{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T09:47:28Z","timestamp":1781516848862,"version":"3.54.1"},"reference-count":50,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T00:00:00Z","timestamp":1745971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>This work develops a scheduling tool for electric buses that accounts for daily disruptions while minimizing the operational costs. The contribution of this study lies in the development of electric bus schedules that consider many factors, such as multiple depots, multiple charging stations, and stochastic travel times, providing schedules resilient to extreme conditions. The developed model is a mixed-integer linear program (MILP) with chance constraints. The main decision variables are the assignment of electric vehicles to scheduled trips and charging events to ensure the improved operation of daily services under uncertain conditions. Numerical experiments and a sensitivity analysis based on the variation in travel times are conducted, demonstrating the performance of our solution approach. The results from these experiments indicate that the variant of the model with the chance constraint produces schedules with lower operational costs compared to the case where the chance constraints are not introduced.<\/jats:p>","DOI":"10.3390\/info16050376","type":"journal-article","created":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T09:16:12Z","timestamp":1746090972000},"page":"376","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Electric Bus Scheduling Problem with Time Windows and Stochastic Travel Times"],"prefix":"10.3390","volume":"16","author":[{"given":"Vladyslav","family":"Kost","sequence":"first","affiliation":[{"name":"Department of Transportation Planning and Engineering, School of Civil Engineering, National Technical University of Athens, Zografou Campus, 9, Iroon Polytechniou Str., 15780 Athens, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marilena","family":"Merakou","sequence":"additional","affiliation":[{"name":"Department of Transportation Planning and Engineering, School of Civil Engineering, National Technical University of Athens, Zografou Campus, 9, Iroon Polytechniou Str., 15780 Athens, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3009-1527","authenticated-orcid":false,"given":"Konstantinos","family":"Gkiotsalitis","sequence":"additional","affiliation":[{"name":"Department of Transportation Planning and Engineering, School of Civil Engineering, National Technical University of Athens, Zografou Campus, 9, Iroon Polytechniou Str., 15780 Athens, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,30]]},"reference":[{"key":"ref_1","unstructured":"ITF (2023). ITF Transport Outlook 2023, OECD Publishing."},{"key":"ref_2","unstructured":"Ritchie, H., Rosado, P., and Roser, M. (2024, December 19). Breakdown of Carbon Dioxide, Methane and Nitrous Oxide Emissions by Sector. Our World in Data. Available online: https:\/\/ourworldindata.org\/emissions-by-sector."},{"key":"ref_3","unstructured":"European Commission (2023). European Green Deal: Commission Proposes 2030 Zero-Emissions Target for New City Buses and 90% Emissions Reductions for New Trucks by 2040, European Commission."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"108116","DOI":"10.1016\/j.envint.2023.108116","article-title":"The co-benefits of electric mobility in reducing traffic noise and chemical air pollution: Insights from a transit-oriented city","volume":"178","author":"Tsoi","year":"2023","journal-title":"Environ. Int."},{"key":"ref_5","unstructured":"Bor\u00e9n, S., Nurhadi, L., and Ny, H. (2016, January 24\u201325). Preference of electric buses in public transport: Conclusions from real life testing in eight swedish municipalities. Proceedings of the 18th International Conference on Sustainable Urban Transport and Environment, Madrid, Spain."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.trpro.2018.12.206","article-title":"Modelling noise reductions using electric buses in urban traffic. A case study from Stuttgart, Germany","volume":"37","author":"Laib","year":"2019","journal-title":"Transp. Res. Procedia"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.apacoust.2016.09.018","article-title":"The effect of electric vehicles on urban noise maps","volume":"116","year":"2017","journal-title":"Appl. Acoust."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1080\/03081060.2023.2224311","article-title":"Electric taxi licensing under a tradable credit scheme: Model and application","volume":"46","author":"Iliopoulou","year":"2023","journal-title":"Transp. Plan. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1353\/gia.2021.0039","article-title":"The Geoeconomics of Critical Rare Earth Minerals","volume":"22","author":"Vekasi","year":"2021","journal-title":"Georget. J. Int. Aff."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Kiggins, R. (2015). The Strategic and Security Implications of Rare Earths. The Political Economy of Rare Earth Elements, Palgrave Macmillan.","DOI":"10.1057\/9781137364241"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103130","DOI":"10.1016\/j.trd.2021.103130","article-title":"Comparative assessment of zero emission electric and hydrogen buses in Australia","volume":"102","author":"Hensher","year":"2022","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_12","unstructured":"Matzoros, A. (2000, January 11\u201313). Electric trolley buses or thermal buses? The case of Athens. Proceedings of the Seminar E of the European Transport Conference 2000, Cambridge, UK."