## 1 Introduction
### Installation Process for Offshore Wind Farms
It is to mention that after jacking-up close to one position, installation vessels remain stationary until they finished installing all components. In practice, a single position should only be used once for jacking-up to avoid damaging the foundations or even the installation vessel itself, as the jack-up process punctures and loosens the seabed. Figure 1: The conventional installation process for top structures of offshore wind farms (following [16]). Each of the listed offshore operations is restricted by specific weather conditions, given by maximum wind speeds and maximum wave heights. If the current weather conditions do not meet these requirements for the full duration of an operation, it cannot be conducted for safety reasons or has to be aborted to avoid danger to the staff, already installed turbine parts, or the components currently being handled. Aborting an operation, thereby leads to a loss of all current progress. Consequently, weather dynamics can easily result in expensive waiting times for the installation vessel, leading to high, unplanned costs. Moreover, charter contracts often set different prices for vessels being in port and for the vessel to be offshore, which, on average, differ by approximately 30% [9]. As a result of these weather restrictions, installation activities commonly take place in the months April until October to ensure a sufficient amount of good-weather windows. As can be deducted from the process description, efficient scheduling of installation operations is a significant cost factor for this process. The state of the art also supports this conclusion. Most of the presented models deal with the scheduling of installation vessels in one way or another (compare Section 1.2). Weather dynamics are the major influential factor in the scheduling: Only if the weather is good enough, turbines can be installed quickly to avoid expensive waiting times. Nevertheless, to conduct an installation of an offshore wind turbine (OWT), the required components need to be loaded into the jack-up vessel in advance. As given in Table 1, loading a complete set of components takes up around 12 h, whereas the installation itself amounts to 19 h in the best case. The table lists operations used in this article's planning model. Therefore, the column _Base Duration_ refers to the minimum time required to conduct the operation, if the current weather conditions do not exceed the limits given in the columns _Max. Wind_ and _Max. Wave_ for the full base duration. As can be seen, most operations are affected by high wind speeds as they involve the use of a crane. In contrast, most operations omit the influence of the wave height due to the jack-up, which keeps the vessel steady. Moreover, the values given in this table assume that the base port is a controlled environment and that loading bridges are used to omit the influence of wind and waves. The limits and durations in Table 1 closely follow the information provided in [9] and [15] to represent realistic assumptions. Within the literature, other, usually softer bounds, can be found too (compare [5] for a review of the overall planning problem). As a consequence of the weather dependency, an accurate mid- to long-term planning can only rely on weather forecasts. Unfortunately, with an increasing prediction horizon, these forecasts tend to become increasingly uncertain. According to the Deutscher Wetterdienst, current models achieve an accuracy of approximately 75% for a prediction horizon of 168 h (one week) [18]. For horizons of two weeks, an average accuracy of approximately 35% can be assumed, indicating an increasing decline in accuracy with increasing horizons. As a result, an operative decision-support system cannot provide plans for very long prediction horizons. While the state of the art presented in the next section demonstrates that historical weather records can be used to achieve accurate long-term estimations,