# Combining Optimization and Simulation for Designing a Robust Short-Sea Feeder Network
## 5 Computational Study
### The Short Sea Pioneer Logistics System  
The selection of ports is based on the ports currently served by the case shipping company NorthSea Container Line (NCL), which operates a line for container transportation between the Norwegian west coast and the European continent port located at Maasvlakte in the Netherlands. The candidate hub locations are selected close to major local ports and inshore to have stable weather conditions for the cargo transshipment. The port locations of this case study are illustrated in Figure 6.  
The weekly number of containers transported to and from the European continent is based on the number of containers imported and exported in ports along the Norwegian west coast during the first quarter 2016 data [40]. The numbers have been corrected according to NCL's market share to approximate realistic transportation demand. We refer to [PERSON] et al. [10] for detailed input data.  
The possible capacities for the daughter vessels are 100, 200, and 300 twenty-foot-equivalent units (TEU). The capacity of the mother vessels is 2500 TEU, which is sufficient to transport the cargo of the whole system. The design speed for all vessels is set to 12 knots.  
The relationship between speed and wave height for the mother and three candidate daughter vessel types considered in this experiment is shown in Figure 7. We can see from Figure 7a that at design power, the sailing speed significantly decreases as waves become higher, especially for the daughter vessels. Figure 7b illustrates the same relationship, but for speed-up power that can be used to recover from delays. The power output for speed-up is set to be 125% of design power.  
The legs between ports required to simulate sailing speed have been discretized according to container vessel AIS data available from the Norwegian Coastal Administration. Historical wave height data from both the Norwegian Meteorological Institute (MET.no) and the European Centre for Medium-Range Weather Forecasts (ECMWF) is used in the simulations. These data sets provide weather data with a time increment of six hours. Figure 8 shows a visualization of the data grid for both data sources. The data from ECMWF has a resolution of 0.75\({}^{\circ}\)\(\times\) 0.75\({}^{\circ}\), which is sufficient for the zone between Europe and Norway but not detailed enough for vessels sailing the Norwegian coastline. The data from Norwegian Meteorological Institute offers a better resolution, i.e., 0.3\({}^{\circ}\)\(\times\) 0.15\({}^{\circ}\) and is used for latitudes higher than 57.5\({}^{\circ}\) N. Please note that no wave height data is available inside fjords or very close to land. If a vessel is within these areas, it is assumed to sail at design speed, i.e., 12 knots.  
In our simulations, we use data of two successive years (2000 and 2001). To make the simulation by weeks easier, we assume that the length of each month is exactly four weeks, resulting in a total of 96 weeks to simulate. The winter season is defined as lasting from October to March, and the summer season lasts from April to September.  
Figure 6: A map showing ports considered in the case study. The possible ocean hubs are represented with yellow squares.  
Figure 7: Impact of significant wave heights on the sailing speed for the fleet of vessels considered in the experimentation.