## 1 Introduction  
In the last years, awareness of climate change and sustainable operations has increased significantly throughout the entire economy and public life. Electromobility is currently considered a highly relevant technology in order to make public transport systems more sustainable and environmentally friendly. Therefore, traditional buses with combustion engines are being progressively replaced by electric buses. Electrically powered buses facilitate a locally emission-free movement which leads to minimal emission levels of greenhouse gases, dust particles, and nitrogen oxides. Seeking to improve the quality of life, especially in congested urban areas, electric buses enable much more quietly operations [1]. At present, the electric energy required for powering electric buses is either provided by batteries or is generated by fuel cells from hydrogen, methanol, or similar fuel [2]. Due to the lower energy density of modern electric batteries compared to common tank capacities for hydrogen or methanol, battery-powered buses involve the greatest challenges for bus operations. For this reason, we focus on battery electric buses (BEBs) within this work. However, the methodology and results of this work can be transferred to any other type of electric engine. We will consider electric bus and battery electric bus as synonyms. Traditional combustion engine buses can often operate for an entire day without having to refuel. By contrast, modern BEBs have only a fraction of the ranges of combustion engine buses and need to recharge their batteries several times a day [3]. Nowadays, BEBs are charged overnight at vehicle depots after the completion of their daily operations. In addition, the vehicles are charged at charging stations during shorter waiting periods while operating (opportunity charging). Energy transmission occurs either conductively by a wire or inductively. In some cases, the vehicle batteries are also replaced with a fully charged battery (battery swapping). With a view, for example, to the current real-world bus project at the Schiphol Airport in Amsterdam, the Netherlands, the bus company Connexxion operates with up to 100 BEBs at the present time [4]. Electric VDL Citea buses are operated within this project, with batteries capable of storing 215 kWh which results in a range between 80 and 120 km. The batteries are charged inductively with fast charging systems. Most modern electric buses like the _Irizar ie Bus_ are able to store about 350 kWh and may operate up to 17 h in urban bus systems without charging [5]. In recent years, many other public transport companies have launched similar pilot projects testing the operation of BEBs. An overview on current projects is provided by [6]. Most projects initiated aim towards substituting diesel buses with BEBs during the daily services while retaining cost-minimal vehicle rotations. In such cases, charging systems are established at some stops on the bus lines to facilitate the recharging of the vehicle batteries during operation. For a cost-efficient deployment of BEBs, the charging stations must be built within the road network so that deadhead trips are as short as possible or are not necessary at all. Longer deadhead trips increase the operational costs and may lead to higher demands for buses. Therefore, construction costs for charging stations as well as the buses' purchase and operational costs have to be considered at the planning stage. The planning process of public transport companies consists principally of strategic, tactical, and operational planning tasks, which differ with regard to the time periods considered. Figure 1 provides an overview of the planning process. Strategic planning comprises the network design and line planning. The network design determines stop points and necessary infrastructure, particularly including the distribution of charging stations within the road network.