Exact method for the two-machine flow-shop problem with time delays

Mohamed Amine Mkadem (1) , Aziz Moukrim (1, 2) , Mehdi Serairi (2, 1)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
2 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"

We address the two-machine flow-shop scheduling problem with time delays in order to minimize the makespan, i.e., the maximum completion time. We present a comprehensive theoretical analysis of the different lower bounds of the state of the art and we elucidate dominance relationships between them. We then introduce an exact method based on a branch-and-bound scheme. This method includes a local search-based heuristic and three dominance rules. Finally, a computer simulation of the branch-and-bound method is given on a set of 480 instances. We point out the good performance of our branch-and-bound method that outperforms the state of the art exact method. Precisely, we manage to solve all the sate of the art instances except one in a very short time.

Mots clés: makespan; lower bound; Two-machine flow-shop; time delay; branch-and-bound

Domaines: Recherche opérationnelle [math.OC]

Mohamed Amine Mkadem, Aziz Moukrim, Mehdi Serairi. Exact method for the two-machine flow-shop problem with time delays. Annals of Operations Research, 2021, 298, pp.375-406. ⟨10.1007/s10479-018-3082-x⟩. ⟨hal-01897163⟩