We study a robust single-machine scheduling problem with uncertain processing times on a serial-batch processing machine to minimize maximum lateness. The problem can model many practical production and logistics applications which involve uncertain factors such as defect rates. A solution to a batch scheduling problem can be represented as a combination of a job-processing sequence and a partition of this sequence (batch sizing). To solve the problem, we prove that the job ordering rule for the earliest due date is optimal for any uncertainty set. For the batch sizing problem, we propose an exact algorithm based on dynamic programming with the same time complexity as solving the nominal problem.

我们研究了在串行批处理机器上具有不确定处理时间的鲁棒单机调度问题，以最大限度地减少最大延迟。该问题可以对许多涉及缺陷率等不确定因素的实际生产和物流应用进行建模。批量调度问题的解决方案可以表示为作业处理序列和该序列的分区（批量大小）的组合。为了解决这个问题，我们证明了最早到期日的作业排序规则对于任何不确定性集都是最优的。对于批量大小问题，我们提出了一种基于动态规划的精确算法，其时间复杂度与解决标称问题相同。