A bi-objective model for the single-machine scheduling problem with rejection cost and total tardiness minimization

Roberto Cordone (1) , Pierre Hosteins (2)

1 UNIMI - Università degli Studi di Milano = University of Milan
2 IFSTTAR/COSYS/ESTAS - Évaluation des Systèmes de Transports Automatisés et de leur Sécurité

We study the problem of scheduling jobs on a single machine with a rejection possibility, concurrently minimizing the total tardiness of the scheduled jobs and the total cost of the rejected ones. The model we consider is fully bi-objective, i.e. its aim is to enumerate the Pareto front. We tackle the problem both with and without the presence of hard deadlines. For the case without deadlines, we provide a pseudo-polynomial time algorithm, based on the dynamic program of [25], thereby proving that the problem is weakly NP-hard. For the case with deadlines, we propose a branch-and-bound algorithm and prove its efficiency by comparing it to an µ-constrained approach on benchmark instances based on those proposed in the literature on similar problems.

Mots clés: SCHEDULING WITH REJECTION; TOTAL TARDINESS; BI-OBJECTIVE OPTIMIZATION; DYNAMIC PROGRAMMING; BRANCH-AND-BOUND

Mots clés: PLANIFICATION; OPTIMISATION; PROGRAMMATION; TRANSPORT FERROVIAIRE; MODELISATION; ALGORITHME

Domaines: Optimisation et contrôle [math.OC]

Roberto Cordone, Pierre Hosteins. A bi-objective model for the single-machine scheduling problem with rejection cost and total tardiness minimization. Computers and Operations Research, 2019, 102, pp130-140. ⟨10.1016/j.cor.2018.10.006⟩. ⟨hal-01985204⟩