# Combining Optimization and Simulation for Designing a Robust Short-Sea Feeder Network
## 2 Problem Description
### Network Design Problem  
The shipping company serves each port on a weekly basis. The Norwegian ports are classified according to their size. Small ports are only served by daughter vessels, whereas large ports can be visited by either a mother or a daughter vessel. All mother vessels start their voyage at a European continental main port. Transshipment of cargo between mother and daughter vessels occurs at the so-called ocean hubs, which are suitable locations along the Norwegian coast and offer enough stability for vessels to perform transshipment at sea. For presentation and modeling purposes, each ocean hub is artificially split into a north-going and a south-going ocean hub. A mother vessel serves a north-going ocean hub during its northbound journey and a south-going ocean hub on its southbound journey.  
The feeder routes taken by daughter vessels are referred to as daughter routes. Each daughter route is served by one daughter vessel. These routes have a maximum duration of one week to ensure weekly port visits. The route served by the mother vessel is referred to as main route. Since the duration of the main route is typically more than one week, the number of deployed mother vessels is equal to the number of weeks rounded up to the nearest integer, thus ensuring weekly service.  
The major activity of the shipping company case is to transport cargo between the main continental port and Norwegian ports. There is also some local demand between Norwegian ports, but can be considered as negligible in this study. The aim is to determine the optimal main and daughter routes and the optimal fleet of mother and daughter vessels to be deployed. This problem is at a tactical level, where the established routes last for typically four to 12 months, and, therefore, the weekly demand is assumed to be known and constant.  
Transshipment of cargo between mother and daughter vessels is only possible at ocean hubs. During its northbound journey, mother and daughter vessels meet at a north-going ocean hub where cargo is delivered to the daughter vessel. The same mother and daughter vessels meet again at the corresponding south-going ocean hub during the southbound journey of the mother vessel to transship cargo from the daughter vessel. In the case an ocean hub is the northernmost point of the main route, there is no artificial distinction between north- and south-going ocean hub, and the ocean hub is therefore only visited once.  
A solution to the problem consists of a set of main and daughter routes serving the ports and an allocation of vessels to routes (as illustrated in Figure 1). This also includes determining the number of deployed mother and daughter vessels. The mother vessels are considered to have enough capacity to transport all cargo. The size of the daughter vessels can be selected from a given set of available capacities. The problem is separable in the size of the daughter vessel because all daughter vessels must have the same capacity due to the technical requirements of the SSP design. The objective is to minimize the weekly operating costs, including weekly time charter costs for each vessel in the selected fleet, bunker, port, and cargo handling costs.