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The Hierarchical Mixed Rural Postman Problem

Author

Listed:
  • Marco Colombi

    (Department of Information Engineering, University of Brescia, 25123 Brescia, Italy)

  • Ángel Corberán

    (Department of Statistics and Operational Research, University of Valencia, 46100 Burjassot, Valencia, Spain)

  • Renata Mansini

    (Department of Information Engineering, University of Brescia, 25123 Bresica, Italy)

  • Isaac Plana

    (Department of Mathematics for Economics and Business, University of Valencia, 46100 Burjassot, Valencia, Spain)

  • José M. Sanchis

    (Department of Applied Mathematics, Polytechnic University of Valencia, 46100 Burjassot, Valencia, Spain)

Abstract

In this paper, we study a generalization of the Hierarchical Chinese Postman Problem on a mixed graph where only a subset of arcs and edges require a service to be accomplished following a hierarchical order. The problem, called the Hierarchical Mixed Rural Postman Problem, also generalizes the Rural Postman Problem and thus is NP-hard. We propose a new mathematical formulation, and introduce two effective solution algorithms. The first procedure is a matheuristic that is based on the exact solution of a variant of the Mixed Rural Postman Problem for each hierarchy. The second approach is a tabu search algorithm based on different improvement and diversification strategies. Computational results on an extended set of instances show how the proposed solution methods are quite effective and efficient when compared to the solutions of a branch-and-cut algorithm stopped after one hour of computation.

Suggested Citation

  • Marco Colombi & Ángel Corberán & Renata Mansini & Isaac Plana & José M. Sanchis, 2017. "The Hierarchical Mixed Rural Postman Problem," Transportation Science, INFORMS, vol. 51(2), pages 755-770, May.
    • Handle: RePEc:inm:ortrsc:v:51:y:2017:i:2:p:755-770
    DOI: 10.1287/trsc.2016.0686
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    References listed on IDEAS

    as
    1. Cabral, Edgar Alberto & Gendreau, Michel & Ghiani, Gianpaolo & Laporte, Gilbert, 2004. "Solving the hierarchical Chinese postman problem as a rural postman problem," European Journal of Operational Research, Elsevier, vol. 155(1), pages 44-50, May.
    2. Korteweg, Peter & Volgenant, Ton, 2006. "On the Hierarchical Chinese Postman Problem with linear ordered classes," European Journal of Operational Research, Elsevier, vol. 169(1), pages 41-52, February.
    3. Nathalie Perrier & André Langevin & Ciro-Alberto Amaya, 2008. "Vehicle Routing for Urban Snow Plowing Operations," Transportation Science, INFORMS, vol. 42(1), pages 44-56, February.
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    Cited by:

    1. Colombi, Marco & Corberán, Ángel & Mansini, Renata & Plana, Isaac & Sanchis, José M., 2017. "The directed profitable rural postman problem with incompatibility constraints," European Journal of Operational Research, Elsevier, vol. 261(2), pages 549-562.
    2. Xiaoguang Bao & Xinhao Ni, 2024. "Approximation algorithms for two clustered arc routing problems," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-12, July.
    3. Jessica Rodríguez-Pereira & Gilbert Laporte, 2022. "The target visitation arc routing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 60-76, April.
    4. Jianbin Xin & Benyang Yu & Andrea D’Ariano & Heshan Wang & Meng Wang, 2022. "Time-dependent rural postman problem: time-space network formulation and genetic algorithm," Operational Research, Springer, vol. 22(3), pages 2943-2972, July.

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