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New Results on the Mixed General Routing Problem

Author

Listed:
  • Angel Corberán

    (Departament d’Estadística i Investigació Operativa, Universitat de València, València, Spain)

  • Gustavo Mejía

    (Departamento de Ciencias Básicas, Universidad EAFIT, Medellín, Colombia)

  • José M. Sanchis

    (Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Valencia, Spain)

Abstract

In this paper, we deal with the polyhedral description and the resolution of the Mixed General Routing Problem. This problem, in which the service activity occurs both at some of the nodes and at some of the arcs and edges of a mixed graph, contains a large number of important arc and node routing problems as special cases. Here, a large family of facet-defining inequalities, the Honeycomb inequalities, is described. Furthermore, a cutting-plane algorithm for this problem that incorporates new separation procedures for the K-C, Regular Path-Bridge, and Honeycomb inequalities is presented. Branch and bound is invoked when the final solution of the cutting-plane procedure is fractional. Extensive computational experiments over different sets of instances are included.

Suggested Citation

  • Angel Corberán & Gustavo Mejía & José M. Sanchis, 2005. "New Results on the Mixed General Routing Problem," Operations Research, INFORMS, vol. 53(2), pages 363-376, April.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:2:p:363-376
    DOI: 10.1287/opre.1040.0168
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    References listed on IDEAS

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    Cited by:

    1. Jinghao Sun & Yakun Meng & Guozhen Tan, 2015. "An integer programming approach for the Chinese postman problem with time-dependent travel time," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 565-588, April.
    2. 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.
    3. Benavent, Enrique & Corberán, Ángel & Laganà, Demetrio & Vocaturo, Francesca, 2023. "A two-phase hybrid algorithm for the periodic rural postman problem with irregular services on mixed graphs," European Journal of Operational Research, Elsevier, vol. 307(1), pages 64-81.
    4. Thais Ávila & Ángel Corberán & Isaac Plana & José M. Sanchis, 2016. "A New Branch-and-Cut Algorithm for the Generalized Directed Rural Postman Problem," Transportation Science, INFORMS, vol. 50(2), pages 750-761, May.

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