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The Windy Clustered Prize-Collecting Arc-Routing Problem

Author

Listed:
  • Ángel Corberán

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

  • Elena Fernández

    (Statistics and Operations Research Department, Technical University of Catalonia, 08034 Barcelona, Spain)

  • Carles Franquesa

    (Statistics and Operations Research Department, Technical University of Catalonia, 08034 Barcelona, Spain)

  • José María Sanchis

    (Applied Mathematics Department, Technical University of Valencia, 46022 Valencia, Spain)

Abstract

This paper introduces the windy clustered prize-collecting arc-routing problem. It is an arc-routing problem where each demand edge is associated with a profit that is collected once if the edge is serviced, independent of the number of times the edge is traversed. It is further required that if a demand edge is serviced, then all the demand edges of its component are also serviced. A mathematical programming formulation is given and some polyhedral results including several facet-defining and valid inequalities are presented. The separation problem for the different families of inequalities is studied. Numerical results from computational experiments are analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:45:y:2011:i:3:p:317-334
    DOI: 10.1287/trsc.1110.0370
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    References listed on IDEAS

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    1. 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.
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    3. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    4. 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.
    5. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "The Profitable Arc Tour Problem: Solution with a Branch-and-Price Algorithm," Transportation Science, INFORMS, vol. 39(4), pages 539-552, November.
    6. Benavent, Enrique & Carrotta, Alessandro & Corberan, Angel & Sanchis, Jose M. & Vigo, Daniele, 2007. "Lower bounds and heuristics for the Windy Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 855-869, January.
    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.
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    Cited by:

    1. Fernández, Elena & Roca-Riu, Mireia & Speranza, M. Grazia, 2018. "The Shared Customer Collaboration Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1078-1093.
    2. Kasaei, Maziar & Salman, F. Sibel, 2016. "Arc routing problems to restore connectivity of a road network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 177-206.
    3. Archetti, Claudia & Bertazzi, Luca & Laganà, Demetrio & Vocaturo, Francesca, 2017. "The Undirected Capacitated General Routing Problem with Profits," European Journal of Operational Research, Elsevier, vol. 257(3), pages 822-833.
    4. 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.
    5. Colombi, Marco & Mansini, Renata, 2014. "New results for the Directed Profitable Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 760-773.
    6. Claudia Archetti & M. Grazia Speranza & Ángel Corberán & José M. Sanchis & Isaac Plana, 2014. "The Team Orienteering Arc Routing Problem," Transportation Science, INFORMS, vol. 48(3), pages 442-457, August.
    7. 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.
    8. Elena Fernández & Jessica Rodríguez-Pereira, 2017. "Multi-depot rural postman problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 340-372, July.

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