## 3 Problem Description and Cost Model
### Savings Algorithm for Generating Initial Solutions
Again based on the bus project in Amsterdam, the equipment of a stop point with charging technology is incorporated with fixed costs of 200,000 monetary units. We use the term \"monetary units\" here since we assume that these units are roughly comparable--at least in terms of scale--and, based on this, that monetary units form a system of imputed cost components. Location Planning of Charging Stations for the Electrification of Cost-Minimal Vehicle Rotations, Computed without Range Limitations

We begin our computational analysis by discussing the results of solving a location planning problem for charging stations for the electrification of given cost-minimal vehicle rotations computed without range limitations. The vehicle rotations were generated using the exact optimization method for the traditional VSP by [PERSON] et al. [16], which is based on a time-space network. In order to enable the operation of these rotations by BEBs, charging stations are added to the network and charging procedures are inserted into the vehicle rotations. Partial charging procedures are performed, since the idle times at potential charging stations are given by the vehicle rotations. The objective is to maximize the proportion of vehicle rotations that are feasible for BEBs. Ideally, this procedure should ensure the holistic operation of the timetabled service trips by BEBs. For this purpose, we adapt the location planning problem for charging stations introduced by [PERSON] et al. [24] and solve it using standard optimization libraries. Table 2 provides the results of solving a location planning problem for charging stations, containing the proportions and absolute numbers of feasible vehicle rotations for BEBs together with the numbers and proportions of charging stations needed for each instance and each battery capacity. Additionally, the optimal number of vehicles used is indicated when no range limitations are considered. If the totality of all vehicle rotations is feasible for BEBs, the operational and total costs are specified for subsequent analyses. First, we observe that in the vast majority of cases the holistic electrification of vehicle rotations by means of inserting charging procedures is not possible. It is apparent that this observation holds regardless of the instance to be solved. However, the proportion of feasible vehicle rotations grows with increasing battery capacities. We can observe that every instance can be entirely served by BEBs in the case of a battery capacity of 500 kWh. In some cases, this situation already occurs with a battery capacity of 300 kWh and in a single case with 120 kWh. However, none of the instances can be entirely served by BEBs with a battery capacity of 60 kWh. Regarding a battery capacity of 60 kWh, the proportions of feasible vehicle rotations fluctuates widely and ranges between 7.25% and 79.63%. With regard to charging stations, it can be concluded that the numbers of stop points equipped with charging technology decreases significantly when the battery capacities grow. Instance t1296_s88 shows the biggest reduction in the number of charging stations needed from

48.86% to 6.81%. The operational costs of feasible vehicle rotations decrease slightly when the battery capacities grow, which can be attributed to fewer charging procedures required. In summary, a sequential planning solving at first a standard VSP without incorporating the special features of BEBs and subsequently a location planning problem for charging stations is generally insufficient, leading to widely infeasible solutions. This approach is only suitable if the ranges of BEBs rise sharply in the future. The results obtained serve as lower bounds for the numbers of BEBs used and as an upper bound for the numbers of charging stations needed in the evaluation of the simultaneous solution approach. ### Scheduling of Electric Buses Given Fixed Locations of Charging Stations

We now discuss the results of solving an E-VSP with given locations of charging stations.