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Constraints

, 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
Article

Abstract

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.

Keywords

Vehicle routing problem Synchronization 

Notes

Acknowledgments

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

References

  1. 1.
    Bard, J.F., Kontoravdis, G., & Yu, G. (2002). A branch-and-cut procedure for the vehicle routing problem with time windows. Transportation Science, 36(2), 250–269.CrossRefzbMATHGoogle Scholar
  2. 2.
    Beck, J. (2010). Checking-up on branch-and-check. In Cohen, D. (Ed.), Principles and practice of constraint programming – cp 2010, lecture notes in computer science (Vol. 6308, pp. 84–98). Berlin Heidelberg: Springer.Google Scholar
  3. 3.
    Beck, J., Prosser, P., & Selensky, E. (2002). On the reformulation of vehicle routing problems and scheduling problems. In Koenig, S., Holte, R. (Eds.), Abstraction, reformulation, and approximation, lecture notes in computer science (Vol. 2371, pp. 282–289). Berlin Heidelberg: Springer.Google Scholar
  4. 4.
    Beck, J.C., Prosser, P., & Selensky, E. (2003). Vehicle routing and job shop scheduling: What’s the difference? In ICAPS (pp. 267–276).Google Scholar
  5. 5.
    Bent, R., & Van Hentenryck, P. (2004). A two-stage hybrid local search for the vehicle routing problem with time windows. Transportation Science, 38(4), 515–530.CrossRefGoogle Scholar
  6. 6.
    Desaulniers, G., Desrosiers, J., & Solomon, M. (2002). Accelerating strategies in column generation methods for vehicle routing and crew scheduling problems. In Essays and surveys in metaheuristics, operations research/computer science interfaces series (Vol. 15, pp. 309–324). US: Springer.Google Scholar
  7. 7.
    Desaulniers, G., Desrosiers, J., & Solomon, M.M. (2005). Column generation (Vol. 5). Springer.Google Scholar
  8. 8.
    Drexl, M. (2012). Synchronization in vehicle routing—a survey of VRPs with multiple synchronization constraints. Transportation Science, 46(3), 297–316.CrossRefGoogle Scholar
  9. 9.
    Dumas, Y., Desrosiers, J., & Soumis, F. (1991). The pickup and delivery problem with time windows. European Journal of Operational Research, 54(1), 7–22.CrossRefzbMATHGoogle Scholar
  10. 10.
    Hachemi, N.E., Gendreau, M., & Rousseau, L.M. (2013). A heuristic to solve the synchronized log-truck scheduling problem. Computers & Operations Research, 40 (3), 666–673. Transport Scheduling.CrossRefGoogle Scholar
  11. 11.
    Hempsch, C., & Irnich, S. (2008). Vehicle routing problems with inter-tour resource constraints. In Golden, B., Raghavan, S., Wasil E. (Eds.), The vehicle routing problem: latest advances and new challenges, operations research/computer science interfaces (Vol. 43, pp. 421–444). US: Springer.Google Scholar
  12. 12.
    Hooker, J. (1994). Logic-based methods for optimization. In Borning, A. (Ed.) Principles and practice of constraint programming, lecture notes in computer science (Vol. 874, pp. 336–349). Berlin Heidelberg: Springer.Google Scholar
  13. 13.
    Hooker, J.N., & Mitchell, J.E. (2008). Integrated methods for optimization. SIAM review, 50(1), 183.Google Scholar
  14. 14.
    Kallehauge, B., Larsen, J., Madsen, O.B., & Solomon, M.M. (2005). Vehicle routing problem with time windows. In Desaulniers, G., Desrosiers, J., Solomon, M.M. (Eds.), Column generation (pp. 67–98). US: Springer.Google Scholar
  15. 15.
    Lübbecke, M.E., & Desrosiers, J. (2005). Selected topics in column generation. Operations Research, 53(6), 1007–1023.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Rix, G., Rousseau, L.M., & Pesant, G. (2015). A column generation algorithm for tactical timber transportation planning. Journal of the Operational Research Society, 66(2), 278–287.CrossRefGoogle Scholar
  17. 17.
    Ropke, S., & Cordeau, J.F. (2009). Branch and cut and price for the pickup and delivery problem with time windows. Transportation Science, 43(3), 267–286.CrossRefGoogle Scholar
  18. 18.
    Ropke, S., Cordeau, J.F., & Laporte, G. (2007). Models and branch-and-cut algorithms for pickup and delivery problems with time windows. Networks, 49(4), 258–272.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. In Maher, M., Puget, J.F. (Eds.), Principles and practice of constraint programming — cp98, lecture notes in computer science (Vol. 1520, pp. 417–431), Berlin Heidelberg: Springer.Google Scholar
  20. 20.
    Thorsteinsson, E. (2001). Branch-and-check: A hybrid framework integrating mixed integer programming and constraint logic programming. In Walsh, T. (Ed.), Principles and practice of constraint programming — cp 2001, lecture notes in computer science (Vol. 2239, pp. 16–30). Berlin Heidelberg: Springer.Google Scholar
  21. 21.
    Toth, P., & Vigo, D. (2002). The vehicle routing problem. Society for industrial and applied mathematics. Philadelphia.Google Scholar

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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