## 3 Problem Description and Cost Model
### Savings Algorithm for Generating Initial Solutions
We also focused on a consideration of complete and partial battery charging procedures of the

Figure 4: Overview of convergence behaviour for all problem instances solved by Algorithm 3.

batteries within vehicle rotations. In our study we compared the simultaneous solution approach to sequential planning to tackle the underlying problems. Our experiments showed that simultaneous solving of location planning of charging stations and vehicle scheduling of BEBs is necessary as opposed to sequential planning. First, we demonstrated that sequential planning, first solving a standard VSP and afterwards a location planning problem for charging stations, generally leads to infeasible vehicle rotations for BEBs with regard to current battery technologies. Second, solving an E-VSP with given locations of charging stations entails significant increases in costs. Solving the E-VSP-LP, on the one hand, ensures the feasibility of the vehicle rotations. On the other hand, significantly lower total costs are achieved by comparison to solving an E-VSP, due to the higher degrees of freedom. This is particularly relevant for public transport companies that start operating electric bus fleets. With regard to complete and partial battery chargings, we found large cost savings in most cases when enabling partial chargings within the vehicle rotations. Our paper can be extended by the following aspects. First, the proposed models do not deal with multiple depots. Incorporating this extension would most likely open up further potentials for cost savings, as already shown for the traditional VSP. Second, our solution method solves the E-VSP-LP heuristically. Exact solution approaches would be interesting for a better verification of the quality of heuristic solution methods. In addition, an interesting path for future research would be to develop additional algorithms for the generation of initial solutions as well as for improvement. Finally, more accurate models regarding the technical aspects of BEBs may be considered. It is conceivable to presume uncertain energy consumptions that may depend on weather conditions or the volume of traffic. Conceptualization, N.O. and N.K. ; methodology, N.O. and N.K. ; software, N.O. and N.K. ; validation, N.O. and N.K. ; formal analysis, N.O. and N.K. ; investigation, N.O. and N.K. ; resources, N.O. and N.K. ; data curation, N.O. and N.K. ; writing--original draft preparation, N.O. and N.K. ; writing--review and editing, N.O. and N.K. ; visualization, N.O. and N.K. ; supervision, N.K. ; project administration, N.K. ; funding acquisition, N.K. All authors have read and agreed to the published version of the manuscript. This work has been financially supported by the German Research Foundation [grant KL 2152/5-1]. The publication of this article was funded by Freie Universitat Berlin. Not applicable. The authors declare no conflict of interest. ## References

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