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A Branch-and-Cut Algorithm for the Multidepot Rural Postman Problem

Author

Listed:
  • Elena Fernández

    (Department of Statistics and Operations Research, Universitat Politècnica de Catalunya–BarcelonaTech, 08034 Barcelona, Spain; Barcelona Graduate School of Mathematics, Universitat de Barcelona, 08007 Barcelona, Spain)

  • Gilbert Laporte

    (HEC Montréal, Montréal, Québec H3T 2A7, Canada)

  • Jessica Rodríguez-Pereira

    (Department of Statistics and Operations Research, Universitat Politècnica de Catalunya–BarcelonaTech, 08034 Barcelona, Spain)

Abstract

This paper considers the Multidepot Rural Postman Problem, an extension of the classical Rural Postman Problem in which there are several depots instead of only one. The aim is to construct a minimum cost set of routes traversing each required edge of the graph, where each route starts and ends at the same depot. The paper makes the following scientific contributions: (i) It presents optimality conditions and a worst case analysis for the problem; (ii) It proposes a compact integer linear programming formulation containing only binary variables, as well as a polyhedral analysis; (iii) It develops a branch-and-cut algorithm that includes several new exact and heuristic separation procedures. Instances involving up to four depots, 744 vertices, and 1,315 edges are solved to optimality. These instances contain up to 140 required components and 1,000 required edges.

Suggested Citation

  • Elena Fernández & Gilbert Laporte & Jessica Rodríguez-Pereira, 2018. "A Branch-and-Cut Algorithm for the Multidepot Rural Postman Problem," Transportation Science, INFORMS, vol. 52(2), pages 353-369, March.
    • Handle: RePEc:inm:ortrsc:v:52:y:2018:i:2:p:353-369
    DOI: 10.1287/trsc.2017.0783
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    References listed on IDEAS

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    1. Elena Fernández & Oscar Meza & Robert Garfinkel & Maruja Ortega, 2003. "On the Undirected Rural Postman Problem: Tight Bounds Based on a New Formulation," Operations Research, INFORMS, vol. 51(2), pages 281-291, April.
    2. Aráoz, Julián & Fernández, Elena & Meza, Oscar, 2009. "Solving the Prize-collecting Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 196(3), pages 886-896, August.
    3. Alain Hertz & Gilbert Laporte & Pierrette Nanchen Hugo, 1999. "Improvement Procedures for the Undirected Rural Postman Problem," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 53-62, February.
    4. Corberan, A. & Sanchis, J. M., 1998. "The general routing problem polyhedron: Facets from the RPP and GTSP polyhedra," European Journal of Operational Research, Elsevier, vol. 108(3), pages 538-550, August.
    5. Ángel Corberán & Elena Fernández & Carles Franquesa & José María Sanchis, 2011. "The Windy Clustered Prize-Collecting Arc-Routing Problem," Transportation Science, INFORMS, vol. 45(3), pages 317-334, August.
    6. Muyldermans, L. & Cattrysse, D. & Van Oudheusden, D. & Lotan, T., 2002. "Districting for salt spreading operations," European Journal of Operational Research, Elsevier, vol. 139(3), pages 521-532, June.
    7. Corberan, A. & Sanchis, J. M., 1994. "A polyhedral approach to the rural postman problem," European Journal of Operational Research, Elsevier, vol. 79(1), pages 95-114, November.
    8. Amberg, Anita & Domschke, Wolfgang & Vo[ss], Stefan, 2000. "Multiple center capacitated arc routing problems: A tabu search algorithm using capacitated trees," European Journal of Operational Research, Elsevier, vol. 124(2), pages 360-376, July.
    9. Alexander Butsch & Jörg Kalcsics & Gilbert Laporte, 2014. "Districting for Arc Routing," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 809-824, November.
    10. Amberg, Anita & Domschke, Wolfgang & Voß, S., 2000. "Multiple center capacitated arc routing problems: a tabu search algorithm using capacitated trees," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 15855, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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    2. 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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