},{"key":"ref_13","unstructured":"International Council on Clean Transportation (2024, December 19). Decarbonizing Bus Fleets: Global Overview of Targets for Phasing Out Combustion Engine Vehicles. Available online: https:\/\/theicct.org\/decarbonizing-bus-fleets-global-overview-of-targets-for-phasing-out-combustion-engine-vehicles\/."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"ten Have, S.Y., Gkiotsalitis, K., and Geurs, K.T. (2020). Investigating the future of ultrafast charging: A choice experiment in The Netherlands. World Electr. Veh. J., 11.","DOI":"10.3390\/wevj11040070"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6760","DOI":"10.1109\/TITS.2020.2994538","article-title":"Bus holding of electric buses with scheduled charging times","volume":"22","author":"Gkiotsalitis","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e12450","DOI":"10.1002\/eem2.12450","article-title":"High-Energy Lithium-Ion Batteries: Recent Progress and a Promising Future in Applications","volume":"6","author":"Xu","year":"2023","journal-title":"Energy Environ. Mater."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"125242","DOI":"10.1016\/j.apenergy.2024.125242","article-title":"Electric bus charging station location selection problem with slow and fast charging","volume":"382","author":"Gkiotsalitis","year":"2025","journal-title":"Appl. Energy"},{"key":"ref_18","unstructured":"(2024, December 19). Electric Bus Basics|US Department of Transportation, Available online: https:\/\/www.transportation.gov\/rural\/electric-vehicles\/ev-toolkit\/electric-bus-basics."},{"key":"ref_19","unstructured":"(2024, December 19). How Long Does It Take to Charge an Electric Bus?\u2014eCity Powered by Solaris. Available online: https:\/\/ecity.solarisbus.com\/en\/knowledge-base\/how-long-does-it-take-to-charge-an-electric-bus."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.ijtst.2022.02.007","article-title":"Electric bus charging station location optimization considering queues","volume":"12","author":"Tzamakos","year":"2023","journal-title":"Int. J. Transp. Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"103653","DOI":"10.1016\/j.trd.2023.103653","article-title":"Joint optimization of electric bus charging infrastructure, vehicle scheduling, and charging management","volume":"117","author":"He","year":"2023","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"103732","DOI":"10.1016\/j.trc.2022.103732","article-title":"A joint optimisation model for charger locating and electric bus charging scheduling considering opportunity fast charging and uncertainties","volume":"141","author":"Hu","year":"2022","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Al-Saadi, M., Bhattacharyya, S., Tichelen, P.V., Mathes, M., K\u00e4sgen, J., Mierlo, J.V., and Berecibar, M. (2022). Impact on the Power Grid Caused via Ultra-Fast Charging Technologies of the Electric Buses Fleet. Energies, 15.","DOI":"10.3390\/en15041424"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s12469-010-0018-5","article-title":"An overview on vehicle scheduling models","volume":"1","author":"Bunte","year":"2009","journal-title":"Public Transp."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"103410","DOI":"10.1016\/j.trd.2022.103410","article-title":"Robust optimization for integrated planning of electric-bus charger deployment and charging scheduling","volume":"110","author":"Zhou","year":"2022","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"100006","DOI":"10.1016\/j.multra.2022.100006","article-title":"A two-stage stochastic programming model of coordinated electric bus charging scheduling for a hybrid charging scheme","volume":"1","author":"Huang","year":"2022","journal-title":"Multimodal Transp."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s12469-017-0164-0","article-title":"Scheduling electric vehicles","volume":"9","author":"Hoogeveen","year":"2017","journal-title":"Public Transp."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.trb.2021.11.007","article-title":"The multi-depot electric vehicle scheduling problem with power grid characteristics","volume":"155","author":"Wu","year":"2022","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"103955","DOI":"10.1016\/j.trd.2023.103955","article-title":"A robust coordinated charging scheduling approach for hybrid electric bus charging systems","volume":"125","author":"Huang","year":"2023","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.trc.2020.02.009","article-title":"Battery-electric transit vehicle scheduling with optimal number of stationary chargers","volume":"114","author":"Liu","year":"2020","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.ejor.2022.07.017","article-title":"An exact approach for the multi-depot electric bus scheduling problem with time windows","volume":"306","author":"Gkiotsalitis","year":"2023","journal-title":"Eur. J. Oper. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1191443","DOI":"10.1155\/2021\/1191443","article-title":"Optimal Electric Bus Scheduling under Travel Time Uncertainty: A Robust Model and Solution Method","volume":"2021","author":"Jiang","year":"2021","journal-title":"J. Adv. Transp."