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On the Undirected Rural Postman Problem: Tight Bounds Based on a New Formulation

Author

Listed:
  • Elena Fernández

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

  • Oscar Meza

    (Computer Science and Information Technology Department, Simón Bolívar University, Baruta, Venezuela)

  • Robert Garfinkel

    (School of Business Administration, University of Connecticut, Storrs, Connecticut 06269)

  • Maruja Ortega

    (Computer Science and Information Technology Department, Simón Bolívar University, Baruta, Venezuela)

Abstract

The Rural Postman Problem (RPP) is a classic “edge-routing” problem. A mathematical programming formulation of the RPP that differs fundamentally from those in the literature was introduced, but not tested computationally, by Garfinkel and Webb (1999). A rudimentary algorithm that yields lower bounds via cutting planes and upper bounds via heuristics is developed and tested for a variation of that formulation. Computational results are encouraging, especially in terms of the relatively small number of added inequalities needed to get good lower bounds, and the fact that the vast majority of these have efficient, exact separation procedures. Note that a first algorithm based on this new formulation is computationally competitive, allowing the possibility of far more efficient and complex future realizations.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:2:p:281-291
    DOI: 10.1287/opre.51.2.281.12790
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    References listed on IDEAS

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    Cited by:

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    3. 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.
    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. Elena Fernández & Oscar Meza, 2004. "Even Cycles and Perfect Matching Problems with Side Constraints," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 381-396, September.
    6. 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.
    7. Julián Aráoz & Elena Fernández & Carles Franquesa, 2009. "The Clustered Prize-Collecting Arc Routing Problem," Transportation Science, INFORMS, vol. 43(3), pages 287-300, August.

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