Layered formulation for the robust vehicle routing problem with time windows

Authors:
Agostinho Agra;Marielle Christiansen;Rosa Figueiredo;Lars Magnus Hvattum;Michael Poss;Cristina Requejo
Affiliations:
CIDMA, Department of Mathematics, University of Aveiro, Aveiro, Portugal;Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway;CIDMA, Department of Mathematics, University of Aveiro, Aveiro, Portugal;Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway;CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal,Centre de Recherches de Royallieu, UMR CNRS 6599 Heudiasyc, Université de Technologie de Compiègne, Compièg ...;CIDMA, Department of Mathematics, University of Aveiro, Aveiro, Portugal
Venue:
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Year:
2012

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Abstract

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.