IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i23p4583-d992453.html
   My bibliography  Save this article

Hybrid Heuristic for the Multi-Depot Static Bike Rebalancing and Collection Problem

Author

Listed:
  • Xue Bai

    (School of Economics and Management, Chang’an University, Xi’an 710064, China)

  • Ning Ma

    (School of Public Policy and Administration, Xi’an Jiaotong University, Xi’an 710049, China)

  • Kwai-Sang Chin

    (Department of System Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong)

Abstract

The bike rebalancing problem is one of the major operational challenges in the urban bike-sharing system, which involves the redistribution of bikes among stations to prevent stations from being empty or overloaded. This paper investigates a new bike rebalancing problem, which considers the collection of broken bikes in the multi-depot system. The proposed problem can be classified as a two-commodity vehicle routing problem with pick-up and delivery. An integer programming model is formulated to find the optimal vehicle assignment and visiting sequences with the minimum total working time and fixed cost of vehicles. A hybrid heuristic algorithm integrating variable neighborhood search and dynamic programming is proposed to solve the problem. The computational results show that the proposed method can find 26 best solutions out of 36 instances, while the CPLEX obtains 16 best solutions. Impact of broken bikes collection and distribution of depots is examined. Comparison of different practical strategies indicates that the number of vehicles can be significantly reduced by allowing multiple visits to depots. Allowing vehicles to return to different depots can help reduce the total working time.

