Scheduling Electric Buses with Stochastic Driving Times

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

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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

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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


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