Mixed-fleet single-terminal bus scheduling problem: Modelling, solution scheme and potential applications

Marco Rinaldi, Erika Picarelli, Andrea D'Ariano, Francesco Viti

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)


Reducing pollutant emissions and promoting sustainable mobility solutions, including Public Transport (PT), are increasingly becoming key objectives for policymakers worldwide. In this work we develop an optimal vehicle scheduling approach for next generation PT systems, considering the instance of mixed electric / hybrid fleet. Our objective is that of investigating to what extent electrification, coupled with optimal fleet management, can yield operational cost savings for PT operators. We propose a Mixed Integer Linear Program (MILP) to address the problem of optimal scheduling of a mixed fleet of electric and hybrid / non-electric buses, coupled with an ad-hoc decomposition scheme aimed at enhancing the scalability of the proposed MILP. Two case studies arising from the PT network of the city of Luxembourg are employed in order to validate the model; sensitivity analysis to fleet design parameters is performed, specifically in terms of fleet size and fleet composition. Conclusions point to the fact that careful modelling and handling of mixed-fleet conditions are necessary to achieve operational savings, and that marginal savings gradually reduce as more conventional buses are replaced by their electric counterparts. We believe the methodology proposed may be a key part of advanced decision support systems for policymakers and operators that are dealing with the on-going transition from conventional bus fleets towards greener transport solutions.

Original languageEnglish
Article number102070
JournalOmega (United Kingdom)
Publication statusPublished - Oct 2020
Externally publishedYes


  • Decomposition scheme
  • MILP
  • Mixed-fleet
  • Public transport optimization
  • Vehicle scheduling


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