IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v306y2023i2p828-848.html
   My bibliography  Save this article

Multi-depot electric vehicle scheduling in in-plant production logistics considering non-linear charging models

Author

Listed:
  • Diefenbach, Heiko
  • Emde, Simon
  • Glock, Christoph H.

Abstract

Electric vehicle scheduling is concerned with assigning a fleet of electrically powered vehicles to a set of timetabled trips. Since the range of these vehicles is limited, charging breaks need to be scheduled in-between trips, which require detours and time. This paper presents a novel electric vehicle scheduling problem with multiple charging stations in an in-plant logistics setting with the objective of minimizing the required fleet size. Contrary to previous works, we consider constant, linear and non-linear battery charging functions, which, among other things, allows to model realistic non-linear lithium-ion battery charging. We present an integer programming model and an exact branch-and-check solution procedure, which is based on decomposing the problem into a master and a subproblem. The former is concerned with assigning vehicles to trips while relaxing the battery constraints. The latter schedules charging breaks and checks if the master problem’s solution is feasible with regard to the non-relaxed battery constraints. Our computational tests show that solving the IP model with a standard solver (CPLEX) is inferior to the branch-and-check approach, which generally performs well even for practically relevant instance sizes. Furthermore, we derive some insights into the influence of the charging mode and maximum battery capacity on the required fleet size. Lastly, we investigate the effects of the number of warehouses (with respective charging stations).

