IDEAS home Printed from https://ideas.repec.org/a/eee/transe/v204y2025ics1366554525004776.html

Two-echelon container drayage with multiple transportation modes and overall-network time interdependence

Author

Listed:
  • Wang, Decheng
  • Xie, Xiaolan
  • Moon, Ilkyeong

Abstract

This study addresses a two-echelon container drayage problem incorporating multiple transportation modes, and attempts to explore its potential application advantages. The problem concentrates on truckload transportation, and represents a variation of the classical two-echelon capacity-constrained vehicle routing problem. In the first echelon, a fleet of tractors, often employing long combination vehicles, transports trailers between a central depot and multiple satellites. In the second echelon, a fleet of tractors, restricted to a single-trailer stay-with mode, due to transportation regulations, executes multi-trip trailer transportation between satellites and customers. The tractor can perform two operations of dropping-off and pulling-up trailers (i.e., simultaneous delivery and collection of containers are involved). These characteristics make the routes of the two echelons couple tightly, and result in intertwined time interdependence within the entire network. A mathematical formulation is developed to address this two-echelon scheduling with time interdependence. To enhance computational efficiency, two groups of valid inequalities are provided. A two-stage matheuristic algorithm integrating the proposed mathematical model and heuristic techniques is developed. A route-string scheduling framework combined with a fixing and releasing mechanism is introduced to mitigate the complexity associated with the time-interdependence nature of the network. This algorithm, possessing fewer parameters than comparable (meta-) heuristics, offers a practical implementation. The mathematical model, along with the valid inequalities and the performance of the matheuristic algorithm, are validated through computational experiments using established instances from prior studies. Furthermore, experiments are undertaken to investigate the effects of customer distribution patterns and maximum permissible trailers count on operational efficiency.

