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An exact method for a last-mile delivery routing problem with multiple deliverymen

Author

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  • Senna, Fernando
  • Coelho, Leandro C.
  • Morabito, Reinaldo
  • Munari, Pedro

Abstract

The demand for efficient last-mile delivery systems in large cities creates an opportunity to develop innovative logistics schemes. In this paper, we study a problem in which each vehicle may travel with more than one deliveryman to serve multiple customers with a single stop of the vehicle, increasing the delivery efficiency. We extend the vehicle routing problem with time windows and multiple deliverymen by explicitly considering the deliveryman routes. We introduce the problem, formally define it with a formulation, propose valid inequalities, and develop a tailored branch-and-Benders-cut (BBC) algorithm to solve it. The BBC is capable of solving 89% of the instances to proven optimality in reasonable times, many of them of realistic sizes. Additionally, we show the benefits of evaluating the deliveryman routes considering a cost minimization perspective, and discuss relevant solutions for urban logistics problems that can help decrease congestion and emissions.

Suggested Citation

  • Senna, Fernando & Coelho, Leandro C. & Morabito, Reinaldo & Munari, Pedro, 2024. "An exact method for a last-mile delivery routing problem with multiple deliverymen," European Journal of Operational Research, Elsevier, vol. 317(2), pages 550-562.
    • Handle: RePEc:eee:ejores:v:317:y:2024:i:2:p:550-562
    DOI: 10.1016/j.ejor.2024.04.007
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    References listed on IDEAS

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    1. Moreno, Alfredo & Munari, Pedro & Alem, Douglas, 2019. "A branch-and-Benders-cut algorithm for the Crew Scheduling and Routing Problem in road restoration," European Journal of Operational Research, Elsevier, vol. 275(1), pages 16-34.
    2. Nils Boysen & Stefan Fedtke & Stefan Schwerdfeger, 2021. "Last-mile delivery concepts: a survey from an operational research perspective," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(1), pages 1-58, March.
    3. Ouyang, Zhiyuan & Leung, Eric K.H. & Huang, George Q., 2023. "Community logistics and dynamic community partitioning: A new approach for solving e-commerce last mile delivery," European Journal of Operational Research, Elsevier, vol. 307(1), pages 140-156.
    4. Li, Hongqi & Chen, Jun & Wang, Feilong & Bai, Ming, 2021. "Ground-vehicle and unmanned-aerial-vehicle routing problems from two-echelon scheme perspective: A review," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1078-1095.
    5. Gianni Codato & Matteo Fischetti, 2006. "Combinatorial Benders' Cuts for Mixed-Integer Linear Programming," Operations Research, INFORMS, vol. 54(4), pages 756-766, August.
    6. Gerald Senarclens de Grancy & Marc Reimann, 2015. "Evaluating two new heuristics for constructing customer clusters in a VRPTW with multiple service workers," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(2), pages 479-500, June.
    7. Marius M. Solomon, 1987. "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints," Operations Research, INFORMS, vol. 35(2), pages 254-265, April.
    8. Bayliss, Christopher & Bektaş, Tolga & Tjon-Soei-Len, Vernon & Rohner, Remo, 2023. "Designing a multi-modal and variable-echelon delivery system for last-mile logistics," European Journal of Operational Research, Elsevier, vol. 307(2), pages 645-662.
    9. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    10. Ostermeier, Manuel & Heimfarth, Andreas & Hübner, Alexander, 2023. "The multi-vehicle truck-and-robot routing problem for last-mile delivery," European Journal of Operational Research, Elsevier, vol. 310(2), pages 680-697.
    11. Alfandari, Laurent & Ljubić, Ivana & De Melo da Silva, Marcos, 2022. "A tailored Benders decomposition approach for last-mile delivery with autonomous robots," European Journal of Operational Research, Elsevier, vol. 299(2), pages 510-525.
    12. Antonio Martinez-Sykora & Fraser McLeod & Carlos Lamas-Fernandez & Tolga Bektaş & Tom Cherrett & Julian Allen, 2020. "Optimised solutions to the last-mile delivery problem in London using a combination of walking and driving," Annals of Operations Research, Springer, vol. 295(2), pages 645-693, December.
    13. Pedro Munari & Reinaldo Morabito, 2018. "A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 437-464, October.
    14. Pureza, Vitória & Morabito, Reinaldo & Reimann, Marc, 2012. "Vehicle routing with multiple deliverymen: Modeling and heuristic approaches for the VRPTW," European Journal of Operational Research, Elsevier, vol. 218(3), pages 636-647.
    15. Reed, Sara & Campbell, Ann Melissa & Thomas, Barrett W., 2024. "Does parking matter? The impact of parking time on last-mile delivery optimization," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 181(C).
    16. Le Colleter, Théo & Dumez, Dorian & Lehuédé, Fabien & Péton, Olivier, 2023. "Small and large neighborhood search for the park-and-loop routing problem with parking selection," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1233-1248.
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