Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates (Short Paper)

Authors Fabian Löbel , Ralf Borndörfer , Steffen Weider

Thumbnail PDF


  • Filesize: 0.54 MB
  • 6 pages

Document Identifiers

Author Details

Fabian Löbel
  • Zuse Institute Berlin, Germany
Ralf Borndörfer
  • Zuse Institute Berlin, Germany
Steffen Weider
  • LBW Optimization GmbH, Berlin, Germany

Cite AsGet BibTex

Fabian Löbel, Ralf Borndörfer, and Steffen Weider. Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates (Short Paper). In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 15:1-15:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The ongoing electrification of logistics systems and vehicle fleets increases the complexity of associated vehicle routing or scheduling problems. Battery-powered vehicles have to be scheduled to recharge in-service, and the relationship between charging time and replenished driving range is non-linear. In order to access the powerful toolkit offered by mixed-integer and linear programming techniques, this battery behavior has to be linearized. Moreover, as electric fleets grow, power draw peaks have to be avoided to save on electricity costs or to adhere to hard grid capacity limits, such that it becomes desirable to keep recharge rates dynamic. We suggest a novel linearization approach of battery charging behavior for vehicle scheduling problems, in which the recharge rates are optimization variables and not model parameters.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Integer programming
  • Mathematics of computing → Linear programming
  • Applied computing → Transportation
  • Electric Vehicle Scheduling
  • Battery Powered Vehicles
  • Charging Process
  • Non-linear Charging
  • Recharge Modeling
  • Dynamic Recharge Rate


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. H. Diefenbach, S. Emde, and C.H. Glock. Multi-depot electric vehicle scheduling in in-plant production logistics considering non-linear charging models. European Journal of Operational Research, 306(2):828-848, 2023. URL:
  2. T. Erdelić and T. Carić. A Survey on the Electric Vehicle Routing Problem: Variants and Solution Approaches. Journal of Advanced Transportation, 2019:1-48, May 2019. URL:
  3. D. Jefferies and D. Göhlich. A Comprehensive TCO Evaluation Method for Electric Bus Systems Based on Discrete-Event Simulation Including Bus Scheduling and Charging Infrastructure Optimisation. World Electric Vehicle Journal, 11, August 2020. URL:
  4. L. Li, H.K. Lo, and F. Xiao. Mixed bus fleet scheduling under range and refueling constraints. Transportation Research Part C: Emerging Technologies, 104:443-462, 2019. URL:
  5. S. Lösel. Elektrobusse im ländlichen Raum: VLP startet Sektorenkopplung Energiewirtschaft und Verkehr. Der Nahverkehr Elektrobus-Spezial 2023, 41:40-43, March 2023. (German). Google Scholar
  6. B. Messaoudi and A. Oulamara. Electric Bus Scheduling and Optimal Charging. In Carlos Paternina-Arboleda and Stefan Voß, editors, Computational Logistics, pages 233-247. Springer International Publishing, 2019. URL:
  7. A. Montoya, C. Guéret, J.E. Mendoza, and J.G. Villegas. The electric vehicle routing problem with nonlinear charging function. Transportation Research Part B: Methodological, 103:87-110, 2017. Green Urban Transportation. URL:
  8. N. Olsen and N. Kliewer. Scheduling Electric Buses in Public Transport: Modeling of the Charging Process and Analysis of Assumptions. Logistics Research, 13(4), 2020. URL:
  9. S. Pelletier, O. Jabali, G. Laporte, and M. Veneroni. Battery degradation and behaviour for electric vehicles: Review and numerical analyses of several models. Transportation Research Part B: Methodological, 103:158-187, 2017. URL:
  10. S.S.G. Perumal, R.M. Lusby, and J. Larsen. Electric bus planning & scheduling: A review of related problems and methodologies. European Journal of Operational Research, 2022. URL:
  11. M.E. van Kooten Niekerk, J.M. van den Akker, and J.A. Hoogeveen. Scheduling electric vehicles. Public Transport, 9:155-176, 2017. URL:
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail