## 3 Problem Description and Cost Model
### Savings Algorithm for Generating Initial Solutions
Within Algorithm 3, we modify the Algorithms 5 and 9 by disabling Algorithm 8 within each procedure. This approach means that the set of charging stations cannot change in this experiment. While the following results are not necessarily optimal due to the heuristic solving, we show that they provide reasonable bounds for our analysis within the next section. An overview of the results of this experiment is given by Table 3, providing the numbers of vehicles used as well as operational and total costs. The number of charging stations is taken from the previous experiment. In contrast to that, now each solution is feasible, which was to be expected because of the constraints imposed by the E-VSP. Consequently, the total costs are specified for each instance and each battery capacity, containing fixed costs for buses used and charging stations as well as operational costs. First of all, the results show that in most cases where feasible vehicle rotations were computed in the first experiment described in Section 5.2, the solving of an E-VSP provides similar results regarding the numbers of vehicles used and total costs. In some cases, the number of vehicles required is slightly higher than in the first experiment, which can be traced back to the heuristic solution approach. Furthermore, the operational costs are marginally increased. However, the solutions of this experiment converge towards the optimal solutions and thus provide a reasonable benchmark for subsequent analyses. Regarding the numbers of vehicles used, one can observe that the fewer the proportions of feasible vehicle rotations determined within the first experiment, the more vehicles are required when solving the E-VSP. This is understandable because the closely-timed service trips of the vehicle rotations when no range limitations are considered do not provide enough time for rechargings. This leads to an increasing demand for vehicles. For example, considering instance t1580_s209, the optimal numbers of vehicles used is obtained for battery capacities of 500 kWh and 300 kWh. As the proportion of feasible vehicle rotations reduces rapidly for 120 kWh and 60 kWh within the first experiment (81.33% respectively 52%), the need for additional vehicles rises significantly (6 respectively 12 additional vehicles). Regarding the operational costs, we note that higher demands for vehicles generally leads to decreasing operational costs. This is because less deadhead trips and chargings have to be performed due to the shorter rotations. In conclusion, solving an E-VSP with given locations of charging stations always leads to feasible vehicle rotations, which is in contrast to the first experiment. However, this solution approach generally entails increases in costs due to additional deadhead trips, likely leading to increasing demands for vehicles. The results obtained serve as upper bounds for the analysis of the simultaneous problem solving to be conducted in the following section. ### Simultaneous Optimization of Vehicle Scheduling and Charging Infrastructure

We now discuss the results of simultaneous optimization of scheduling of BEBs and location planning for charging stations, i.e., solving the E-VSP-LP, using our solution method given by Algorithm 1. We begin by presenting the results obtained by Algorithm 2 for generating initial solutions. Then, we discuss the results of Algorithm 3 for finding new solutions with lower total costs. In this experiment we consider complete as well as partial charging procedures in order to enable a comparison with the previous experiments. We conclude this chapter by a runtime analysis. #### 5.4.1 Summary of Results for Generating Initial Solutions

Table 4 provides the results of using Algorithm 2 for generating initial solutions containing feasible sets of vehicle rotations and charging stations. The results contain the total and operational costs as well as the numbers of buses and charging stations used for each instance and each battery capacity. Additionally, the differences in the total costs