Suggested Citation

  • Diefenbach, Heiko & Emde, Simon & Glock, Christoph H., 2023. "Multi-depot electric vehicle scheduling in in-plant production logistics considering non-linear charging models," European Journal of Operational Research, Elsevier, vol. 306(2), pages 828-848.
    • Handle: RePEc:eee:ejores:v:306:y:2023:i:2:p:828-848
    DOI: 10.1016/j.ejor.2022.06.050
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221722005252
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2022.06.050?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. Simon Emde & Malte Fliedner & Nils Boysen, 2012. "Optimally loading tow trains for just-in-time supply of mixed-model assembly lines," IISE Transactions, Taylor & Francis Journals, vol. 44(2), pages 121-135.
    2. Emde, Simon & Schneider, Michael, 2018. "Just-In-Time Vehicle Routing for In-House Part Feeding to Assembly Lines," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 96055, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    3. Boysen, Nils & Emde, Simon & Hoeck, Michael & Kauderer, Markus, 2015. "Part logistics in the automotive industry: Decision problems, literature review and research agenda," European Journal of Operational Research, Elsevier, vol. 242(1), pages 107-120.
    4. C. Briand & Y. He & S. U. Ngueveu, 2018. "Energy-efficient planning for supplying assembly lines with vehicles," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(4), pages 387-414, December.
    5. Goeke, D. & Schneider, M., 2015. "Routing a Mixed Fleet of Electric and Conventional Vehicles," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 65939, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    6. Ons Sassi & Ammar Oulamara, 2017. "Electric vehicle scheduling and optimal charging problem: complexity, exact and heuristic approaches," International Journal of Production Research, Taylor & Francis Journals, vol. 55(2), pages 519-535, January.
    7. Emde, Simon & Fliedner, Malte & Boysen, Nils, 2012. "Optimally loading tow trains for just-in-time supply of mixed-model assembly lines," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 79434, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    8. Jonathan D. Adler & Pitu B. Mirchandani, 2017. "The Vehicle Scheduling Problem for Fleets with Alternative-Fuel Vehicles," Transportation Science, INFORMS, vol. 51(2), pages 441-456, May.
    9. Nils Olsen & Natalia Kliewer, 2018. "Electric Vehicle Scheduling—A Study on Charging Modeling for Electric Vehicles," Operations Research Proceedings, in: Andreas Fink & Armin Fügenschuh & Martin Josef Geiger (ed.), Operations Research Proceedings 2016, pages 653-658, Springer.
    10. M. E. Kooten Niekerk & J. M. Akker & J. A. Hoogeveen, 2017. "Scheduling electric vehicles," Public Transport, Springer, vol. 9(1), pages 155-176, July.
    11. Gianni Codato & Matteo Fischetti, 2006. "Combinatorial Benders' Cuts for Mixed-Integer Linear Programming," Operations Research, INFORMS, vol. 54(4), pages 756-766, August.
    12. 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.
    13. Gschwind, Timo & Irnich, Stefan & Tilk, Christian & Emde, Simon, 2019. "Branch-cut-and-price for scheduling deliveries with time windows in a direct shipping network," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 116501, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    14. Boysen, Nils & Emde, Simon & Hoeck, Michael & Kauderer, Markus, 2015. "Part logistics in the automotive industry: Decision problems, literature review and research agenda," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 79443, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    15. Emde, Simon & Gendreau, Michel, 2017. "Scheduling in-house transport vehicles to feed parts to automotive assembly lines," European Journal of Operational Research, Elsevier, vol. 260(1), pages 255-267.
    16. Jing-Quan Li, 2014. "Transit Bus Scheduling with Limited Energy," Transportation Science, INFORMS, vol. 48(4), pages 521-539, November.
    17. Kovalyov, Mikhail Y. & Ng, C.T. & Cheng, T.C. Edwin, 2007. "Fixed interval scheduling: Models, applications, computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 178(2), pages 331-342, April.
    18. Emde, Simon & Abedinnia, Hamid & Glock, C. H., 2018. "Scheduling electric vehicles making milk-runs for just-in-time delivery," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 105768, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    19. Simon Emde & Shohre Zehtabian, 2019. "Scheduling direct deliveries with time windows to minimise truck fleet size and customer waiting times," International Journal of Production Research, Taylor & Francis Journals, vol. 57(5), pages 1315-1330, March.
    20. Wang, Yusheng & Huang, Yongxi & Xu, Jiuping & Barclay, Nicole, 2017. "Optimal recharging scheduling for urban electric buses: A case study in Davis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 100(C), pages 115-132.
    21. Antoon W.J. Kolen & Jan Karel Lenstra & Christos H. Papadimitriou & Frits C.R. Spieksma, 2007. "Interval scheduling: A survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 530-543, August.
    22. Goeke, Dominik & Schneider, Michael, 2015. "Routing a mixed fleet of electric and conventional vehicles," European Journal of Operational Research, Elsevier, vol. 245(1), pages 81-99.
    23. Michael Schneider & Andreas Stenger & Dominik Goeke, 2014. "The Electric Vehicle-Routing Problem with Time Windows and Recharging Stations," Transportation Science, INFORMS, vol. 48(4), pages 500-520, November.
    24. Emde, Simon & Gendreau, Michel, 2017. "Scheduling in-house transport vehicles to feed parts to automotive assembly lines," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 109727, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    25. Pelletier, Samuel & Jabali, Ola & Laporte, Gilbert & Veneroni, Marco, 2017. "Battery degradation and behaviour for electric vehicles: Review and numerical analyses of several models," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 158-187.
