Branch-and-bound-and-memorize for the blocking permutation flowshop problem

Flow scheduling problems are among the most studied problems in the optimization literature and different technological constraints characterize the many variants of the general problem. This paper deals with the flowshop scheduling problem where there is no infinite buffer between subsequent machines: a job may lay on the current machine without leaving until the buffer has sufficient room. Such a situation is called blocking. In this paper, a branch-and-bound-based algorithm is proposed to optimally solve instances of the problem. The proposed method relies on a fast upper bounding procedure for early node pruning and passive node memorization that further speeds up the problem resolution. The proposed approach is compared with previous results in the literature and assessed as outperforming.