Bounded dynamic programming approach to minimize makespan in the blocking flowshop problem with sequence dependent setup times

This paper aims at presenting an algorithm for solving the blocking flow shop problem with sequence dependent setup times (BFSP-SDST) with minimization of the makespan. In order to do so, we propose an adapted Bounded Dynamic Programming (BDP-SN) algorithm as solution method, since the problem itself does not present a significant number of sources in the state-of-art references and also because Dynamic Programming and its variants have been resurfacing in the flowshop literature. Therefore, we apply the modified method to two sets of problems and compare the results computationally and statistically for instances with a MILP and a B&B method for at most 20 jobs and 20 machines. The results show that BDP-SN is promising and outperforms both MILP and B&B within the established time limit. In addition, some suggestions are made in order to improve the method and employ it in parallel research regarding other branches of machine scheduling.