A two-stage robust approach for the weighted number of tardy jobs with objective uncertainty

Henri Lefebvre (1) , François Clautiaux (2, 3) , Boris Detienne (2, 3)

1 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
2 IMB - Institut de Mathématiques de Bordeaux
3 Realopt - Reformulations based algorithms for Combinatorial Optimization

Minimizing the weighted number of tardy jobs is a classical and intensively studied scheduling problem. In this paper, we develop a two-stage robust approach, where exact weights are known after accepting to perform the jobs, and before sequencing them on the machine. This assumption allows diverse recourse decisions to be taken in order to better adapt one's tactical plan. The contribution of this paper is twofold: first, we introduce a new scheduling problem and model it as a min-max-min optimization problem with mixed-integer recourse by extending existing models proposed for the classical problem where all the costs are assumed to be known. Second, we take advantage of the special structure of the problem to propose two solution approaches based on results from the recent robust optimization literature, namely finite adaptability (Bertsimas and Caramanis, 2010) and a convexification-based approach (Arslan and Detienne, 2020). We also study the cost of finding anchored solutions, where the sequence of jobs has to be decided before the uncertainty is revealed. Computational experiments to analyze the effectiveness of our approaches are reported.

Mots clés: One-machine scheduling; Robust optimization; Two-stage optimization; Mixed-integer recourse; Exact approach; Integer programming

Domaines: Recherche opérationnelle [math.OC]; Optimisation et contrôle [math.OC]

Henri Lefebvre, François Clautiaux, Boris Detienne. A two-stage robust approach for the weighted number of tardy jobs with objective uncertainty. 2020. ⟨hal-02905849v1⟩