IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v118y2018icp457-487.html
   My bibliography  Save this article

A new formulation and a column generation-based heuristic for the multiple depot vehicle scheduling problem

Author

Listed:
  • Kulkarni, Sarang
  • Krishnamoorthy, Mohan
  • Ranade, Abhiram
  • Ernst, Andreas T.
  • Patil, Rahul

Abstract

The multiple depot vehicle scheduling problem (MDVSP) with a single vehicle type considers the assignment of timetabled trips to homogeneous vehicles that are stationed at different depots. The assignment of trips to a vehicle also provides a schedule for a vehicle. The objective is to minimise the total cost due to waiting and travelling empty while covering all the trips. In this paper, we propose a new formulation for the MDVSP (termed as the inventory formulation) that uses assignment arcs in a multi-commodity time-space network flow formulation. A general way to solve this multi-commodity network flow problem is to decompose the problem for each commodity (in this case, for each depot). However, we apply Dantzig–Wolfe decomposition to the inventory formulation by decomposing it for each trip. Column generation is used to solve the linear relaxation of the trip-based decomposition. Column generation requires less time to solve the new trip-based decomposition than the existing depot-based decompositions. To obtain a good-quality integer solution to the MDVSP, we propose a solution framework that solves the linear relaxation of the MDVSP iteratively. At each iteration, schedules for certain vehicles in the fleet are finalised. The iterations continue until all the trips receive an allocation. Three different heuristics are proposed based on the solution framework. The computational experiments suggest that the new heuristics provide better quality solutions than the existing heuristics. For instances with a large number of trips, the new heuristics provide solutions in less time than that required by the existing heuristics.

