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The pickup and delivery problem with transfers: Formulation and a branch-and-cut solution method

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  • Cortés, Cristián E.
  • Matamala, Martín
  • Contardo, Claudio

Abstract

In this paper, a strict formulation of a generalization of the classical pickup and delivery problem is presented. Here, we add the flexibility of providing the option for passengers to transfer from one vehicle to another at specific locations. As part of the mathematical formulation, we include transfer nodes where vehicles may interact interchanging passengers. Additional variables to keep track of customers along their route are considered. The formulation has been proven to work correctly, and by means of a simple example instance, we conclude that there exist some configurations in which a scheme allowing transfers results in better quality optimal solutions. Finally, a solution method based on Benders decomposition is addressed. We compare the computational effort of this application with a straight branch and bound strategy; we also provide insights to develop more efficient set partitioning formulations and associated algorithms for solving real-size problems.

Suggested Citation

  • Cortés, Cristián E. & Matamala, Martín & Contardo, Claudio, 2010. "The pickup and delivery problem with transfers: Formulation and a branch-and-cut solution method," European Journal of Operational Research, Elsevier, vol. 200(3), pages 711-724, February.
  • Handle: RePEc:eee:ejores:v:200:y:2010:i:3:p:711-724
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    References listed on IDEAS

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    Cited by:

    1. Park, Junhyuk & Tae, Hyunchul & Kim, Byung-In, 2012. "A post-improvement procedure for the mixed load school bus routing problem," European Journal of Operational Research, Elsevier, vol. 217(1), pages 204-213.
    2. repec:spr:eurjtl:v:6:y:2017:i:1:d:10.1007_s13676-015-0085-5 is not listed on IDEAS
    3. Drexl, Michael, 2013. "Applications of the vehicle routing problem with trailers and transshipments," European Journal of Operational Research, Elsevier, vol. 227(2), pages 275-283.
    4. Masson, Renaud & Ropke, Stefan & Lehuédé, Fabien & Péton, Olivier, 2014. "A branch-and-cut-and-price approach for the pickup and delivery problem with shuttle routes," European Journal of Operational Research, Elsevier, vol. 236(3), pages 849-862.
    5. repec:eee:transb:v:99:y:2017:i:c:p:1-29 is not listed on IDEAS
    6. Park, Junhyuk & Kim, Byung-In, 2010. "The school bus routing problem: A review," European Journal of Operational Research, Elsevier, vol. 202(2), pages 311-319, April.
    7. Chou, Yon-Chun & Chen, Yao-Hung & Chen, Hui-Min, 2014. "Pickup and delivery routing with hub transshipment across flexible time periods for improving dual objectives on workload and waiting time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 98-114.
    8. Yildiz, Hakan & Ravi, R. & Fairey, Wayne, 2010. "Integrated optimization of customer and supplier logistics at Robert Bosch LLC," European Journal of Operational Research, Elsevier, vol. 207(1), pages 456-464, November.
    9. repec:spr:annopr:v:259:y:2017:i:1:d:10.1007_s10479-017-2525-0 is not listed on IDEAS
    10. Shangyao Yan & Chun-Ying Chen & Chuan-Che Wu, 2012. "Solution methods for the taxi pooling problem," Transportation, Springer, vol. 39(3), pages 723-748, May.
    11. Rais, A. & Alvelos, F. & Carvalho, M.S., 2014. "New mixed integer-programming model for the pickup-and-delivery problem with transshipment," European Journal of Operational Research, Elsevier, vol. 235(3), pages 530-539.
    12. Correia, Gonçalo Homem de Almeida & van Arem, Bart, 2016. "Solving the User Optimum Privately Owned Automated Vehicles Assignment Problem (UO-POAVAP): A model to explore the impacts of self-driving vehicles on urban mobility," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 64-88.
    13. Ting, Chuan-Kang & Liao, Xin-Lan, 2013. "The selective pickup and delivery problem: Formulation and a memetic algorithm," International Journal of Production Economics, Elsevier, vol. 141(1), pages 199-211.
    14. Renaud Masson & Anna Trentini & Fabien Lehuédé & Nicolas Malhéné & Olivier Péton & Houda Tlahig, 0. "Optimization of a city logistics transportation system with mixed passengers and goods," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 0, pages 1-29.
    15. Agatz, Niels & Erera, Alan & Savelsbergh, Martin & Wang, Xing, 2012. "Optimization for dynamic ride-sharing: A review," European Journal of Operational Research, Elsevier, vol. 223(2), pages 295-303.
    16. Neves-Moreira, F. & Amorim, P. & Guimarães, L. & Almada-Lobo, B., 2016. "A long-haul freight transportation problem: Synchronizing resources to deliver requests passing through multiple transshipment locations," European Journal of Operational Research, Elsevier, vol. 248(2), pages 487-506.
    17. Reinhardt, Line Blander & Clausen, Tommy & Pisinger, David, 2013. "Synchronized dial-a-ride transportation of disabled passengers at airports," European Journal of Operational Research, Elsevier, vol. 225(1), pages 106-117.
    18. Repoussis, Panagiotis P. & Tarantilis, Christos D. & Zachariadis, Emmanouil E., 2017. "Moving products between location pairs: Cross-docking versus direct-shippingAuthor-Name: Nikolopoulou, Amalia I," European Journal of Operational Research, Elsevier, vol. 256(3), pages 803-819.

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