Minimizing Makespan in a Pallet-Constrained Flowshop

We consider the problem of scheduling n jobs in a pallet-constrained two-machine flowshop so as to minimize the makespan. In such a flowshop environment, each job needs a pallet the entire time, from the start of its first operation until the completion of the last operation, and the number of pallets in the shop at any given time is limited by a positive integer K <= n. We look on the impact of the number of pallets on the makespan. We identify a class of instances for which we can prove a worst-case bound on the minimum K that guarantees the least possible makespan. Furthermore, we look at the trade-off between the number of pallets used and the obtained makespan if we process the jobs in the order dictated by Gilmore-Gomory's algorithm