Layered Formulation for the Robust Vehicle Routing Problem with Time Windows

  • Agostinho Agra
  • Marielle Christiansen
  • Rosa Figueiredo
  • Lars Magnus Hvattum
  • Michael Poss
  • Cristina Requejo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)


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.


vehicle routing problem robust programming time windows maritime transportation layered formulation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Agostinho Agra
    • 1
  • Marielle Christiansen
    • 2
  • Rosa Figueiredo
    • 1
  • Lars Magnus Hvattum
    • 2
  • Michael Poss
    • 3
    • 4
  • Cristina Requejo
    • 1
  1. 1.CIDMA, Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Department of Industrial Economics and Technology ManagementNorwegian University of Science and TechnologyTrondheimNorway
  3. 3.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal
  4. 4.Centre de Recherches de RoyallieuUMR CNRS 6599 Heudiasyc, Université de Technologie de CompiègneCompiègneFrance

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