    26. Masood Fathi & Victoria Rodríguez & Dalila B.M.M. Fontes & Maria Jesus Alvarez, 2016. "A modified particle swarm optimisation algorithm to solve the part feeding problem at assembly lines," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 878-893, February.
    27. Emde, Simon & Boysen, Nils, 2012. "Optimally routing and scheduling tow trains for JIT-supply of mixed-model assembly lines," European Journal of Operational Research, Elsevier, vol. 217(2), pages 287-299.
    28. Schneider, M. & Stenger, A. & Goeke, D., 2014. "The Electric Vehicle Routing Problem with Time Windows and Recharging Stations," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 62382, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    29. Simon Emde & Hamid Abedinnia & Christoph H. Glock, 2018. "Scheduling electric vehicles making milk-runs for just-in-time delivery," IISE Transactions, Taylor & Francis Journals, vol. 50(11), pages 1013-1025, November.
    30. 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.
    31. Simon Emde & Michael Schneider, 2018. "Just-In-Time Vehicle Routing for In-House Part Feeding to Assembly Lines," Transportation Science, INFORMS, vol. 52(3), pages 657-672, June.
    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. Diefenbach, Heiko & Emde, Simon & Glock, Christoph H., 2020. "Loading tow trains ergonomically for just-in-time part supply," European Journal of Operational Research, Elsevier, vol. 284(1), pages 325-344.
    2. Emilio Moretti & Elena Tappia & Martina Mauri & Marco Melacini, 2022. "A performance model for mobile robot-based part feeding systems to supermarkets," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 580-613, September.
    3. Alvo, Matías & Angulo, Gustavo & Klapp, Mathias A., 2021. "An exact solution approach for an electric bus dispatch problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
    4. Simon Emde & Michael Schneider, 2018. "Just-In-Time Vehicle Routing for In-House Part Feeding to Assembly Lines," Transportation Science, INFORMS, vol. 52(3), pages 657-672, June.
    5. Simon Emde & Lukas Polten, 2019. "Sequencing assembly lines to facilitate synchronized just-in-time part supply," Journal of Scheduling, Springer, vol. 22(6), pages 607-621, December.
    6. Li, Lu & Lo, Hong K. & Huang, Wei & Xiao, Feng, 2021. "Mixed bus fleet location-routing-scheduling under range uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 155-179.
    7. Masood Fathi & Morteza Ghobakhloo, 2020. "Enabling Mass Customization and Manufacturing Sustainability in Industry 4.0 Context: A Novel Heuristic Algorithm for in-Plant Material Supply Optimization," Sustainability, MDPI, vol. 12(16), pages 1-15, August.
    8. Baals, Julian & Emde, Simon & Turkensteen, Marcel, 2023. "Minimizing earliness-tardiness costs in supplier networks—A just-in-time truck routing problem," European Journal of Operational Research, Elsevier, vol. 306(2), pages 707-741.
    9. Erfan Ghorbani & Mahdi Alinaghian & Gevork. B. Gharehpetian & Sajad Mohammadi & Guido Perboli, 2020. "A Survey on Environmentally Friendly Vehicle Routing Problem and a Proposal of Its Classification," Sustainability, MDPI, vol. 12(21), pages 1-71, October.
    10. Masmoudi, Mohamed Amine & Hosny, Manar & Demir, Emrah & Genikomsakis, Konstantinos N. & Cheikhrouhou, Naoufel, 2018. "The dial-a-ride problem with electric vehicles and battery swapping stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 392-420.
    11. Schiffer, Maximilian & Walther, Grit, 2018. "Strategic planning of electric logistics fleet networks: A robust location-routing approach," Omega, Elsevier, vol. 80(C), pages 31-42.
    12. Zhang, Shuai & Gajpal, Yuvraj & Appadoo, S.S. & Abdulkader, M.M.S., 2018. "Electric vehicle routing problem with recharging stations for minimizing energy consumption," International Journal of Production Economics, Elsevier, vol. 203(C), pages 404-413.
    13. Pelletier, Samuel & Jabali, Ola & Laporte, Gilbert, 2018. "Charge scheduling for electric freight vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 246-269.
    14. Bock, Stefan, 2020. "Optimally solving a versatile Traveling Salesman Problem on tree networks with soft due dates and multiple congestion scenarios," European Journal of Operational Research, Elsevier, vol. 283(3), pages 863-882.
    15. Stefan Bock, 2016. "Finding optimal tour schedules on transportation paths under extended time window constraints," Journal of Scheduling, Springer, vol. 19(5), pages 527-546, October.
    16. Schiffer, Maximilian & Schneider, Michael & Laporte, Gilbert, 2018. "Designing sustainable mid-haul logistics networks with intra-route multi-resource facilities," European Journal of Operational Research, Elsevier, vol. 265(2), pages 517-532.
    17. Zhou, Yu & Meng, Qiang & Ong, Ghim Ping, 2022. "Electric Bus Charging Scheduling for a Single Public Transport Route Considering Nonlinear Charging Profile and Battery Degradation Effect," Transportation Research Part B: Methodological, Elsevier, vol. 159(C), pages 49-75.
    18. Asghari, Mohammad & Mirzapour Al-e-hashem, S. Mohammad J., 2021. "Green vehicle routing problem: A state-of-the-art review," International Journal of Production Economics, Elsevier, vol. 231(C).
    19. Dönmez, Sercan & Koç, Çağrı & Altıparmak, Fulya, 2022. "The mixed fleet vehicle routing problem with partial recharging by multiple chargers: Mathematical model and adaptive large neighborhood search," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 167(C).
    20. C. Briand & Y. He & S. U. Ngueveu, 2018. "Energy-efficient planning for supplying assembly lines with vehicles," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(4), pages 387-414, December.

    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:ejores:v:306:y:2023:i:2:p:828-848. 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/locate/eor .

    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.