## 1 Introduction
### Installation Process for Offshore Wind Farms  
According to [PERSON] and [PERSON] [12] and [PERSON] et al. [13], the installation process comprises three main stages: First, the construction of foundations and the connection to the energy grid. Second, the installation of top structures. Third, the ramp-up and commissioning. Commonly, different companies take responsibility for the first stage and the remaining two stages of the process. Generally, these tasks proceed sequentially: First, one company installs the foundations and cables, and afterward, often in the following year, another company installs and commissions the wind turbines. While the components and resources in the first and second stages differ, the overall process remains the same. In the literature, authors have proposed two different types of installation concepts: The conventional concept, as depicted in Figure 1, and feeder-based concepts. These concepts mainly differ in how installation vessels are applied. For the conventional concept, these vessels travel between the base port and the installation site, while feeder-based concepts try to avoid these tours by applying specific feeder vessels. For more information in feeder-based concepts, refer to [14] or [15]. The conventional concept assumes that the base-port buffers the components before installation. So-called heavy-lift vessels perform the transport from production sites to the base port as these vessels usually come at comparably low charter rates. During the construction process, more expensive installation vessels pick up these components from the port, travel to the installation site, and perform construction there. The same process applies to the construction of founding structures. Similarly, the components are transported by heavy-lift vessels to the base port. In contrast to the installation of top structures, the installation of founding structures involves two different types of vessels, i.e., specially equipped installation vessels, and so-called cable vessels. In general, the installation requires several types of vessels. While so-called heavy-lift vessels do not provide any special equipment, they usually have large transportation capacities. Generally, these vessels have comparably low charter rates of about \(\copyright\)10,000 to \(\copyright\)20,000 a day [17]. Specially equipped installation and cable vessels conduct the construction of founding structures. These installation vessels, so-called jack-up vessels, can be equipped with different tools. As an example, hydro hammers are a standard tool for the installation of founding structures. Cable vessels are used to mount and lay cables between the turbines and the offshore network hubs to establish a connection to the power grid. During the installation, jack-up vessels are usually equipped with a crane to perform installation operations. Moreover, these vessels use retractable pillars, to mount themselves above the sea level. Therefore, the pillars are lowered into the seabed until the vessel rises out of the ocean. This jack-up operation is generally used to steady the vessels, enabling the vessel to conduct installation operations even under comparably rough sea conditions. These jack-up vessels come at high charter rates of between \(\copyright\)70,000 and \(\copyright\)145,000 a day [17]. As the planning problem for foundations and top structures is more or less identical, this article uses the actual turbines as an example. Their installation is performed sequentially, generally in a single session [9]. Therefore, the installation vessel first positions itself next to the foundation and performs its jack-up operation. Afterward, the components are assembled from bottom to top, in the order of tower, nacelle, blades, and finally, the connecting hub. After completing the installation, the vessel jacks-down again. Afterward, it moves to the next foundation or back to the base port.