Exact solution of the two-machine flow shop problem with three operations

We consider the NP-hard two-machine flow shop problem with three operations with the objective of minimizing the makespan. We exploit the links between this problem and another two-machine flow shop problem with common due date and jobs selection. We show how to tailor to this problem the constraint generation approach already successfully applied in the literature to the latter problem. Computational testing indicates that the proposed approach solves to optimality, within 120 s all instances with up to 40000 jobs.