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Selective pricing in branch-price-and-cut algorithms for vehicle routing

  • Guy Desaulniers
  • Diego Pecin
  • Claudio Contardo
Research Paper
  • 135 Downloads

Abstract

Branch-price-and-cut is a leading methodology for solving various vehicle routing problems (VRPs). For many VRPs, the pricing subproblem of a branch-price-and-cut algorithm is highly time consuming, and to alleviate this difficulty, a relaxed pricing subproblem is used. In this paper, we introduce a new paradigm, called selective pricing, that can be applied in this context to reduce the time required for solving hard-to-solve VRPs by branch-price-and-cut. This paradigm requires the development of a labeling algorithm specific to the pricing subproblem. To illustrate selective pricing, we apply it to a branch-price-and-cut algorithm for the VRP with time windows, where the relaxed pricing subproblem is a shortest ng-path problem with resource constraints. We develop a labeling algorithm for this subproblem and show through computational experiments that it can yield significant time reductions (up to 32%) to reach a good lower bound on certain very-hard-to-solve VRPTW instances with 200 customers. We also introduce a new labeling heuristic which also leads to computational time reductions.

Keywords

Column generation Vehicle routing problem Branch-and-price Shortest path problem under resource constraints Selective pricing 

Notes

Acknowledgements

This work has been partially financed by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Fonds de recherche du Québec-Nature et technologies (FRQNT) and the GERAD.

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Copyright information

© Springer-Verlag GmbH Germany and EURO - The Association of European Operational Research Societies 2017

Authors and Affiliations

  1. 1.GERAD and Department of Mathematics and Industrial Engineering Polytechnique MontréalMontréalCanada
  2. 2.GERAD, CIRRELT and Department of Management and TechnologyESG UQÀMMontréalCanada
  3. 3.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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