A lexicographic minimax approach to the vehicle routing problem with route balancing

Fabien Lehuédé (1, 2, 3) , Olivier Péton (1, 2, 3) , Fabien Tricoire (4, 5)

1 LS2N - équipe SLP - Systèmes Logistiques et de Production
2 IMT Atlantique - DAPI - Département Automatique, Productique et Informatique
3 LS2N - Laboratoire des Sciences du Numérique de Nantes
4 Institute for production and logistics management
5 Universität Wien = University of Vienna

Vehicle routing problems generally aim at designing routes that minimize transportation costs. However, in practical settings, many companies also pay attention at how the workload is distributed among its drivers. Accordingly, two main approaches for balancing the workload have been proposed in the literature. They are based on minimizing the duration of the longest route, or the difference between the longest and the shortest routes, respectively. Recently, it has been shown on several occasions that both approaches have some flaws. In order to model equity we investigate the lexicographic minimax approach, which is rooted in social choice theory. We define the leximax vehicle routing problem which considers the bi-objective optimization of transportation costs and of workload balancing. This problem is solved by a heuristic based on the multi-directional local search framework. It involves dedicated large neighborhood search operators. Several LNS operators are proposed and compared in experimentations.

Mots clés: large neighborhood search; workload balancing; equity in route duration; multi-directional local search; vehicle routing problem

Domaines: Recherche opérationnelle [math.OC]

Fabien Lehuédé, Olivier Péton, Fabien Tricoire. A lexicographic minimax approach to the vehicle routing problem with route balancing. European Journal of Operational Research, 2020, 282 (1), pp.129-147. ⟨10.1016/j.ejor.2019.09.010⟩. ⟨hal-02296076v2⟩