## 3 Problem Description and Cost Model
### Savings Algorithm for Generating Initial Solutions
With regard to the total costs, our observations are twofold: In those cases in which the solving of a location planning problem led to infeasible vehicle rotations, the application of Algorithm 2 leads to lower total costs by comparison to the results obtained by solving an E-VSP. In the other cases where feasible solutions were obtained, the total costs are higher, arising from a higher demand for vehicles needed as indicated previously. Basically, the results computed by Algorithm 2 merely serve as the input for improvement methods and thus do not serve as the final results. For this reason, the clarified statements are not particularly significant. In the next section, we present the results of improvement using our solution approach based on VNS. #### 5.4.2 Summary of Results for Variable Neighborhood Search for Improvement

In order to carry out a final comparison between sequential planning and simultaneous problem solving, we now present the results of our solution method given by Algorithm 3 for finding new solutions with lower total costs. We use the initial solutions presented in the previous section as the input data. Table 5 shows the results, containing numbers of vehicles and charging stations used, as well as operational and total costs for each instance and each battery capacity. Additionally, the differences in the total costs are specified when enabling partial charging procedures, and the best solutions found are in bold. Again, we first compare the results to solving a location planning problem for charging stations at given vehicle rotations. In those cases, where feasible solutions were computed and shown in Section 5.2, the total costs obtained by applying Algorithm 3 are almost of the same quality. In some cases, the total costs are slightly higher, which is most likely due to the heuristic solving. However, in certain scenarios, even better solutions are achieved which can be explained by the utilization of the degrees of freedom. Simultaneous problem solving enables shorter and fewer deadhead trips to charging stations, leading to lower operational and fixed costs for vehicles. This effect would be intensified if exact solution methods were used. As the sequential planning approach leads mostly to infeasible solutions, the simultaneous problem solving is generally preferable. We now discuss the results with regard to solving an E-VSP with given locations of charging stations as carried out and described in Section 5.3. The most significant observation is that the total costs obtained by the simultaneous problem solving are always below the results of solving an E-VSP with fixed charging stations. This holds true for each combination of instance and battery capacity. The primary reasons for this are that the VNS based approach leads either to the same or slightly higher numbers of vehicles. Similarly, considerably lower numbers of charging stations needed are achieved due to the simultaneous solution procedure, leading to significant cost savings. Additionally, the operational costs are reduced for the most part, which can be explained by the shorter deadhead trips to charging stations. As the cost savings exceed the increased costs for additional vehicles, the solutions generated entail significantly lower total costs. It is interesting to oberserve that the greatest costs savings are achieved for instances that contain peak times of cumulative service trips over the day. This can be explained by the fact that peak times of service trips over the day allow the vehicles to recharge their batteries during times with reduced offers. In conclusion, simultaneous problem solving enables significant cost savings and is always preferable to solving an E-VSP with given locations of charging stations. Lastly, we investigate the impact of enabling partial charging procedures within vehicle rotations. The results clearly specify that the incorporation of partial chargings is more realistic and opens up optimization potentials.