Flow-shop batch scheduling with identical processing-time jobs

In many practical situations of production scheduling, it is either necessary or recommended to group a large number of jobs into a relatively small number of batches. A decision needs to be made regarding both the batching (i.e., determining the number and the size of the batches) and the sequencing (of batches and of jobs within batches). A setup cost is incurred whenever a batch begins processing on a given machine. This paper focuses on batch scheduling of identical processing-time jobs, and machine- and sequence-independent setup times on an m-machine flow-shop. The objective is to find an allocation to batches and their schedule in order to minimize flow-time. We introduce a surprising and nonintuitive solution for the problem.