# Combining Optimization and Simulation for Designing a Robust Short-Sea Feeder Network
## 5 Computational Study
### Determining Global Estimated Optimal Routes
#### 5.3.2 Best Routes with and without Weather Uncertainty  
We first solve the problem deterministically and use its solution as a benchmark when comparing the solutions considering weather uncertainty. For the deterministic case, the solution using daughter vessels with a capacity of 300 TEU has the lowest total weekly cost with an objective function value of 457,800 USD. Two mother vessels and two daughter vessels are deployed in this optimal solution, as shown in Figure 9. In particular, the main route visits two ocean hubs at Tananger and Haugesund, as well as the main port at Tananger. The hub Haugesund is the northernmost port served by the main route and is therefore visited only once. The mother vessel is more expensive in terms of bunker cost and port visits, which causes the model to select a short main route. We then solve the network design problem using our optimization-simulation method, applying each of the performance-improving strategies separately. In all best solutions, two mother vessels and two daughter vessels are deployed. However, the solution without the performance-improving strategy deploys smaller daughter vessels than other solutions. Table 3 summarizes the results for the different performance-improving strategies. The cost of the best solutions is compared to the cost of the best deterministic solution, where 100% representing the cost of the deterministic solution. In this comparison, the penalty costs  
Figure 9: The optimal routes for the Short Sea Pioneer (SSP) deterministic version. The mother route visits two hub ports that are connected to two daughter routes. model are excluded as they are fictional and only used to identify low-performing solutions. However, the increased costs due to speeding up are included. This comparison facilitates evaluating the solution quality since the deterministic solution is obtained under ideal weather conditions and, thus, can be considered as a lower bound. Table 3 also shows important performance characteristics for the different solutions, such as the total number and accumulated time (in hours) of both duration and synchronization violations. It also reports the total amount of planned idle time included in the selected routes and how much time this idle time is used to recover from incurred delays. The last column indicates the daughter vessel size of the solutions. All obtained solutions result in a slight increase in operational costs compared to the deterministic solution, where the Combined strategy gives the lowest operational cost with an increase of only 1.2%. Only one duration violation occurs with a negligible magnitude. The number of synchronization violations and the related magnitude is also significantly lower than for other strategies. The utilization of idle time is also low, implying that the vessels usually keep the estimated arrival times set up in the route generation procedure. As such, the solution obtained when using the combined performance-improving strategy is quite robust without increasing the cost level by much. Note that the solution resulting from not using a performance-improving strategy does not incur any duration violation but is exposed to many synchronization violations. The solution includes a lot of idle time, a large share of which needs to be used for sailing to recover from delays. Figure 10 shows the optimal seasonal routes for the Combined strategy. The solid red line is the main route that continues further south to Maasvlakte port. The blue and pink dashed lines are daughter routes 1 and 2, respectively. The corresponding ocean hubs are marked as squares. As seen in Figure 10, the main route extends further north in the winter than during the summer season. Compared to a daughter vessel, a mother vessel is more expensive in terms of bunker and port costs. By having a mother vessel sailing further north, the daughter vessels can reduce their total sailing distance, resulting in planned idle time.