, Volume 21, Issue 3, pp 394–412 | Cite as

A branch-and-price-and-check model for the vehicle routing problem with location congestion

  • Edward LamEmail author
  • Pascal Van Hentenryck


This paper considers a vehicle routing problem with pickup and delivery, time windows and location congestion. Locations provide a number of cumulative resources that are utilized by vehicles either during service (e.g., forklifts) or for the entirety of their visit (e.g., parking bays). Locations can become congested if insufficient resources are available, upon which vehicles must wait until a resource becomes available before proceeding. The problem is challenging from a computational standpoint since it incorporates the vehicle routing problem and the resource-constrained project scheduling problem. The main contribution of this paper is a branch-and-price-and-check model that uses a branch-and-price algorithm that solves the underlying vehicle routing problem, and a constraint programming subproblem that checks the feasibility of the location resource constraints, and then adds combinatorial nogood cuts to the master problem if the resource constraints are violated. Experimental results show the benefits of the branch-and-price-and-check approach.


Vehicle routing problem Synchronization 



We would like to thank the reviewers for their constructive comments and suggestions.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.University of MelbourneParkvilleAustralia
  2. 2.NICTAWest MelbourneAustralia
  3. 3.University of MichiganAnn ArborUSA

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