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Transformations of node‐balanced routing problems

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  • Antonio Martinez‐Sykora
  • Tolga Bektaş

Abstract

This article describes a polynomial transformation for a class of unit‐demand vehicle routing problems, named node‐balanced routing problems (BRP), where the number of nodes on each route is restricted to be in an interval such that the workload across the routes is balanced. The transformation is general in that it can be applied to single or multiple depot, homogeneous or heterogeneous fleet BRPs, and any combination thereof. At the heart of the procedure lies transforming the BRP into a generalized traveling salesman problem (TSP), which can then be transformed into a TSP. The transformed graph exhibits special properties which can be exploited to significantly reduce the number of arcs, and used to construct a formulation for the resulting TSP that amounts to no more than that of a constrained assignment problem. Computational results on a number of instances are presented. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 370–387, 2015

Suggested Citation

  • Antonio Martinez‐Sykora & Tolga Bektaş, 2015. "Transformations of node‐balanced routing problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 370-387, August.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:5:p:370-387
    DOI: 10.1002/nav.21634
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    References listed on IDEAS

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    1. Yang GuoXing, 1995. "Transformation of multidepot multisalesmen problem to the standard travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 81(3), pages 557-560, March.
    2. Laporte, Gilbert, 1992. "The traveling salesman problem: An overview of exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 59(2), pages 231-247, June.
    3. M. R. Rao, 1980. "Technical Note—A Note on the Multiple Traveling Salesmen Problem," Operations Research, INFORMS, vol. 28(3-part-i), pages 628-632, June.
    4. Bektaş, Tolga, 2012. "Formulations and Benders decomposition algorithms for multidepot salesmen problems with load balancing," European Journal of Operational Research, Elsevier, vol. 216(1), pages 83-93.
    5. Gilbert Laporte, 2007. "What you should know about the vehicle routing problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(8), pages 811-819, December.
    6. Kritikos, Manolis N. & Ioannou, George, 2010. "The balanced cargo vehicle routing problem with time windows," International Journal of Production Economics, Elsevier, vol. 123(1), pages 42-51, January.
    7. Hu, Chao-Fang & Teng, Chang-Jun & Li, Shao-Yuan, 2007. "A fuzzy goal programming approach to multi-objective optimization problem with priorities," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1319-1333, February.
    8. Calvete, Herminia I. & Gale, Carmen & Oliveros, Maria-Jose & Sanchez-Valverde, Belen, 2007. "A goal programming approach to vehicle routing problems with soft time windows," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1720-1733, March.
    9. Roy Jonker & Ton Volgenant, 1988. "Technical Note—An Improved Transformation of the Symmetric Multiple Traveling Salesman Problem," Operations Research, INFORMS, vol. 36(1), pages 163-167, February.
    10. Saman Hong & Manfred W. Padberg, 1977. "Technical Note—A Note on the Symmetric Multiple Traveling Salesman Problem with Fixed Charges," Operations Research, INFORMS, vol. 25(5), pages 871-874, October.
    11. Laporte, Gilbert, 1992. "The vehicle routing problem: An overview of exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 59(3), pages 345-358, June.
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