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The distance constrained multiple vehicle traveling purchaser problem

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  • Bianchessi, N.
  • Mansini, R.
  • Speranza, M.G.

Abstract

In the Distance Constrained Multiple Vehicle Traveling Purchaser Problem (DC-MVTPP) a fleet of vehicles is available to visit suppliers offering products at different prices and with different quantity availabilities. The DC-MVTPP consists in selecting a subset of suppliers so to satisfy products demand at the minimum traveling and purchasing costs, while ensuring that the distance traveled by each vehicle does not exceed a predefined upper bound. The problem generalizes the classical Traveling Purchaser Problem (TPP) and adds new realistic features to the decision problem. In this paper we present different mathematical programming formulations for the problem. A branch-and-price algorithm is also proposed to solve a set partitioning formulation where columns represent feasible routes for the vehicles. At each node of the branch-and-bound tree, the linear relaxation of the set partitioning formulation, augmented by the branching constraints, is solved through column generation. The pricing problem is solved using dynamic programming. A set of instances has been derived from benchmark instances for the asymmetric TPP. Instances with up to 100 suppliers and 200 products have been solved to optimality.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:235:y:2014:i:1:p:73-87
    DOI: 10.1016/j.ejor.2013.10.018
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    References listed on IDEAS

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    Cited by:

    1. Zahra Sadat Hasanpour Jesri & Kourosh Eshghi & Majid Rafiee & Tom Van Woensel, 2022. "The Multi-Depot Traveling Purchaser Problem with Shared Resources," Sustainability, MDPI, vol. 14(16), pages 1-26, August.
    2. 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.
    3. Nicola Bianchessi & Stefan Irnich & Christian Tilk, 2020. "A Branch-Price-and-Cut Algorithm for the Capacitated Multiple Vehicle Traveling Purchaser Problem with Unitary Demand," Working Papers 2003, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. 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.
    5. E. Angelelli & R. Mansini & M. Vindigni, 2016. "The Stochastic and Dynamic Traveling Purchaser Problem," Transportation Science, INFORMS, vol. 50(2), pages 642-658, May.
    6. 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.
    7. 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.
    8. 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.
    9. Gambella, Claudio & Maggioni, Francesca & Vigo, Daniele, 2019. "A stochastic programming model for a tactical solid waste management problem," European Journal of Operational Research, Elsevier, vol. 273(2), pages 684-694.
    10. Jaehn, Florian & Meissner, Finn, 2022. "The rebound effect in transportation," Omega, Elsevier, vol. 108(C).
    11. 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.
    12. Ruslan Sadykov & François Vanderbeck & Artur Pessoa & Issam Tahiri & Eduardo Uchoa, 2019. "Primal Heuristics for Branch and Price: The Assets of Diving Methods," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 251-267, April.

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