Single machine scheduling with batch-dependent setup times

We address a single-machine batch scheduling problem. The setup times (incurred whenever starting a new batch) are assumed to be a function of the number of batches processed previously, i.e., batch-dependent. The objective is minimum total flow-time. We focus on the case of identical processing time jobs. Given the number of jobs and the setup times, we have to determine the optimal number of batches and their (integer) size. An efficient (O(n)) solution procedure is introduced.