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Mathematical Programming

, Volume 137, Issue 1–2, pp 409–452 | Cite as

Improved lower bounds and exact algorithm for the capacitated arc routing problem

  • Enrico Bartolini
  • Jean-François Cordeau
  • Gilbert Laporte
Full Length Paper Series A

Abstract

In the capacitated arc routing problem (CARP), a subset of the edges of an undirected graph has to be serviced at least cost by a fleet of identical vehicles in such a way that the total demand of the edges serviced by each vehicle does not exceed its capacity. This paper describes a new lower bounding method for the CARP based on a set partitioning-like formulation of the problem with additional cuts. This method uses cut-and-column generation to solve different relaxations of the problem, and a new dynamic programming method for generating routes. An exact algorithm based on the new lower bounds was also implemented to assess their effectiveness. Computational results over a large set of classical benchmark instances show that the proposed method improves most of the best known lower bounds for the open instances, and can solve several of these for the first time.

Keywords

Arc routing Set partitioning Valid inequalities Column generation Dynamic programming 

Mathematics Subject Classification (2000)

90C10 90C39 90C57 

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Copyright information

© Springer and Mathematical Optimization Society 2011

Authors and Affiliations

  • Enrico Bartolini
    • 1
  • Jean-François Cordeau
    • 1
  • Gilbert Laporte
    • 1
  1. 1.HEC Montréal, and Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT)MontrealCanada

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