A bicriteria flow-shop scheduling problem with two serial batching machines

We consider a bicriteria two-machine flow-shop serial-batch problem where the batches have limited size. The first criterion is the number of batches to be minimized. This criterion reflects situations where processing of any batch induces a fixed cost, which leads to a total cost proportional to the number of batches. The second criterion is the makespan. We provide a dynamic programming algorithm in the case where the jobs processing times on the first machine are constant. We also establish a dominance relation allowing us to derive an alternative algorithm with better complexity when the batch size is equal to two.