## 3 Problem Description and Cost Model  
In this section, we present the _Electric Vehicle Scheduling Problem with Location Planning of Charging Stations_ (E-VSP-LP) as the key problem being solved in this paper. In the following, we first introduce the parameters of the problem. Afterwards, we introduce decision variables and the objective function. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & \multirow{2}{*}{
\begin{tabular}{c} **E-VSP** \\ \end{tabular} } & **E-VRP** & **Mixed** & **Electric** & **w/o Line** & **Fixed** & **Fixed** & **Partial** \\  & & **VRP** & **veh.fleet** & **veh.fleet** & **Changes** & **chrg.stat.** & **veh.rot.** & **Charging** \\ \hline [PERSON] and [PERSON] [14] & \(\bullet\) & & \(\bullet\) & & & \(\bullet\) & \(\bullet\) & \\ \hline [PERSON] and [PERSON] [17] & \(\bullet\) & & & \(\bullet\) & & \(\bullet\) & & \\ \hline [PERSON] et al. [28] & & \(\bullet\) & & \(\bullet\) & & & & \\ \hline [PERSON] and [PERSON] [18] & \(\bullet\) & & & \(\bullet\) & & \(\bullet\) & & \\ \hline [PERSON] [19] & \(\bullet\) & & & \(\bullet\) & & \(\bullet\) & & \\ \hline [PERSON] et al. [15] & \(\bullet\) & & \(\bullet\) & & & \(\bullet\) & & \\ \[PERSON] and [PERSON] [20] & \(\bullet\) & & & \(\bullet\) & & \(\bullet\) & & \\ \[PERSON] et al. [21] & \(\bullet\) & & & \(\bullet\) & & \(\bullet\) & & \(\bullet\) \\ \[PERSON] et al. [24] & \(\bullet\) & & \(\bullet\) & \(\bullet\) & & \(\bullet\) & \(\bullet\) \\ \[PERSON] et al. [22] & \(\bullet\) & & \(\bullet\) & & \(\bullet\) & & \(\bullet\) \\ \[PERSON] et al. [25] & \(\bullet\) & & \(\bullet\) & \(\bullet\) & & \(\bullet\) & \(\bullet\) \\ \hline [PERSON] et al. [26] & \(\bullet\) & & \(\bullet\) & & & \(\bullet\) & \(\bullet\) \\ \hline [PERSON] and [PERSON] [29] & & \(\bullet\) & \(\bullet\) & & & & \(\bullet\) \\ \hline [PERSON] et al. [27] & \(\bullet\) & & \(\bullet\) & & & \(\bullet\) & \(\bullet\) \\ \hline [PERSON] et al. [23] & \(\bullet\) & & \(\bullet\) & & \(\bullet\) & & \(\bullet\) \\ \hline [PERSON] et al. [13] & \(\bullet\) & & \(\bullet\) & & & \(\bullet\) & \(\bullet\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of the main characteristics of related literature. We assume a public transportation network given by a set \(S=\{s_{1},\ldots,s_{n}\}\) of \(n\in\mathbb{N}\) stop points also containing the set of vehicle depots \(D\subseteq S\). Service trips are defined by a given timetable as a set \(T=\{t_{1},\ldots,t_{m}\}\) with \(m\in\mathbb{N}\). A service trip \(t\in T\) is characterized by its departure and arrival time as well as its departure and arrival stop. For any pair \((s_{i},s_{j})\in S\times S\) of stop points there is a specific distance and travel time that can be different depending on whether the trip is a service or deadhead trip. In our study, we do not consider opportunity charging of BEBs during the execution of service trips. Consequently, the set \(S\) contains the departure and arrival stop of each service trip \(t\in T\) as well as the set of depots. The aim is to assign the service trips contained in \(T\) to a set of BEBs that are substantially determined by their battery capacities. There may be other specifications such as vehicle dimensions or passenger capacities. Each combination of these features is denoted as a _vehicle type_. To recharge the vehicle batteries, charging stations can be built at each stop point of \(S\). The installed charging system at a charging station considerably influences the time needed for charging. A vehicle can be either fully or partially charged, which also affects the charging time. For the deployment of a BEB fixed costs \(c_{fixed}^{bus}>0\) incure independently of the executed trips. Each charging or trip operated during a vehicle rotation results in operational costs. Therefore, we consider time costs per hour \(c_{time}^{bus}>0\) and for the distances covered of \(c_{distance}^{bus}>0\). The equipment of stop points with charging technology causes fixed costs \(c_{fixed}^{ charging}>0\).