Suggested Citation

  • Xue Bai & Ning Ma & Kwai-Sang Chin, 2022. "Hybrid Heuristic for the Multi-Depot Static Bike Rebalancing and Collection Problem," Mathematics, MDPI, vol. 10(23), pages 1-28, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4583-:d:992453
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/23/4583/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/23/4583/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Li, Yanfeng & Szeto, W.Y. & Long, Jiancheng & Shui, C.S., 2016. "A multiple type bike repositioning problem," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 263-278.
    2. Stefan Ropke & David Pisinger, 2006. "An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 40(4), pages 455-472, November.
    3. Paul M. Thompson & Harilaos N. Psaraftis, 1993. "Cyclic Transfer Algorithm for Multivehicle Routing and Scheduling Problems," Operations Research, INFORMS, vol. 41(5), pages 935-946, October.
    4. Andreas Stenger & Daniele Vigo & Steffen Enz & Michael Schwind, 2013. "An Adaptive Variable Neighborhood Search Algorithm for a Vehicle Routing Problem Arising in Small Package Shipping," Transportation Science, INFORMS, vol. 47(1), pages 64-80, February.
    5. Szeto, W.Y. & Shui, C.S., 2018. "Exact loading and unloading strategies for the static multi-vehicle bike repositioning problem," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 176-211.
    6. Regue, Robert & Recker, Will, 2014. "Proactive vehicle routing with inferred demand to solve the bikesharing rebalancing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 192-209.
    7. Diego Cattaruzza & Nabil Absi & Dominique Feillet, 2016. "Vehicle routing problems with multiple trips," 4OR, Springer, vol. 14(3), pages 223-259, September.
    8. Legros, Benjamin, 2019. "Dynamic repositioning strategy in a bike-sharing system; how to prioritize and how to rebalance a bike station," European Journal of Operational Research, Elsevier, vol. 272(2), pages 740-753.
    9. T. Ibaraki & S. Imahori & M. Kubo & T. Masuda & T. Uno & M. Yagiura, 2005. "Effective Local Search Algorithms for Routing and Scheduling Problems with General Time-Window Constraints," Transportation Science, INFORMS, vol. 39(2), pages 206-232, May.
    10. Du, Mingyang & Cheng, Lin & Li, Xuefeng & Tang, Fang, 2020. "Static rebalancing optimization with considering the collection of malfunctioning bikes in free-floating bike sharing system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    11. Marian Rainer-Harbach & Petrina Papazek & Günther Raidl & Bin Hu & Christian Kloimüllner, 2015. "PILOT, GRASP, and VNS approaches for the static balancing of bicycle sharing systems," Journal of Global Optimization, Springer, vol. 63(3), pages 597-629, November.
    12. Erdoğan, Güneş & Laporte, Gilbert & Wolfler Calvo, Roberto, 2014. "The static bicycle relocation problem with demand intervals," European Journal of Operational Research, Elsevier, vol. 238(2), pages 451-457.
    13. Ho, Sin C. & Szeto, W.Y., 2017. "A hybrid large neighborhood search for the static multi-vehicle bike-repositioning problem," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 340-363.
    14. Dell'Amico, Mauro & Hadjicostantinou, Eleni & Iori, Manuel & Novellani, Stefano, 2014. "The bike sharing rebalancing problem: Mathematical formulations and benchmark instances," Omega, Elsevier, vol. 45(C), pages 7-19.
    15. Chang, Ximing & Wu, Jianjun & Sun, Huijun & Correia, Gonçalo Homem de Almeida & Chen, Jianhua, 2021. "Relocating operational and damaged bikes in free-floating systems: A data-driven modeling framework for level of service enhancement," Transportation Research Part A: Policy and Practice, Elsevier, vol. 153(C), pages 235-260.
    16. Bulhões, Teobaldo & Subramanian, Anand & Erdoğan, Güneş & Laporte, Gilbert, 2018. "The static bike relocation problem with multiple vehicles and visits," European Journal of Operational Research, Elsevier, vol. 264(2), pages 508-523.
    17. Schuijbroek, J. & Hampshire, R.C. & van Hoeve, W.-J., 2017. "Inventory rebalancing and vehicle routing in bike sharing systems," European Journal of Operational Research, Elsevier, vol. 257(3), pages 992-1004.
    18. Maggioni, Francesca & Cagnolari, Matteo & Bertazzi, Luca & Wallace, Stein W., 2019. "Stochastic optimization models for a bike-sharing problem with transshipment," European Journal of Operational Research, Elsevier, vol. 276(1), pages 272-283.
    19. Berbeglia, Gerardo & Cordeau, Jean-François & Laporte, Gilbert, 2010. "Dynamic pickup and delivery problems," European Journal of Operational Research, Elsevier, vol. 202(1), pages 8-15, April.
    20. Erdoğan, Güneş & Battarra, Maria & Wolfler Calvo, Roberto, 2015. "An exact algorithm for the static rebalancing problem arising in bicycle sharing systems," European Journal of Operational Research, Elsevier, vol. 245(3), pages 667-679.
    21. Nagy, Gabor & Salhi, Said, 2005. "Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 162(1), pages 126-141, April.
    22. Forma, Iris A. & Raviv, Tal & Tzur, Michal, 2015. "A 3-step math heuristic for the static repositioning problem in bike-sharing systems," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 230-247.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shichang Xiao & Pan Peng & Peng Zheng & Zigao Wu, 2024. "A Hybrid Adaptive Simulated Annealing and Tempering Algorithm for Solving the Half-Open Multi-Depot Vehicle Routing Problem," Mathematics, MDPI, vol. 12(7), pages 1-21, March.

