Robust scheduling for minimizing maximum lateness on a serial-batch processing machine

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.