A single machine batch scheduling problem with bounded batch size

We address a single-machine batch scheduling problem to minimize total flow time. Processing times are assumed to be identical for all jobs. Setup times are assumed to be identical for all batches. As in many practical situations, batch sizes may be bounded. In the first setting studied in this paper, all batch sizes cannot exceed a common upper bound. In the second setting, all batch sizes share a common lower bound. An optimal solution consists of the number of batches and their (integer) size. We introduce an efficient solution for both problems.