    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. Du, Mingyang & Cheng, Lin & Li, Xuefeng & Tang, Fang, 2020. "Static rebalancing optimization with considering the collection of malfunctioning bikes in free-floating bike sharing system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    2. Dell’Amico, Mauro & Iori, Manuel & Novellani, Stefano & Subramanian, Anand, 2018. "The Bike sharing Rebalancing Problem with Stochastic Demands," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 362-380.
    3. Huang, Di & Chen, Xinyuan & Liu, Zhiyuan & Lyu, Cheng & Wang, Shuaian & Chen, Xuewu, 2020. "A static bike repositioning model in a hub-and-spoke network framework," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    4. Carlos M. Vallez & Mario Castro & David Contreras, 2021. "Challenges and Opportunities in Dock-Based Bike-Sharing Rebalancing: A Systematic Review," Sustainability, MDPI, vol. 13(4), pages 1-26, February.
    5. Ye Ding & Jiantong Zhang & Jiaqing Sun, 2022. "Branch-and-Price-and-Cut for the Heterogeneous Fleet and Multi-Depot Static Bike Rebalancing Problem with Split Load," Sustainability, MDPI, vol. 14(17), pages 1-24, August.
    6. Gilbert Laporte & Frédéric Meunier & Roberto Wolfler Calvo, 2018. "Shared mobility systems: an updated survey," Annals of Operations Research, Springer, vol. 271(1), pages 105-126, December.
    7. Szeto, W.Y. & Shui, C.S., 2018. "Exact loading and unloading strategies for the static multi-vehicle bike repositioning problem," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 176-211.
    8. Zhou, Yaoming & Lin, Zeyu & Guan, Rui & Sheu, Jiuh-Biing, 2023. "Dynamic battery swapping and rebalancing strategies for e-bike sharing systems," Transportation Research Part B: Methodological, Elsevier, vol. 177(C).
    9. Li, Yanfeng & Liu, Yang, 2021. "The static bike rebalancing problem with optimal user incentives," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 146(C).
    10. Wang, Xu & Sun, Huijun & Zhang, Si & Lv, Ying & Li, Tongfei, 2022. "Bike sharing rebalancing problem with variable demand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    11. Bruno Albert Neumann-Saavedra & Teodor Gabriel Crainic & Bernard Gendron & Dirk Christian Mattfeld & Michael Römer, 2020. "Integrating Resource Management in Service Network Design for Bike-Sharing Systems," Transportation Science, INFORMS, vol. 54(5), pages 1251-1271, September.
    12. Gleditsch, Marte D. & Hagen, Kristine & Andersson, Henrik & Bakker, Steffen J. & Fagerholt, Kjetil, 2024. "A column generation heuristic for the dynamic bicycle rebalancing problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 762-775.
    13. Cheng, Yao & Wang, Junwei & Wang, Yan, 2021. "A user-based bike rebalancing strategy for free-floating bike sharing systems: A bidding model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    14. Gan, Jinxiang & Zhang, Guochuan & Zhang, Yuhao, 2024. "Bike rebalancing: How to find a balanced matching in the k center problem?," European Journal of Operational Research, Elsevier, vol. 316(3), pages 845-855.
    15. Fu, Chenyi & Zhu, Ning & Ma, Shoufeng & Liu, Ronghui, 2022. "A two-stage robust approach to integrated station location and rebalancing vehicle service design in bike-sharing systems," European Journal of Operational Research, Elsevier, vol. 298(3), pages 915-938.
    16. 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.
    17. Neumann-Saavedra, Bruno Albert & Mattfeld, Dirk Christian & Hewitt, Mike, 2021. "Assessing the operational impact of tactical planning models for bike-sharing redistribution," Transportation Research Part A: Policy and Practice, Elsevier, vol. 150(C), pages 216-235.
    18. Maggioni, Francesca & Cagnolari, Matteo & Bertazzi, Luca & Wallace, Stein W., 2019. "Stochastic optimization models for a bike-sharing problem with transshipment," European Journal of Operational Research, Elsevier, vol. 276(1), pages 272-283.
    19. Bahman Lahoorpoor & Hamed Faroqi & Abolghasem Sadeghi-Niaraki & Soo-Mi Choi, 2019. "Spatial Cluster-Based Model for Static Rebalancing Bike Sharing Problem," Sustainability, MDPI, vol. 11(11), pages 1-21, June.
    20. Wang, Yi-Jia & Kuo, Yong-Hong & Huang, George Q. & Gu, Weihua & Hu, Yaohua, 2022. "Dynamic demand-driven bike station clustering," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 160(C).

    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:gam:jmathe:v:10:y:2022:i:23:p:4583-:d:992453. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.