Suggested Citation

  • Wang, Decheng & Xie, Xiaolan & Moon, Ilkyeong, 2025. "Two-echelon container drayage with multiple transportation modes and overall-network time interdependence," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:transe:v:204:y:2025:i:c:s1366554525004776
    DOI: 10.1016/j.tre.2025.104436
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1366554525004776
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tre.2025.104436?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Xue, Zhaojie & Zhang, Canrong & Lin, Wei-Hua & Miao, Lixin & Yang, Peng, 2014. "A tabu search heuristic for the local container drayage problem under a new operation mode," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 62(C), pages 136-150.
    2. Grangier, Philippe & Gendreau, Michel & Lehuédé, Fabien & Rousseau, Louis-Martin, 2016. "An adaptive large neighborhood search for the two-echelon multiple-trip vehicle routing problem with satellite synchronization," European Journal of Operational Research, Elsevier, vol. 254(1), pages 80-91.
    3. Yu, Shaohua & Puchinger, Jakob & Sun, Shudong, 2020. "Two-echelon urban deliveries using autonomous vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    4. Liu, Dan & Kaisar, Evangelos I. & Yang, Yang & Yan, Pengyu, 2022. "Physical Internet-enabled E-grocery delivery Network:A load-dependent two-echelon vehicle routing problem with mixed vehicles," International Journal of Production Economics, Elsevier, vol. 254(C).
    5. 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.
    6. Fazi, Stefano & Choudhary, Sourabh Kumar & Dong, Jing-Xin, 2023. "The multi-trip container drayage problem with synchronization for efficient empty containers re-usage," European Journal of Operational Research, Elsevier, vol. 310(1), pages 343-359.
    7. Chen, Rui & Chen, Shukai & Cui, Haipeng & Meng, Qiang, 2021. "The container drayage problem for heterogeneous trucks with multiple loads: A revisit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    8. Xue, Zhaojie & Lin, Hui & You, Jintao, 2021. "Local container drayage problem with truck platooning mode," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    9. Escudero-Santana, Alejandro & Muñuzuri, Jesús & Cortés, Pablo & Onieva, Luis, 2021. "The one container drayage problem with soft time windows," Research in Transportation Economics, Elsevier, vol. 90(C).
    10. Govindan, K. & Jafarian, A. & Khodaverdi, R. & Devika, K., 2014. "Two-echelon multiple-vehicle location–routing problem with time windows for optimization of sustainable supply chain network of perishable food," International Journal of Production Economics, Elsevier, vol. 152(C), pages 9-28.
    11. Zhou, Lin & Baldacci, Roberto & Vigo, Daniele & Wang, Xu, 2018. "A Multi-Depot Two-Echelon Vehicle Routing Problem with Delivery Options Arising in the Last Mile Distribution," European Journal of Operational Research, Elsevier, vol. 265(2), pages 765-778.
    12. Zhang, Ruiyou & Zhao, Haishu & Moon, Ilkyeong, 2018. "Range-based truck-state transition modeling method for foldable container drayage services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 225-239.
    13. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti & Roberto Wolfler Calvo, 2013. "An Exact Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem," Operations Research, INFORMS, vol. 61(2), pages 298-314, April.
    14. Elhassania Messaoud, 2022. "Solving a stochastic programming with recourse model for the stochastic electric capacitated vehicle routing problem using a hybrid genetic algorithm," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 16(1), pages 71-90.
    15. You, Jintao & Wang, Yuan & Xue, Zhaojie, 2023. "An exact algorithm for the multi-trip container drayage problem with truck platooning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).
    16. Shan, Wenxuan & Peng, Zixuan & Liu, Jiaming & Yao, Baozhen & Yu, Bin, 2020. "An exact algorithm for inland container transportation network design," Transportation Research Part B: Methodological, Elsevier, vol. 135(C), pages 41-82.
    17. Lv, Chang & Zhang, Chaoyong & Lian, Kunlei & Ren, Yaping & Meng, Leilei, 2022. "A two-echelon fuzzy clustering based heuristic for large-scale bike sharing repositioning problem," Transportation Research Part B: Methodological, Elsevier, vol. 160(C), pages 54-75.
    18. Benantar, A. & Abourraja, M.N. & Boukachour, J. & Boudebous, D. & Duvallet, C., 2020. "On the integration of container availability constraints into daily drayage operations arising in France: Modelling and optimization," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    19. You, Jintao & Miao, Lixin & Zhang, Canrong & Xue, Zhaojie, 2020. "A generic model for the local container drayage problem using the emerging truck platooning operation mode," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 181-209.
