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Mathematical Programming

, Volume 100, Issue 2, pp 423–445 | Cite as

A new branch-and-cut algorithm for the capacitated vehicle routing problem

  • Jens LysgaardEmail author
  • Adam N. Letchford
  • Richard W. Eglese
Article

Abstract.

We present a new branch-and-cut algorithm for the capacitated vehicle routing problem (CVRP). The algorithm uses a variety of cutting planes, including capacity, framed capacity, generalized capacity, strengthened comb, multistar, partial multistar, extended hypotour inequalities, and classical Gomory mixed-integer cuts.

For each of these classes of inequalities we describe our separation algorithms in detail. Also we describe the other important ingredients of our branch-and-cut algorithm, such as the branching rules, the node selection strategy, and the cut pool management. Computational results, for a large number of instances, show that the new algorithm is competitive. In particular, we solve three instances (B-n50-k8, B-n66-k9 and B-n78-k10) of Augerat to optimality for the first time.

Keywords

vehicle routing branch-and-cut separation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jens Lysgaard
    • 1
    Email author
  • Adam N. Letchford
    • 2
  • Richard W. Eglese
    • 3
  1. 1.Department of Management Science and LogisticsAarhus School of BusinessDenmark
  2. 2.Department of Management ScienceLancaster UniversityEngland
  3. 3.Department of Management ScienceLancaster UniversityEngland

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