# Combining Optimization and Simulation for Designing a Robust Short-Sea Feeder Network
## 5 Computational Study
### Determining Global Estimated Optimal Routes
#### 5.3.1 Performance-Improving Strategies  
We combine the optimization-simulation solution method with different performance-improving strategies to impose additional robustness and exploit operational flexibility. The different strategies are listed in Table 2 and are explained in more detail below.  
We test three different performance-enhancing strategies for enhancing the robustness of the routes and one strategy for recovery from delays. The Slack 10% and the Realistic strategies are implemented as part of the route generation procedure. The Slack 10% strategy is characterized by calculating the sailing time along a leg (based on design speed) and then adding 10% additional sailing to immunize the route against delays. While adding robustness to a route, this strategy may result in considerable amounts of unnecessary idle time in the schedule. The Realistic strategy tries to account for the fact that particular sailing legs are more likely to be subject to delays than others. Sailing speeds along the different legs are first simulated using weather data from 1998 to 2000. To further improve robustness, the resulting average sailing time on each leg is then increased by an additional 5%.  
With the Seasonal strategy, the routes sailed by the vessels are allowed to change for each season. We distinguish here between the summer season and winter season. The seasonal routes are obtained by solving the simulation-optimization framework for each season with a set of routes based on design speed. Note that the same fleet has to be used in all seasons.  
The Speed-up strategy is part of the simulation model. This strategy allows delayed vessels to increase their speed by increasing their power output. Mother and daughter vessels speed-up independently according to their routes, but the conditions for when they do so are slightly different. A mother vessel will try to speed-up once it is more than one hour delayed compared to its generated route. Increased speed will be maintained until the vessel is no longer delayed. Daughter vessels usually have a certain amount of idle time included in their schedules, e.g., waiting for the mother vessel to arrive in an ocean hub. The daughter vessel starts to speed-up as soon as the remaining idle time falls below a given threshold (for the case study, this is set to one hour) and will continue to sail  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(n\)} & **Itr.** & **Rout Gen.** & **Opt.** & **Sim.** & **Total** & **Solutions** \\  & **needed** & **Time** & **Time** & **Time** & **Time** & **Simulated** \\ \hline
1 & 75 & 94 & 2855 & 131 & 3080 & 75 \\
5 & 19 & 94 & 771 & 149 & 1014 & 89 \\
10 & 13 & 94 & 510 & 182 & 786 & 113 \\
20 & 9 & 94 & 390 & 246 & **730** & 157 \\
50 & 7 & 94 & 405 & 473 & 972 & 297 \\
100 & 6 & 9 at increased speed until it has up to two hours idle time available. However, a daughter vessel will never speed-up to get more than its original amount of idle time.  
The Combined strategy applies realistic, speed-up, and seasonal strategies simultaneously. The realistic sailing times used in the combined strategy are calculated separately for each season during the preliminary simulation of sailing time. This implies that more absolute slack will be added in the winter season than in the summer season.