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Chau, M., Koutsompina, D., and Gkiotsalitis, K. (2024). The Electric Vehicle Scheduling Problem for Buses in Networks with Multi-Port Charging Stations. Sustainability, 16.","DOI":"10.3390\/su16031305"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.trc.2019.05.032","article-title":"Robust scheduling strategies of electric buses under stochastic traffic conditions","volume":"105","author":"Tang","year":"2019","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1530","DOI":"10.1111\/mice.12684","article-title":"Optimization of electric bus scheduling considering stochastic volatilities in trip travel time and energy consumption","volume":"36","author":"Bie","year":"2021","journal-title":"Comput.-Aided Civ. Infrastruct. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"8863905","DOI":"10.1155\/2020\/8863905","article-title":"Joint Optimization of Regular Charging Electric Bus Transit Network Schedule and Stationary Charger Deployment considering Partial Charging Policy and Time-of-Use Electricity Prices","volume":"2020","author":"Li","year":"2020","journal-title":"J. Adv. Transp."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.tre.2017.01.001","article-title":"Optimal recharging scheduling for urban electric buses: A case study in Davis","volume":"100","author":"Wang","year":"2017","journal-title":"Transp. Res. Part E Logist. Transp. Review"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.endm.2014.11.029","article-title":"A Variable Neighborhood Search Branching for the Electric Vehicle Routing Problem with Time Windows","volume":"47","author":"Bruglieri","year":"2015","journal-title":"Electron. Notes Discret. Math."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.cor.2016.06.013","article-title":"An adaptive large neighborhood search heuristic for the Electric Vehicle Scheduling Problem","volume":"76","author":"Wen","year":"2016","journal-title":"Comput. Oper. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"107774","DOI":"10.1016\/j.asoc.2021.107774","article-title":"Solving multi-depot electric vehicle scheduling problem by column generation and genetic algorithm","volume":"112","author":"Wang","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_41","first-page":"1237","article-title":"Heuristic approaches for solving transit vehicle scheduling problem with route and fueling time constraints","volume":"190","author":"Wang","year":"2007","journal-title":"Appl. Math. Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.trpro.2020.03.099","article-title":"Model and Solution Methods for the Mixed-Fleet Multi-Terminal Bus Scheduling Problem","volume":"47","author":"Picarelli","year":"2020","journal-title":"Transp. Res. Procedia"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"103197","DOI":"10.1016\/j.trc.2021.103197","article-title":"Electric bus fleet composition and scheduling","volume":"129","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"8056","DOI":"10.1109\/ACCESS.2020.2964391","article-title":"Collaborative optimization of vehicle and charging scheduling for a bus fleet mixed with electric and traditional buses","volume":"8","author":"Zhou","year":"2020","journal-title":"IEEE Access"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.apenergy.2017.11.051","article-title":"Electric bus fleet size and mix problem with optimization of charging infrastructure","volume":"211","author":"Rogge","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"9222636","DOI":"10.1155\/2022\/9222636","article-title":"Multi-Objective Stochastic Synchronous Timetable Optimization Model Based on a Chance-Constrained Programming Method Combined with Augmented Epsilon Constraint Algorithm","volume":"2022","author":"Yuan","year":"2022","journal-title":"Math. Probl. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2446","DOI":"10.1111\/itor.13211","article-title":"Heuristic feeder-bus operation strategy considering weather information: A chance-constrained model","volume":"31","author":"Liu","year":"2024","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_48","first-page":"312","article-title":"Fuzzy Bi-objective Chance-Constrained Programming Model for Timetable Optimization of a Bus Route","volume":"Volume 650","author":"Du","year":"2018","journal-title":"Advances in Intelligent Systems and Computing, Proceedings of the 17th UK Workshop on Computational Intelligence, Cardiff, UK, 6\u20138 September 2017"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"66","DOI":"10.3141\/2315-07","article-title":"Speed modeling and travel time estimation based on truncated normal and lognormal distributions","volume":"2315","author":"Wang","year":"2012","journal-title":"Transp. Res. Rec."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"104058","DOI":"10.1016\/j.tra.2024.104058","article-title":"Lognormal distribution of daily travel time and a utility model for its emergence","volume":"183","author":"Wang","year":"2024","journal-title":"Transp. Res. Part A Policy Pract."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/5\/376\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:25:36Z","timestamp":1760030736000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/16\/5\/376"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,30]]},"references-count":50,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["info16050376"],"URL":"https:\/\/doi.org\/10.3390\/info16050376","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,30]]}}}