## 3 Results
### Evaluation of the Influence of the Number of Planning Periods on the Incremental Approach  
This evaluation focuses on several combinations of the parameters \(P\) and \(T\) using the presented MPC-based approach to determine good settings for the sampling step size and the number of planning periods. Therefore, it simulates a single vessel with a project starting date for each month between April and October 2000 to cover several different compositions of weather conditions. This evaluation uses the number of wind turbines finished within a four weeks horizon, and the number of plans, required to cover these four weeks, to compare the results. The experiments use a time frame of four weeks to cover enough time but to prevent overlaps between the months. Therefore, the number of finished turbines indicates an efficient plan, while a low number of plans indicates that few plan failures occur, which always causes recourse actions. Table 6 summarizes the results of these experiments. These experiments again follow a factorial design: \(T\) is either chosen as 84 h (half-a week) or 168 h (one week), and \(P\) is selected as either 1, 2, or 3 times the sampling step size. The latter follows previous results, which demonstrate that longer prediction horizons do not increase the solution quality [9]. The values for \(P\) have been chosen for an easier interpretation and result in prediction horizons of one, two, and three weeks for the case of \(T=168\) h. The same values apply for the case of \(T=84\) h to retain comparability, resulting in prediction horizons of half-a week, one week, and one-and-a-half week. It must be noted that \(P\) does not necessarily need to be an integer as long as it is guaranteed that \(T\) and \(N\) are integers. The approach uses the latter for indexing and thus requires integer values. As can be seen from the results, a prediction horizon of 84 h (\(T=84\), \(P=1\)) results in comparably inefficient plans. Thus, this experiment does not consider smaller sampling step sizes. In contrast, the calculation time for each iteration increases drastically with an increasing prediction horizon. The optimizer is not capable of obtaining optimal solutions for a prediction horizon of three weeks (\(T=168\), \(P=3\)), and all simulations finish due to stagnation. While this does not necessarily mean that the solution is sub-optimal, the optimizer could not prove its optimality in time. For this reason, this experiment excludes longer sampling step sizes as well. As can be seen from Table 6, selecting \(P=1\) resulted in the worst plans for each sampling step size, generally resulting in more plans needed. Therefore, for four weeks, a minimum of eight (\(T=84\)) or four (\(T=168\)) plans would be the minimum for the respective sampling step size. Additionally, selecting a single planning period resulted in less built OWTs for both settings. This decrease shows that the application of an MPC scheme is advantageous for such planning problems, as the longer prediction horizons in the open loop result in better solutions than just relying on a simple rolling horizon planning. Comparing the remaining combinations for \(T=84\) and \(T=168\) shows a higher number of finished OWTs for the shorter sampling step size. Moreover, shorter sampling step sizes required fewer additional plans. The influence of forecast uncertainties can explain this decrease. For shorter plans, these uncertainties are less likely to cause plan failures or wrong estimations. Finally, comparing the results for \(P=2\) and \(P=3\) for the shorter sampling step size, it can be observed that \(P=2\) results in one less finished turbine, while also requiring one less plan if