Suggested Citation

  • Kulkarni, Sarang & Krishnamoorthy, Mohan & Ranade, Abhiram & Ernst, Andreas T. & Patil, Rahul, 2018. "A new formulation and a column generation-based heuristic for the multiple depot vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 457-487.
  • Handle: RePEc:eee:transb:v:118:y:2018:i:c:p:457-487
    DOI: 10.1016/j.trb.2018.11.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261518301115
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.trb.2018.11.007?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Mauro Dell'Amico & Matteo Fischetti & Paolo Toth, 1993. "Heuristic Algorithms for the Multiple Depot Vehicle Scheduling Problem," Management Science, INFORMS, vol. 39(1), pages 115-125, January.
    2. Forbes, M. A. & Holt, J. N. & Watts, A. M., 1994. "An exact algorithm for multiple depot bus scheduling," European Journal of Operational Research, Elsevier, vol. 72(1), pages 115-124, January.
    3. Boyer, Vincent & Ibarra-Rojas, Omar J. & Ríos-Solís, Yasmín Á., 2018. "Vehicle and Crew Scheduling for Flexible Bus Transportation Systems," Transportation Research Part B: Methodological, Elsevier, vol. 112(C), pages 216-229.
    4. Desfontaines, Lucie & Desaulniers, Guy, 2018. "Multiple depot vehicle scheduling with controlled trip shifting," Transportation Research Part B: Methodological, Elsevier, vol. 113(C), pages 34-53.
    5. Dennis Huisman & Richard Freling & Albert P. M. Wagelmans, 2005. "Multiple-Depot Integrated Vehicle and Crew Scheduling," Transportation Science, INFORMS, vol. 39(4), pages 491-502, November.
    6. Ahmed Hadjar & Odile Marcotte & François Soumis, 2006. "A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 54(1), pages 130-149, February.
    7. Avishai Ceder & Helman I. Stern, 1981. "Deficit Function Bus Scheduling with Deadheading Trip Insertions for Fleet Size Reduction," Transportation Science, INFORMS, vol. 15(4), pages 338-363, November.
    8. Hassold, Stephan & Ceder, Avishai (Avi), 2014. "Public transport vehicle scheduling featuring multiple vehicle types," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 129-143.
    9. Guedes, Pablo C. & Borenstein, Denis, 2018. "Real-time multi-depot vehicle type rescheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 217-234.
    10. Carraresi, P. & Gallo, G., 1984. "Network models for vehicle and crew scheduling," European Journal of Operational Research, Elsevier, vol. 16(2), pages 139-151, May.
    11. Benchimol, Pascal & Desaulniers, Guy & Desrosiers, Jacques, 2012. "Stabilized dynamic constraint aggregation for solving set partitioning problems," European Journal of Operational Research, Elsevier, vol. 223(2), pages 360-371.
    12. Gavish, B. & Shlifer, E., 1979. "An approach for solving a class of transportation scheduling problems," European Journal of Operational Research, Elsevier, vol. 3(2), pages 122-134, March.
    13. Tomoshi Otsuki & Kazuyuki Aihara, 2016. "New variable depth local search for multiple depot vehicle scheduling problems," Journal of Heuristics, Springer, vol. 22(4), pages 567-585, August.
    14. Kliewer, Natalia & Mellouli, Taieb & Suhl, Leena, 2006. "A time-space network based exact optimization model for multi-depot bus scheduling," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1616-1627, December.
    15. Haghani, Ali & Banihashemi, Mohamadreza, 2002. "Heuristic approaches for solving large-scale bus transit vehicle scheduling problem with route time constraints," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(4), pages 309-333, May.
    16. Celso C. Ribeiro & François Soumis, 1994. "A Column Generation Approach to the Multiple-Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 42(1), pages 41-52, February.
    17. Ibarra-Rojas, O.J. & Delgado, F. & Giesen, R. & Muñoz, J.C., 2015. "Planning, operation, and control of bus transport systems: A literature review," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 38-75.
    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. Enzi, Miriam & Parragh, Sophie N. & Pisinger, David & Prandtstetter, Matthias, 2021. "Modeling and solving the multimodal car- and ride-sharing problem," European Journal of Operational Research, Elsevier, vol. 293(1), pages 290-303.
    2. Wu, Weitiao & Lin, Yue & Liu, Ronghui & Jin, Wenzhou, 2022. "The multi-depot electric vehicle scheduling problem with power grid characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 322-347.
    3. Yan, Ran & Wang, Shuaian & Cao, Jiannong & Sun, Defeng, 2021. "Shipping Domain Knowledge Informed Prediction and Optimization in Port State Control," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 52-78.
    4. Liu, Baoli & Li, Zhi-Chun & Wang, Yadong, 2023. "A branch-and-price heuristic algorithm for the bunkering operation problem of a liquefied natural gas bunkering station in the inland waterways," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 145-170.
    5. Liu, Baoli & Li, Zhi-Chun & Wang, Yadong & Sheng, Dian, 2021. "Short-term berth planning and ship scheduling for a busy seaport with channel restrictions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    6. Timo Gschwind & Stefan Irnich & Christian Tilk & Simon Emde, 2020. "Branch-cut-and-price for scheduling deliveries with time windows in a direct shipping network," Journal of Scheduling, Springer, vol. 23(3), pages 363-377, June.
    7. Wang, Dian & D’Ariano, Andrea & Zhao, Jun & Zhan, Shuguang & Peng, Qiyuan, 2024. "Joint rolling stock rotation planning and depot deadhead scheduling in complicated urban rail transit lines," European Journal of Operational Research, Elsevier, vol. 314(2), pages 665-684.
    8. Luyun Wang & Bo Zhou, 2023. "Optimal Planning of Electric Vehicle Fast-Charging Stations Considering Uncertain Charging Demands via Dantzig–Wolfe Decomposition," Sustainability, MDPI, vol. 15(8), pages 1-23, April.
    9. Perumal, Shyam S.G. & Lusby, Richard M. & Larsen, Jesper, 2022. "Electric bus planning & scheduling: A review of related problems and methodologies," European Journal of Operational Research, Elsevier, vol. 301(2), pages 395-413.
    10. Wang, Zhongxiang & Haghani, Ali, 2020. "Column generation-based stochastic school bell time and bus scheduling optimization," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1087-1102.
    11. Bingtao Quan & Sujian Li & Kuo-Jui Wu, 2022. "Optimizing the Vehicle Scheduling Problem for Just-in-Time Delivery Considering Carbon Emissions and Atmospheric Particulate Matter," Sustainability, MDPI, vol. 14(10), pages 1-19, May.
    12. Wang, Zehao & Zeng, Qingcheng & Li, Xingchun & Qu, Chenrui, 2024. "A branch-and-price heuristic algorithm for the ART and external truck scheduling problem in an automated container terminal with a parallel layout," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    13. Han, Xue & Zhao, Peixin & Kong, Dexin, 2023. "Two-stage optimization of airport ferry service delay considering flight uncertainty," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1103-1116.

    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. Perumal, Shyam S.G. & Lusby, Richard M. & Larsen, Jesper, 2022. "Electric bus planning & scheduling: A review of related problems and methodologies," European Journal of Operational Research, Elsevier, vol. 301(2), pages 395-413.
    2. Niu, Huimin & Zhou, Xuesong & Tian, Xiaopeng, 2018. "Coordinating assignment and routing decisions in transit vehicle schedules: A variable-splitting Lagrangian decomposition approach for solution symmetry breaking," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 70-101.
    3. Shen, Yindong & Xu, Jia & Li, Jingpeng, 2016. "A probabilistic model for vehicle scheduling based on stochastic trip times," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 19-31.
    4. Jing-Quan Li, 2014. "Transit Bus Scheduling with Limited Energy," Transportation Science, INFORMS, vol. 48(4), pages 521-539, November.
    5. Uçar, Ezgi & İlker Birbil, Ş. & Muter, İbrahim, 2017. "Managing disruptions in the multi-depot vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 249-269.
    6. Ibarra-Rojas, O.J. & Delgado, F. & Giesen, R. & Muñoz, J.C., 2015. "Planning, operation, and control of bus transport systems: A literature review," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 38-75.
    7. Gkiotsalitis, K. & Iliopoulou, C. & Kepaptsoglou, K., 2023. "An exact approach for the multi-depot electric bus scheduling problem with time windows," European Journal of Operational Research, Elsevier, vol. 306(1), pages 189-206.
    8. Benchimol, Pascal & Desaulniers, Guy & Desrosiers, Jacques, 2012. "Stabilized dynamic constraint aggregation for solving set partitioning problems," European Journal of Operational Research, Elsevier, vol. 223(2), pages 360-371.
    9. Guedes, Pablo C. & Borenstein, Denis, 2018. "Real-time multi-depot vehicle type rescheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 217-234.
    10. Rinaldi, Marco & Picarelli, Erika & D'Ariano, Andrea & Viti, Francesco, 2020. "Mixed-fleet single-terminal bus scheduling problem: Modelling, solution scheme and potential applications," Omega, Elsevier, vol. 96(C).
    11. Ciancio, Claudio & Laganà, Demetrio & Musmanno, Roberto & Santoro, Francesco, 2018. "An integrated algorithm for shift scheduling problems for local public transport companies," Omega, Elsevier, vol. 75(C), pages 139-153.
    12. Pan, Hanchuan & Liu, Zhigang & Yang, Lixing & Liang, Zhe & Wu, Qiang & Li, Sijie, 2021. "A column generation-based approach for integrated vehicle and crew scheduling on a single metro line with the fully automatic operation system by partial supervision," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    13. Wu, Weitiao & Lin, Yue & Liu, Ronghui & Jin, Wenzhou, 2022. "The multi-depot electric vehicle scheduling problem with power grid characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 322-347.
    14. Chris Martin & David Jones & Pinar Keskinocak, 2003. "Optimizing On-Demand Aircraft Schedules for Fractional Aircraft Operators," Interfaces, INFORMS, vol. 33(5), pages 22-35, October.
    15. Shyam S. G. Perumal & Jesper Larsen & Richard M. Lusby & Morten Riis & Tue R. L. Christensen, 2022. "A column generation approach for the driver scheduling problem with staff cars," Public Transport, Springer, vol. 14(3), pages 705-738, October.
    16. Liu, Tao & (Avi) Ceder, Avishai, 2017. "Deficit function related to public transport: 50 year retrospective, new developments, and prospects," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 1-19.
    17. Tomoshi Otsuki & Kazuyuki Aihara, 2016. "New variable depth local search for multiple depot vehicle scheduling problems," Journal of Heuristics, Springer, vol. 22(4), pages 567-585, August.
    18. Enzi, Miriam & Parragh, Sophie N. & Pisinger, David & Prandtstetter, Matthias, 2021. "Modeling and solving the multimodal car- and ride-sharing problem," European Journal of Operational Research, Elsevier, vol. 293(1), pages 290-303.
    19. Haghani, Ali & Banihashemi, Mohamadreza & Chiang, Kun-Hung, 2003. "A comparative analysis of bus transit vehicle scheduling models," Transportation Research Part B: Methodological, Elsevier, vol. 37(4), pages 301-322, May.
    20. Ingmar Steinzen & Vitali Gintner & Leena Suhl & Natalia Kliewer, 2010. "A Time-Space Network Approach for the Integrated Vehicle- and Crew-Scheduling Problem with Multiple Depots," Transportation Science, INFORMS, vol. 44(3), pages 367-382, August.

    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:transb:v:118:y:2018:i:c:p:457-487. 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/548/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.