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Exact solution of the generalized routing problem through graph transformations

Author

Listed:
  • M Blais

    (HEC Montréal
    Intégrale MBD)

  • G Laporte

    (HEC Montréal)

Abstract

In the general routing problem, the aim is to determine a least cost traversal of a subset of edges, arcs and vertices of a graph. The problem can be transformed into an equivalent traveling salesman problem or rural postman problem and solved optimally. Computational results are reported.

Suggested Citation

  • M Blais & G Laporte, 2003. "Exact solution of the generalized routing problem through graph transformations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 906-910, August.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:8:d:10.1057_palgrave.jors.2601590
    DOI: 10.1057/palgrave.jors.2601590
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    References listed on IDEAS

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    1. Charles E. Noon & James C. Bean, 1991. "A Lagrangian Based Approach for the Asymmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 39(4), pages 623-632, August.
    2. Clifford Orloff & David Caprera, 1976. "Reduction and Solution of Large Scale Vehicle Routing Problems," Transportation Science, INFORMS, vol. 10(4), pages 361-373, November.
    3. Mandell Bellmore & John C. Malone, 1971. "Pathology of Traveling-Salesman Subtour-Elimination Algorithms," Operations Research, INFORMS, vol. 19(2), pages 278-307, April.
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    Cited by:

    1. Ciancio, Claudio & Laganá, Demetrio & Vocaturo, Francesca, 2018. "Branch-price-and-cut for the Mixed Capacitated General Routing Problem with Time Windows," European Journal of Operational Research, Elsevier, vol. 267(1), pages 187-199.
    2. Albiach, José & Sanchis, José Marí­a & Soler, David, 2008. "An asymmetric TSP with time windows and with time-dependent travel times and costs: An exact solution through a graph transformation," European Journal of Operational Research, Elsevier, vol. 189(3), pages 789-802, September.
    3. Michael Drexl, 2014. "A Generic Heuristic for Vehicle Routing Problems with Multiple Synchronization Constraints," Working Papers 1412, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 04 Nov 2014.
    4. D Soler & E Martínez & J C Micó, 2008. "A transformation for the mixed general routing problem with turn penalties," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(4), pages 540-547, April.
    5. H-J Kim & Y-D Kim & D-H Lee, 2005. "Scheduling for an arc-welding robot considering heat-caused distortion," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(1), pages 39-50, January.
    6. Beraldi, Patrizia & Bruni, Maria Elena & Laganà, Demetrio & Musmanno, Roberto, 2015. "The mixed capacitated general routing problem under uncertainty," European Journal of Operational Research, Elsevier, vol. 240(2), pages 382-392.
    7. Irnich, Stefan & Laganà, Demetrio & Schlebusch, Claudia & Vocaturo, Francesca, 2015. "Two-phase branch-and-cut for the mixed capacitated general routing problem," European Journal of Operational Research, Elsevier, vol. 243(1), pages 17-29.

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