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A Lower Bound for the Split Delivery Vehicle Routing Problem

Author

Listed:
  • J. M. Belenguer

    (Departament d'Estadística i Investigació Operativa, Universitat de València, Dr. Moliner, 50, Burjassot, CP.- 46100, Spain)

  • M. C. Martinez

    (Departament d'Estadística i Investigació Operativa, Universitat de València, Dr. Moliner, 50, Burjassot, CP.- 46100, Spain)

  • E. Mota

    (Departament d'Estadística i Investigació Operativa, Universitat de València, Dr. Moliner, 50, Burjassot, CP.- 46100, Spain)

Abstract

In this paper we consider the Split Delivery Vehicle Routing Problem (SDVRP), a relaxation of the known Capacitated Vehicle Routing Problem (CVRP) in which the demand of any client can be serviced by more than one vehicle. We define a feasible solution of this problem, and we show that the convex hull of the associated incidence vectors is a polyhedron ( P SDVRP ), whose dimension depends on whether a vehicle visiting a client must service, or not, at least one unit of the client demand. From a partial and linear description of P SDVRP and a new family of valid inequalities, we develop a lower bound whose quality is exhibited in the computational results provided, which include the optimal resolution of some known instances---one of them with 50 clients. This instance is, as far as we know, the biggest one solved so far.

Suggested Citation

  • J. M. Belenguer & M. C. Martinez & E. Mota, 2000. "A Lower Bound for the Split Delivery Vehicle Routing Problem," Operations Research, INFORMS, vol. 48(5), pages 801-810, October.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:5:p:801-810
    DOI: 10.1287/opre.48.5.801.12407
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    References listed on IDEAS

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    1. Moshe Dror & Pierre Trudeau, 1989. "Savings by Split Delivery Routing," Transportation Science, INFORMS, vol. 23(2), pages 141-145, May.
    2. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    3. Gerard Sierksma & Gert Tijssen, 1998. "Routing helicopters for crew exchanges on off-shore locations," Annals of Operations Research, Springer, vol. 76(0), pages 261-286, January.
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