    20. Shiri, Samaneh & Huynh, Nathan, 2016. "Optimization of drayage operations with time-window constraints," International Journal of Production Economics, Elsevier, vol. 176(C), pages 7-20.
    21. Chen, Rui & Meng, Qiang & Jia, Peng, 2022. "Container port drayage operations and management: Past and future," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).
    22. Moghaddam, Mahboobeh & Pearce, Robin H. & Mokhtar, Hamid & Prato, Carlo G., 2020. "A generalised model for container drayage operations with heterogeneous fleet, multi-container sizes and two modes of operation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 139(C).
    23. Cui, Haipeng & Chen, Shukai & Chen, Rui & Meng, Qiang, 2022. "A two-stage hybrid heuristic solution for the container drayage problem with trailer reposition," European Journal of Operational Research, Elsevier, vol. 299(2), pages 468-482.
    24. Li, Hongqi & Wang, Haotian & Chen, Jun & Bai, Ming, 2021. "Two-echelon vehicle routing problem with satellite bi-synchronization," European Journal of Operational Research, Elsevier, vol. 288(3), pages 775-793.
    25. Bustos-Coral, Daniel & Costa, Alysson M., 2022. "Drayage routing with heterogeneous fleet, compatibility constraints, and truck load configurations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    26. Wang, Naiyu & Meng, Qiang & Zhang, Canrong, 2023. "A branch-price-and-cut algorithm for the local container drayage problem with controllable vehicle interference," Transportation Research Part B: Methodological, Elsevier, vol. 178(C).
    27. 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.
    28. Wang, Mengtong & Zhang, Canrong & Bell, Michael G.H. & Miao, Lixin, 2022. "A branch-and-price algorithm for location-routing problems with pick-up stations in the last-mile distribution system," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1258-1276.
    29. Kenneth Stoop & Mario Pickavet & Didier Colle & Pieter Audenaert, 2024. "The dynamic stochastic container drayage problem with truck appointment scheduling," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 953-985, September.
    30. 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.
    31. Yan, Xiaoyuan & Xu, Min & Xie, Chi, 2023. "Local container drayage problem with improved truck platooning operations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 169(C).
    32. Maximilian Schiffer & Michael Schneider & Grit Walther & Gilbert Laporte, 2019. "Vehicle Routing and Location Routing with Intermediate Stops: A Review," Transportation Science, INFORMS, vol. 53(2), pages 319-343, March.
    33. 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.
    34. Kitjacharoenchai, Patchara & Min, Byung-Cheol & Lee, Seokcheon, 2020. "Two echelon vehicle routing problem with drones in last mile delivery," International Journal of Production Economics, Elsevier, vol. 225(C).
    35. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    36. Liu, Tian & Luo, Zhixing & Qin, Hu & Lim, Andrew, 2018. "A branch-and-cut algorithm for the two-echelon capacitated vehicle routing problem with grouping constraints," European Journal of Operational Research, Elsevier, vol. 266(2), pages 487-497.
    37. Jie, Wanchen & Yang, Jun & Zhang, Min & Huang, Yongxi, 2019. "The two-echelon capacitated electric vehicle routing problem with battery swapping stations: Formulation and efficient methodology," European Journal of Operational Research, Elsevier, vol. 272(3), pages 879-904.
    38. Darvish, Maryam & Archetti, Claudia & Coelho, Leandro C. & Speranza, M. Grazia, 2019. "Flexible two-echelon location routing problem," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1124-1136.
    39. Li, Hongqi & Wang, Haotian & Chen, Jun & Bai, Ming, 2020. "Two-echelon vehicle routing problem with time windows and mobile satellites," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 179-201.
    40. Christian Tilk & Nicola Bianchessi & Michael Drexl & Stefan Irnich & Frank Meisel, 2018. "Branch-and-Price-and-Cut for the Active-Passive Vehicle-Routing Problem," Transportation Science, INFORMS, vol. 52(2), pages 300-319, March.
    41. Song, Yujian & Zhang, Jiantong & Liang, Zhe & Ye, Chunming, 2017. "An exact algorithm for the container drayage problem under a separation mode," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 231-254.
    42. Mühlbauer, Ferdinand & Fontaine, Pirmin, 2021. "A parallelised large neighbourhood search heuristic for the asymmetric two-echelon vehicle routing problem with swap containers for cargo-bicycles," European Journal of Operational Research, Elsevier, vol. 289(2), pages 742-757.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Decheng & Fan, Zhihui & Liu, Yarong & Moon, Ilkyeong, 2026. "A trailer-detention-constrained multi-trailer drop-and-pull container drayage problem with flexible service starting time and time windows," Omega, Elsevier, vol. 138(C).
