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A Branch-and-Cut-and-Price Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem

Author

Listed:
  • Fernando Afonso Santos

    (Universidade Federal de Itajubá, Campus Itabira, Itabira, Minas Gerais 35903-087, Brazil)

  • Geraldo Robson Mateus

    (Departamento de Ciência da Computação, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais 31270-921, Brazil)

  • Alexandre Salles da Cunha

    (Departamento de Ciência da Computação, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais 31270-921, Brazil)

Abstract

In this paper, we introduce a branch-and-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem. The algorithm relies on a reformulation based on q -routes that combines two important features. First, it overcomes symmetry issues observed in a formulation coming from a previous study of the problem. Second, it is strengthened with several classes of valid inequalities. As a result, the branch-and-cut-and-price implementation compares favorably with previous exact solution approaches for the problem—namely, two branch-and-price algorithms and a branch-and-cut method. Overall, 10 new optimality certificates and 8 new best upper bounds are provided in this study. New best lower bounds are also presented for all instances in the hardest test set from the literature.

Suggested Citation

  • Fernando Afonso Santos & Geraldo Robson Mateus & Alexandre Salles da Cunha, 2015. "A Branch-and-Cut-and-Price Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem," Transportation Science, INFORMS, vol. 49(2), pages 355-368, May.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:2:p:355-368
    DOI: 10.1287/trsc.2013.0500
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    References listed on IDEAS

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    2. Kangzhou Wang & Shulin Lan & Yingxue Zhao, 2017. "A genetic-algorithm-based approach to the two-echelon capacitated vehicle routing problem with stochastic demands in logistics service," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1409-1421, November.
    3. Mingyuan Wei & Hao Guan & Yunhan Liu & Benhe Gao & Canrong Zhang, 2020. "Production, Replenishment and Inventory Policies for Perishable Products in a Two-Echelon Distribution Network," Sustainability, MDPI, vol. 12(11), pages 1-26, June.
    4. Alvarez, Jose A. Lopez & Buijs, Paul & Deluster, Rogier & Coelho, Leandro C. & Ursavas, Evrim, 2020. "Strategic and operational decision-making in expanding supply chains for LNG as a fuel," Omega, Elsevier, vol. 97(C).
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    6. Zhou, Hang & Qin, Hu & Cheng, Chun & Rousseau, Louis-Martin, 2023. "An exact algorithm for the two-echelon vehicle routing problem with drones," Transportation Research Part B: Methodological, Elsevier, vol. 168(C), pages 124-150.
    7. Li, Jiliu & Xu, Min & Sun, Peng, 2022. "Two-echelon capacitated vehicle routing problem with grouping constraints and simultaneous pickup and delivery," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 261-291.
    8. Xianlong Ge & Yuanzhi Jin, 2023. "Sustainability Oriented Vehicle Route Planning Based on Time-Dependent Arc Travel Durations," Sustainability, MDPI, vol. 15(4), pages 1-25, February.
    9. Huang, Yixiao & Savelsbergh, Martin & Zhao, Lei, 2018. "Designing logistics systems for home delivery in densely populated urban areas," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 95-125.
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