Document Open Access Logo

Scheduling Electric Buses with Stochastic Driving Times

Authors Philip de Bruin , Marjan van den Akker , Han Hoogeveen , Marcel van Kooten Niekerk

Thumbnail PDF


  • Filesize: 2.04 MB
  • 19 pages

Document Identifiers

Author Details

Philip de Bruin
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Marjan van den Akker
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Han Hoogeveen
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Marcel van Kooten Niekerk
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
  • Qbuzz BV, The Netherlands

Cite AsGet BibTex

Philip de Bruin, Marjan van den Akker, Han Hoogeveen, and Marcel van Kooten Niekerk. Scheduling Electric Buses with Stochastic Driving Times. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 14:1-14:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


To try to make the world more sustainable and reduce air pollution, diesel buses are being replaced with electric buses. This leads to challenges in scheduling, as electric buses need recharging during the day. Moreover, buses encounter varying traffic conditions and passenger demands, leading to delays. Scheduling electric buses with these stochastic driving times is also called the Stochastic Vehicle Scheduling Problem. The classical approach to make a schedule more robust against these delays, is to add slack to the driving time. However, this approach doesn't capture the variance of a distribution well, and it doesn't account for dependencies between trips. We use discrete event simulation in order to evaluate the robustness of a schedule. Then, to create a schedule, we use a hybrid approach, where we combine integer linear programming and simulated annealing with the use of these simulations. We show that with the use of our hybrid algorithm, the punctuality of the buses increase, and they also have a more timely arrival. However, we also see a slight increase in operating cost, as we need slightly more buses compared to when we use deterministic driving times.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Planning and scheduling
  • Computing methodologies → Modeling and simulation
  • Computing methodologies → Planning under uncertainty
  • Computing methodologies → Discrete-event simulation
  • Electric Vehicle Scheduling Problem
  • Simulated Annealing
  • Hybrid Algorithm
  • Simulation
  • Stochastic Driving Times


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


  1. Yiming Bie, Jinhua Ji, Xiangyu Wang, and Xiaobo Qu. Optimization of electric bus scheduling considering stochastic volatilities in trip travel time and energy consumption. Computer-Aided Civil and Infrastructure Engineering, 36(12):1530-1548, 2021. URL:
  2. Zhu Chao and Chen Xiaohong. Optimizing battery electric bus transit vehicle scheduling with battery exchanging: Model and case study. Procedia - Social and Behavioral Sciences, 96:2725-2736, 2013. URL:
  3. Zhibin Chen, Yafeng Yin, and Ziqi Song. A cost-competitiveness analysis of charging infrastructure for electric bus operations. Transportation Research Part C: Emerging Technologies, 93:351-366, 2018. URL:
  4. Philip de Bruin. Scheduling electric buses with stochastic driving times. mathesis, Utrecht University, 2022. URL:
  5. KNMI. Hourly weather station readings. Accessed: 2022-05-24.
  6. Averill M. Law. Simulation Modeling and Analysis. McGraw-Hill, 5th edition, 2015. Google Scholar
  7. Jing-Quan Li. Battery-electric transit bus developments and operations: A review. International Journal of Sustainable Transportation, 10(3):157-169, 2016. URL:
  8. Nils Olsen and Natalia Kliewer. Scheduling electric buses in public transport: Modeling of the charging process and analysis of assumptions. Logistics Research, 13(1):4, 2020. URL:
  9. G. J. P. N. Passage, J. M. van den Akker, and J. A. Hoogeveen. Local search for stochastic parallel machine scheduling: improving performance by estimating the makespan. In European Conference on Stochastic Optimization, 2017. Google Scholar
  10. Jayakrishna Patnaik, Steven Chien, and Athanassios Bladikas. Estimation of bus arrival times using APC data. Journal of Public Transportation, 7(1):1-20, 2004. URL:
  11. Shyam S. G. Perumal, Richard M. Lusby, and Jesper Larsen. Electric bus planning & scheduling: A review of related problems and methodologies. European Journal of Operational Research, 301(2):395-413, 2022. URL:
  12. Samuel J. Raff. Routing and scheduling of vehicles and crews : The state of the art. Computers & Operations Research, 10(2):63-67, 1983. URL:
  13. Xindi Tang, Xi Lin, and Fang He. Robust scheduling strategies of electric buses under stochastic traffic conditions. Transportation Research Part C: Emerging Technologies, 105:163-182, 2019. URL:
  14. W. ten Bosch, J. A. Hoogeveen, and M. E. van Kooten Niekerk. Scheduling electric vehicles by simulated annealing with recombination through ILP. Submitted for publication, 2021. Google Scholar
  15. Marjan van den Akker, Kevin van Blokland, and Han Hoogeveen. Finding robust solutions for the stochastic job shop scheduling problem by including simulation in local search. In Vincenzo Bonifaci, Camil Demetrescu, and Alberto Marchetti-Spaccamela, editors, Experimental Algorithms, 12th International Symposium, SEA 2013, Rome, Italy, June 5-7, 2013. Proceedings, volume 7933 of Lecture Notes in Computer Science, pages 402-413. Springer, 2013. URL:
  16. Marcel E. van Kooten Niekerk, J. M. van den Akker, and J. A. Hoogeveen. Scheduling electric vehicles. Public Transport, 9(1-2):155-176, 2017. URL:
  17. Haixing Wang and Jinsheng Shen. Heuristic approaches for solving transit vehicle scheduling problem with route and fueling time constraints. Applied Mathematics and Computation, 190(2):1237-1249, 2007. URL:
  18. M. Wen, E. Linde, S. Ropke, P. Mirchandani, and A. Larsen. An adaptive large neighborhood search heuristic for the electric vehicle scheduling problem. Computers & Operations Research, 76:73-83, 2016. 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