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The Hierarchical Mixed Rural Postman Problem: Polyhedral analysis and a branch-and-cut algorithm

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  • Colombi, Marco
  • Corberán, Ángel
  • Mansini, Renata
  • Plana, Isaac
  • Sanchis, José M.

Abstract

The Hierarchical Mixed Rural Postman Problem is defined on a mixed graph where arcs and edges that require a service are divided into clusters that have to be serviced in a hierarchical order. The problem generalizes the Mixed Rural Postman Problem and thus is NP-hard. In this paper, we provide a polyhedral analysis of the problem and propose a branch-and-cut algorithm for its solution based on the introduced classes of valid inequalities. Extensive computational experiments are reported on benchmark instances. The exact approach allows to find the optimal solutions in less than 1 hour for instances with up to 999 vertices, 2678 links, and five clusters.

Suggested Citation

  • Colombi, Marco & Corberán, Ángel & Mansini, Renata & Plana, Isaac & Sanchis, José M., 2017. "The Hierarchical Mixed Rural Postman Problem: Polyhedral analysis and a branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 257(1), pages 1-12.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:1:p:1-12
    DOI: 10.1016/j.ejor.2016.07.026
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    References listed on IDEAS

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    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.
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    6. Letchford, A.N. & Eglese, R.W., 1998. "The rural postman problem with deadline classes," European Journal of Operational Research, Elsevier, vol. 105(3), pages 390-400, March.
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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.
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    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.

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