## 3 Results
### Evaluation of Restricted Optimization Times  
In terms of a decision-support system, the response time of the system provides a significant influence on the practical suitability. Although this application allows for response times of several hours, users can modify the response time by allocating a maximum optimization time. As given in the previous results, the optimizer can solve small problem instances for a single vessel to optimality in some minutes. Larger instances involving multiple vessels often take a long time to solve entirely due to the combinatorial nature of the MILP. This subsection compares the results of several simulations for different limits to the maximum optimization time to assess the viability of short optimization times as given in Tables 7-9. The simulations use the months April, June, and August 2000 as starting date, whereby it uses \(T=84\), \(P=2\) as sampling step size and number of planning periods with a varying amount of vessels from 1 to 3. These parameters were chosen based on the results of the previous sections. These simulations are not limited by a maximum plan length to allow for a better comparison in terms of plan quality. Instead, a fixed number of 50 turbines is to be installed, which allows comparing the length of the required plan (Duration) and the average time a vessel spends offshore per turbine (O/T) under the same circumstances. Consequently, the simulations cover more than one month. The starting dates were selected for the same reasons given before: April shows moderate weather conditions, while June comes with comparably bad weather. Finally, the records for August show close to perfect weather conditions. In contrast to the results described earlier, this experiment excludes October as a possible starting date: Weather conditions deteriorate too strongly to finish the  
Figure 8: Cost per finished turbine as average over the scenarios for April until October. installation of 50 turbines in a reasonable time frame. For these simulations, each optimization was just executed once with the given time limit, again using CPLEX's opportunistic search mode. For instances only involving a single vessel (Table 7), the optimizer could solve all plans to optimality in less than five minutes, resulting in the same results for all simulations after this point. Despite the different weather conditions, the optimizer managed to finish the projects with only a difference of 14 h, demonstrating a good usage of bad-weather windows for onshore operations. The offshore time per turbine ranges from 21.3 h to 22.1 h. Therefore, the scenario implies a minimum of 21 h per turbine, showing low offshore waiting times. For the scenarios involving two or three vessels (Tables 8 and 9), the optimizer could only solve single instances with very bad weather conditions to optimality. Consequently, the plans generated within these simulations show variability in the project duration and in the time a vessel spends offshore. Therefore, it cannot be guaranteed that longer, non-optimal runs result in better plans in general, due to the selection of the opportunistic search mode. Additionally, CPLEX applies several heuristics that depend on internal time limits, governed by the overall optimization time. Nevertheless, the results show general trends concerning the solution quality, although, due to the long runtime, only a single experiment with each configuration was conducted. Generally, the results show that the optimizer tries to balance the general project duration with the time a vessel spends offshore, as given by the cost function in Equation (1). The results show a general trend to lower values for both the longer the optimization proceeds. Nevertheless, some results show increases in either the duration or the offshore time, while the other value shows a decrease compared to shorter optimization times.