# Combining Optimization and Simulation for Designing a Robust Short-Sea Feeder Network
## 2 Problem Description
### Impact of Harsh Weather  
A transshipment in an ocean hub requires that both the mother vessel and the daughter vessel have to be present at the same location at the same time. The meeting point is selected in a sheltered location, such that harsh weather will not affect the transshipment operation. However, harsh weather conditions will affect sailing operations as they may force vessels to slow down, causing delays in the vessels' schedules. We refer to the situation of a mother vessel waiting for a daughter vessel in an ocean hub as a synchronization violation. Synchronization violations delay the waiting vessel, potentially delaying later synchronizations and affecting other vessels in the system.  
If a vessel is delayed by too much, it might be unable to complete its route within the maximum allowed duration. This is called a duration violation. Duration violations prevent a weekly port visit frequency because the delay is transferred into the next week. For a logistics system with transshipment at sea to be viable in practice, duration violations must be kept at a minimum.  
Figure 2 illustrates synchronization and duration violations. Consider a logistics system consisting of a mother vessel, M, and two daughter vessels, D1 and D2. Daughter vessel D1 visits the north- and south-going ocean hubs, 1n and 1s, respectively. The mother vessel and Daughter vessel D2 meet at ocean hub 2 for picking-up and delivering cargo because ocean hub 2 is the northernmost point. For simplicity, Norwegian ports and the continental main ports are not shown.  
In the example, the mother vessel is sailing north from the continental main port. In ocean hub 1n, she meets with daughter vessel D1, and after the transshipment, both vessels depart as scheduled. Neither of the vessels is delayed at this point. The mother vessel continues north to ocean hub 2 without any delay. Daughter vessel D2 is not delayed either, and thus both vessels can synchronize as planned in ocean hub 2. In this example, daughter vessel D2 has 10 h of planned idle time before the arrival of the mother vessel. It could, therefore, be up to 10 h delayed and still synchronize with the arriving mother vessel as scheduled.  
After leaving ocean hub 2, the mother vessel starts its southbound journey and sails towards ocean hub 1s to synchronize again with daughter vessel D1. However, harsh weather has caused a delay for daughter vessel D1 after departing from ocean hub 1n. Despite arriving on time in ocean hub 1s, the mother vessel has to wait for daughter vessel D1 and experiences a synchronization violation.  
The schedule for daughter vessel D1 has planned idle time of five hours in ocean hub 1s before the arrival of the mother vessel. As the vessel is delayed by as much as 15 h, the mother vessel has to wait for 10 h. As the mother vessel only has five hours of planned idle time in its schedule, the next departure from the continental main port is five hours of delay. The synchronization violation in ocean hub 1s has caused a duration violation of five hours for the mother vessel.  
Note that daughter vessel D1 does not incur a duration violation, even though it is 10 h delayed when leaving ocean hub 1s. This is because there is enough planned idle time when sailing between ocean hub to 1s and ocean hub 1n to make up for the delay.