A note on batch scheduling on a two-machine flowshop with machine-dependent processing times

We study a batch scheduling problem on a two-machine flowshop. Unlike most relevant research papers focusing on batching with identical job processing times, we assume machine-dependent processing times. The objective function is minimum makespan. For the relaxed version of the problem, where integer batch sizes are not required, we introduce a constant time solution. It consists of: (i) a closed-form expression for the optimal number of batches; and (ii) a geometric sequence of the batch sizes. This optimal non-integer solution is converted into an integer solution by the application of a simple rounding procedure, which runs in O(nlogn) time (where n is the number of jobs).