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An Approximation Algorithm for the Traveling Salesman Problem with Backhauls

Author

Listed:
  • Michel Gendreau

    (Université Montréal, Montréal, Canada)

  • Gilbert Laporte

    (Université Montréal, Montréal, Canada)

  • Alain Hertz

    (Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland)

Abstract

The Traveling Salesman Problem with Backhauls (TSPB) is defined on a graph G = ( V , E ). The vertex set is partitioned into V = ({ v 1 }, L , B ), where v 1 is a depot, L is a set of linehaul customers, and B is a set of backhaul customers. A cost matrix satisfying the triangle inequality is defined on the edge set E . The TSPB consists of determining a least-cost Hamiltonian cycle on G such that all vertices of L are visited contiguously after v 1 , followed by all vertices of B . Following a result by Christofides for the Traveling Salesman Problem, we propose an approximation algorithm with worst-case performance ratio of 3/2 for the TSPB.

Suggested Citation

  • Michel Gendreau & Gilbert Laporte & Alain Hertz, 1997. "An Approximation Algorithm for the Traveling Salesman Problem with Backhauls," Operations Research, INFORMS, vol. 45(4), pages 639-641, August.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:4:p:639-641
    DOI: 10.1287/opre.45.4.639
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    Citations

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    Cited by:

    1. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
    2. Hipólito Hernández-Pérez & Juan-José Salazar-González, 2004. "Heuristics for the One-Commodity Pickup-and-Delivery Traveling Salesman Problem," Transportation Science, INFORMS, vol. 38(2), pages 245-255, May.
    3. Nagy, Gabor & Salhi, Said, 2005. "Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 162(1), pages 126-141, April.
    4. Ganesh, K. & Narendran, T.T., 2007. "CLOVES: A cluster-and-search heuristic to solve the vehicle routing problem with delivery and pick-up," European Journal of Operational Research, Elsevier, vol. 178(3), pages 699-717, May.
    5. Imai, Akio & Nishimura, Etsuko & Current, John, 2007. "A Lagrangian relaxation-based heuristic for the vehicle routing with full container load," European Journal of Operational Research, Elsevier, vol. 176(1), pages 87-105, January.
    6. Tatarakis, A. & Minis, I., 2009. "Stochastic single vehicle routing with a predefined customer sequence and multiple depot returns," European Journal of Operational Research, Elsevier, vol. 197(2), pages 557-571, September.
    7. Mathias Weller & Annie Chateau & Rodolphe Giroudeau & Jean-Claude König & Valentin Pollet, 2018. "On residual approximation in solution extension problems," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1195-1220, November.

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