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Parameterized algorithms and complexity for the traveling purchaser problem and its variants

Author

Listed:
  • Mingyu Xiao

    (University of Electronic Science and Technology of China)

  • Jianan Zhang

    (University of Electronic Science and Technology of China)

  • Weibo Lin

    (Huawei Technologies Co., Ltd.)

Abstract

The traveling purchaser problem (TPP), a generalization of the traveling salesman problem, is to determine a tour of suppliers and purchase needed products from suppliers while minimizing the traveling and purchasing cost. This problem finds applications in the routing and scheduling contexts and its variants with different constraints have been widely studied. Motivated by the phenomenon that most real-world instances of TPP have a small parameter (such as the number of suppliers, the number of products to purchase, and others), we study TPP and its variants from the view of parameterized complexity. We show that TPP and some variants are fixed-parameter tractable by taking the number k of products or the number m of suppliers as the parameter, and W[2]-hard by taking the number q of visited suppliers as the parameter. Furthermore, we implement some of our fixed-parameter tractable algorithms to show that they are practically effective when the parameters are not very large.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00608-x
    DOI: 10.1007/s10878-020-00608-x
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Guy Desaulniers, 2010. "Branch-and-Price-and-Cut for the Split-Delivery Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 58(1), pages 179-192, February.
    6. 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.
    7. 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.
    8. Gendreau, Michel & Manerba, Daniele & Mansini, Renata, 2016. "The multi-vehicle traveling purchaser problem with pairwise incompatibility constraints and unitary demands: A branch-and-price approach," European Journal of Operational Research, Elsevier, vol. 248(1), pages 59-71.
    9. E. Angelelli & R. Mansini & M. Vindigni, 2016. "The Stochastic and Dynamic Traveling Purchaser Problem," Transportation Science, INFORMS, vol. 50(2), pages 642-658, May.
    10. Kang, Seungmo & Ouyang, Yanfeng, 2011. "The traveling purchaser problem with stochastic prices: Exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 209(3), pages 265-272, March.
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