Minimizing makespan for no-wait flowshop scheduling problems with setup times

This study investigates no-wait flowshop scheduling problems with sequence-independent and sequence-dependent setup times aimed at minimizing the makespan. We propose an efficient two-phase matheuristic, which can optimally solve all tested instances of three existing benchmark problem sets and a new generated large-sized test problem set, with up to 20-machine and 2000-job test instances, in acceptable computational times. This is a dramatic improvement over all previously known algorithms. In view of the strongly NP-complete nature of the two problems addressed herein, this study contributes an exact method that can find optimal solutions for solving these problems with the efficiency necessary to meet real-world scheduling requirements.