Layered Formulation for the Robust Vehicle Routing Problem with Time Windows

Agostinho Agra (1) , Marielle Christiansen (2) , Rosa Figueiredo (1) , Lars Magnus Hvattum (2) , Michael Poss (3) , Cristina Requejo (1)

1 CIDMA - Center for Research & Development in Mathematics and Applications [Aveiro]
2 IDI - Department of Computer and Information Science [Trondheim]
3 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

This paper studies the vehicle routing problem with time windows where travel times are uncertain and belong to a predetermined polytope. The objective of the problem is to find a set of routes that services all nodes of the graph and that are feasible for all values of the travel times in the uncertainty polytope. The problem is motivated by maritime transportation where delays are frequent and must be taken into account. We present an extended formulation for the vehicle routing problem with time windows that allows us to apply the classical (static) robust programming approach to the problem. The formulation is based on a layered representation of the graph, which enables to track the position of each arc in its route. We test our formulation on a test bed composed of maritime transportation instances.

Mots clés: vehicle routing problem; robust programming; time windows; maritime transportation; layered formulation

Domaines: Recherche opérationnelle [math.OC]

Agostinho Agra, Marielle Christiansen, Rosa Figueiredo, Lars Magnus Hvattum, Michael Poss, et al.. Layered Formulation for the Robust Vehicle Routing Problem with Time Windows. 2nd International Symposium on Combinatorial Optimization, Apr 2012, athens, Greece. pp.249-260, ⟨10.1007/978-3-642-32147-4_23⟩. ⟨hal-00777762⟩