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Two-phase branch-and-cut for the mixed capacitated general routing problem

Author

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  • Irnich, Stefan
  • Laganà, Demetrio
  • Schlebusch, Claudia
  • Vocaturo, Francesca

Abstract

The Mixed Capacitated General Routing Problem (MCGRP) is defined over a mixed graph, for which some vertices must be visited and some links must be traversed at least once. The problem consists of determining a set of least-cost vehicle routes that satisfy this requirement and respect the vehicle capacity. Few papers have been devoted to the MCGRP, in spite of interesting real-world applications, prevalent in school bus routing, mail delivery, and waste collection. This paper presents a new mathematical model for the MCGRP based on two-index variables. The approach proposed for the solution is a two-phase branch-and-cut algorithm, which uses an aggregate formulation to develop an effective lower bounding procedure. This procedure also provides strong valid inequalities for the two-index model. Extensive computational experiments over benchmark instances are presented.

Suggested Citation

  • Irnich, Stefan & Laganà, Demetrio & Schlebusch, Claudia & Vocaturo, Francesca, 2015. "Two-phase branch-and-cut for the mixed capacitated general routing problem," European Journal of Operational Research, Elsevier, vol. 243(1), pages 17-29.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:1:p:17-29
    DOI: 10.1016/j.ejor.2014.11.005
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Bruno P. Bruck & Manuel Iori, 2017. "Non-Elementary Formulations for Single Vehicle Routing Problems with Pickups and Deliveries," Operations Research, INFORMS, vol. 65(6), pages 1597-1614, December.
    3. Pourhejazy, Pourya & Zhang, Dali & Zhu, Qinghua & Wei, Fangfang & Song, Shuang, 2021. "Integrated E-waste transportation using capacitated general routing problem with time-window," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    4. Ciancio, Claudio & Laganá, Demetrio & Vocaturo, Francesca, 2018. "Branch-price-and-cut for the Mixed Capacitated General Routing Problem with Time Windows," European Journal of Operational Research, Elsevier, vol. 267(1), pages 187-199.
    5. Benavent, Enrique & Corberán, Ángel & Laganà, Demetrio & Vocaturo, Francesca, 2019. "The periodic rural postman problem with irregular services on mixed graphs," European Journal of Operational Research, Elsevier, vol. 276(3), pages 826-839.
    6. Jorge Oyola & Halvard Arntzen & David L. Woodruff, 2018. "The stochastic vehicle routing problem, a literature review, part I: models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 193-221, September.
    7. Gia-Shie Liu & Kuo-Ping Lin, 2020. "The Online Distribution System of Inventory-Routing Problem with Simultaneous Deliveries and Returns Concerning CO 2 Emission Cost," Mathematics, MDPI, vol. 8(6), pages 1-27, June.
    8. Valle, Cristiano Arbex & Beasley, John E. & da Cunha, Alexandre Salles, 2017. "Optimally solving the joint order batching and picker routing problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 817-834.
    9. Thibaut Vidal, 2017. "Node, Edge, Arc Routing and Turn Penalties: Multiple Problems—One Neighborhood Extension," Operations Research, INFORMS, vol. 65(4), pages 992-1010, August.
    10. Jorge Oyola & Halvard Arntzen & David L. Woodruff, 2017. "The stochastic vehicle routing problem, a literature review, Part II: solution methods," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 349-388, December.

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