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A branch-and-cut algorithm for the profitable windy rural postman problem

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  • Ávila, Thais
  • Corberán, Ángel
  • Plana, Isaac
  • Sanchis, José M.

Abstract

In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit associated with some of the edges of the graph, consisting of finding a route maximizing the difference between the total profit collected and the total cost. This problem generalizes the rural postman problem and other well-known arc routing problems and has real-life applications, mainly in snow removal operations. We propose here a formulation for the problem and study its associated polyhedron. Several families of facet-inducing inequalities are described and used in the design of a branch-and-cut procedure. The algorithm has been tested on a large set of benchmark instances and compared with other existing algorithms. The results obtained show that the branch-and-cut algorithm is able to solve large-sized instances optimally in reasonable computing times.

Suggested Citation

  • Ávila, Thais & Corberán, Ángel & Plana, Isaac & Sanchis, José M., 2016. "A branch-and-cut algorithm for the profitable windy rural postman problem," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1092-1101.
  • Handle: RePEc:eee:ejores:v:249:y:2016:i:3:p:1092-1101
    DOI: 10.1016/j.ejor.2015.10.016
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    1. Gianfranco Guastaroba & Renata Mansini & M Grazia Speranza, 2009. "Modeling the Pre Auction Stage The Truckload Case," Lecture Notes in Economics and Mathematical Systems, in: Jo A.E.E. Nunen & M. Grazia Speranza & Luca Bertazzi (ed.), Innovations in Distribution Logistics, chapter 11, pages 219-233, Springer.
    2. 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.
    3. Zachariadis, E.E. & Kiranoudis, C.T., 2011. "Local search for the undirected capacitated arc routing problem with profits," European Journal of Operational Research, Elsevier, vol. 210(2), pages 358-367, April.
    4. Enrique Benavent & Ángel Corberán & Luís Gouveia & Maria Mourão & Leonor Pinto, 2015. "Profitable mixed capacitated arc routing and related problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 244-274, April.
    5. J Euchi & H Chabchoub, 2011. "Hybrid metaheuristics for the profitable arc tour problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 2013-2022, November.
    6. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    7. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "Traveling Salesman Problems with Profits," Transportation Science, INFORMS, vol. 39(2), pages 188-205, May.
    8. Malandraki, Chryssi & Daskin, Mark S., 1993. "The maximum benefit Chinese postman problem and the maximum benefit traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 65(2), pages 218-234, March.
    9. 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.
    10. 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.
    11. Benjamin Dussault & Bruce Golden & Edward Wasil, 2014. "The downhill plow problem with multiple plows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(10), pages 1465-1474, October.
    12. Vansteenwegen, Pieter & Souffriau, Wouter & Oudheusden, Dirk Van, 2011. "The orienteering problem: A survey," European Journal of Operational Research, Elsevier, vol. 209(1), pages 1-10, February.
    13. 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.
    14. J Euchi & H Chabchoub, 2011. "Hybrid metaheuristics for the profitable arc tour problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 2013-2022, November.
    15. 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.
    16. Tunchan Cura, 2013. "An artificial bee colony approach for the undirected capacitated arc routing problem with profits," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 17(4), pages 483-508.
    17. Pearn, W. L. & Wang, K. H., 2003. "On the Maximum Benefit Chinese Postman Problem," Omega, Elsevier, vol. 31(4), pages 269-273, August.
    18. 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.
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    2. Pop, Petrică C. & Cosma, Ovidiu & Sabo, Cosmin & Sitar, Corina Pop, 2024. "A comprehensive survey on the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 314(3), pages 819-835.

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