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Solving the asymmetric traveling purchaser problem

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  • Jorge Riera-Ledesma
  • Juan-José Salazar-González

Abstract

The Asymmetric Traveling Purchaser Problem (ATPP) is a generalization of the Asymmetric Traveling Salesman Problem with several applications in the routing and the scheduling contexts. This problem is defined as follows. Let us consider a set of products and a set of markets. Each market is provided with a limited amount of each product at a known price. The ATPP consists in selecting a subset of markets such that a given demand of each product can be purchased, minimizing the routing cost and the purchasing cost. The aim of this article is to evaluate the effectiveness of a branch-and-cut algorithm based on new valid inequalities. It also proposes a transformation of the ATPP into its symmetric version, so a second exact method is also presented. An extensive computational analysis on several classes of instances from literature evaluates the proposed approaches. A previous work () solves instances with up to 25 markets and 100 products, while the here-presented approaches prove optimality on instances with up to 200 markets and 200 products. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • Jorge Riera-Ledesma & Juan-José Salazar-González, 2006. "Solving the asymmetric traveling purchaser problem," Annals of Operations Research, Springer, vol. 144(1), pages 83-97, April.
    • Handle: RePEc:spr:annopr:v:144:y:2006:i:1:p:83-97:10.1007/s10479-006-0014-y
    DOI: 10.1007/s10479-006-0014-y
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    References listed on IDEAS

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    1. Singh, Kashi N. & van Oudheusden, Dirk L., 1997. "A branch and bound algorithm for the traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 97(3), pages 571-579, March.
    2. Matteo Fischetti & Paolo Toth, 1997. "A Polyhedral Approach to the Asymmetric Traveling Salesman Problem," Management Science, INFORMS, vol. 43(11), pages 1520-1536, November.
    3. Riera-Ledesma, Jorge & Salazar-Gonzalez, Juan Jose, 2005. "A heuristic approach for the Travelling Purchaser Problem," European Journal of Operational Research, Elsevier, vol. 162(1), pages 142-152, April.
    4. Gilbert Laporte & Jorge Riera-Ledesma & Juan-José Salazar-González, 2003. "A Branch-and-Cut Algorithm for the Undirected Traveling Purchaser Problem," Operations Research, INFORMS, vol. 51(6), pages 940-951, December.
    5. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
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    Cited by:

    1. Palomo-Martínez, Pamela J. & Salazar-Aguilar, M. Angélica, 2019. "The bi-objective traveling purchaser problem with deliveries," European Journal of Operational Research, Elsevier, vol. 273(2), pages 608-622.
    2. Carolina Almeida & Richard Gonçalves & Elizabeth Goldbarg & Marco Goldbarg & Myriam Delgado, 2012. "An experimental analysis of evolutionary heuristics for the biobjective traveling purchaser problem," Annals of Operations Research, Springer, vol. 199(1), pages 305-341, October.
    3. Jaehn, Florian & Meissner, Finn, 2022. "The rebound effect in transportation," Omega, Elsevier, vol. 108(C).
    4. Manerba, Daniele & Mansini, Renata & Riera-Ledesma, Jorge, 2017. "The Traveling Purchaser Problem and its variants," European Journal of Operational Research, Elsevier, vol. 259(1), pages 1-18.
    5. Mingyu Xiao & Jianan Zhang & Weibo Lin, 0. "Parameterized algorithms and complexity for the traveling purchaser problem and its variants," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-17.
    6. Mingyu Xiao & Jianan Zhang & Weibo Lin, 2022. "Parameterized algorithms and complexity for the traveling purchaser problem and its variants," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2269-2285, November.
    7. Bianchessi, N. & Mansini, R. & Speranza, M.G., 2014. "The distance constrained multiple vehicle traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 235(1), pages 73-87.

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