machine lot scheduling problem in which each lot contains one or more jobs (or part of jobs). Jobs with different sizes are splittable and should be processed in consecutive lots. Any completed (part of a) job is delivered to the customer on its completion. We generalize the problem studied in Zhang et al. (Inf Process Lett 142:46–51, 2019) such that lots may have different capacities and processing times, and the sizes of jobs are unbounded. We show that for this generalized case, the WSPT (Weighted Shortest Processing Time first) rule is still optimal for both minimizing total weighted completion time and minimizing total weighted discounted completion time.

在本文中，我们研究了单个机器批次调度问题，其中每个批次包含一个或多个作业（或部分作业）。不同大小的作业是可拆分的，应连续处理。任何完成的（一部分）工作都会在完成时交付给客户。我们归纳了张等人研究的问题。（Inf Process Lett 142：46–51，2019），以便批次的容量和处理时间可能不同，并且作业的大小不受限制。我们表明，对于这种一般情况，WSPT（加权最短处理时间优先）规则对于最小化总加权完成时间和最小化总加权折扣完成时间仍然是最佳的。