    2. Bustos-Coral, Daniel & Costa, Alysson M., 2022. "Drayage routing with heterogeneous fleet, compatibility constraints, and truck load configurations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    3. Yan, Xiaoyuan & Xu, Min & Xie, Chi, 2023. "Local container drayage problem with improved truck platooning operations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 169(C).
    4. Sluijk, Natasja & Florio, Alexandre M. & Kinable, Joris & Dellaert, Nico & Van Woensel, Tom, 2023. "Two-echelon vehicle routing problems: A literature review," European Journal of Operational Research, Elsevier, vol. 304(3), pages 865-886.
    5. Chen, Rui & Meng, Qiang & Jia, Peng, 2022. "Container port drayage operations and management: Past and future," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).
    6. Peng, Xiaoshuai & Zhang, Lele & Thompson, Russell G. & Wang, Kangzhou, 2023. "A three-phase heuristic for last-mile delivery with spatial-temporal consolidation and delivery options," International Journal of Production Economics, Elsevier, vol. 266(C).
    7. Yu, Shaohua & Puchinger, Jakob & Sun, Shudong, 2022. "Van-based robot hybrid pickup and delivery routing problem," European Journal of Operational Research, Elsevier, vol. 298(3), pages 894-914.
    8. Cui, Haipeng & Chen, Shukai & Chen, Rui & Meng, Qiang, 2022. "A two-stage hybrid heuristic solution for the container drayage problem with trailer reposition," European Journal of Operational Research, Elsevier, vol. 299(2), pages 468-482.
    9. Etsuko Nishimura & Stratos Papadimitriou & Koichi Shintani & Akio Imai, 2025. "Environmental challenge of vehicle dispatching in marine container drayage," Annals of Operations Research, Springer, vol. 351(1), pages 1049-1107, August.
    10. Liu, Dan & Yan, Pengyu & Pu, Ziyuan & Wang, Yinhai & Kaisar, Evangelos I., 2021. "Hybrid artificial immune algorithm for optimizing a Van-Robot E-grocery delivery system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    11. Chen, Rui & Jia, Shuai & Meng, Qiang, 2023. "Dynamic container drayage booking and routing decision support approach for E-commerce platforms," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    12. Raúl Soto-Concha & John Willmer Escobar & Daniel Morillo-Torres & Rodrigo Linfati, 2025. "The Vehicle-Routing Problem with Satellites Utilization: A Systematic Review of the Literature," Mathematics, MDPI, vol. 13(7), pages 1-29, March.
    13. Dahimi, Aria & Lurkin, Virginie & Mohammadi, Mehrdad & Van Woensel, Tom, 2025. "A two-echelon vehicle routing problem with mobile satellites and multiple commodities," European Journal of Operational Research, Elsevier, vol. 326(1), pages 124-140.
    14. Soares, Ricardo & Marques, Alexandra & Amorim, Pedro & Parragh, Sophie N., 2024. "Synchronisation in vehicle routing: Classification schema, modelling framework and literature review," European Journal of Operational Research, Elsevier, vol. 313(3), pages 817-840.
    15. Yujian Song & Yuting Zhang & Wanli Wang & Ming Xue, 2023. "A Branch and Price Algorithm for the Drop-and-Pickup Container Drayage Problem with Empty Container Constraints," Sustainability, MDPI, vol. 15(7), pages 1-28, March.
    16. Jia, Shuai & Cui, Haipeng & Chen, Rui & Meng, Qiang, 2022. "Dynamic container drayage with uncertain request arrival times and service time windows," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 237-258.
    17. Chen, Shukai & Wang, Hua & Meng, Qiang, 2021. "Autonomous truck scheduling for container transshipment between two seaport terminals considering platooning and speed optimization," Transportation Research Part B: Methodological, Elsevier, vol. 154(C), pages 289-315.
    18. Karademir, Cigdem & Beirigo, Breno A. & Atasoy, Bilge, 2025. "A two-echelon multi-trip vehicle routing problem with synchronization for an integrated water- and land-based transportation system," European Journal of Operational Research, Elsevier, vol. 322(2), pages 480-499.
    19. Xuhui Yu & Yin Feng & Cong He & Chang Liu, 2024. "Modeling and Optimization of Container Drayage Problem with Empty Container Constraints across Multiple Inland Depots," Sustainability, MDPI, vol. 16(12), pages 1-32, June.
    20. Escudero-Santana, Alejandro & Muñuzuri, Jesús & Cortés, Pablo & Onieva, Luis, 2021. "The one container drayage problem with soft time windows," Research in Transportation Economics, Elsevier, vol. 90(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transe:v:204:y:2025:i:c:s1366554525004776. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/600244/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.