# Combining Optimization and Simulation for Designing a Robust Short-Sea Feeder Network
## 1 Introduction  
Maritime transportation is one of the most efficient (per cargo ton-mile) transportation modes to transport large volumes of cargo over long distances [1, 2]. Over short distances, however, competing with road-based transportation is more challenging. Truck-based door-to-door deliveries are often less expensive compared to other shipping solutions and offer frequent and reliable departures [3, 4]. The demand for cargo transportation in Norway is expected to grow by 40% (in tonne-kilometers) until 2030 [5]. This predicted increase i is met by the political ambition to shift more goods from road to sea [6]. Still, new and innovative solutions need to be developed to substantially improve the competitiveness of short-sea shipping and support the transition of cargo from road-based to waterborne transportation. The Short Sea Pioneer (SSP) logistics system is a new suggested solution to improve competitiveness, proposing a new transshipment mode for short-sea feeder networks [7]. The proposed system is inspired by the ship-to-ship cargo transfer method currentlyused to transfer petroleum products and bulk cargo between seagoing vessels. In the SSP system, a mother (large) vessel can be connected to a daughter (small feeder) vessel at a suitable location at sea to transship containerized cargo using a specialized handling cargo system (see [8] for an illustration). One advantage of this system is to reduce the number of port calls, which reduces the operational cost of the shipping system. Indeed, cargo-related port costs can account for up to 30% of the turnover of a smaller short-sea shipping company [9]. Besides, it becomes possible to serve small ports that large vessels cannot visit, for example, due to physical limitations. The SSP logistics system is composed of one main route sailed by mother vessels that transport cargo between the European continent and large ports located at the Norwegian west coast. Small daughter vessels operate feeder routes serving smaller Norwegian ports. Due to size or location, these ports may only be served by the smaller daughter vessels. Potential candidate transshipment locations will be in sheltered locations (e.g., inside a fjord or inshorc) such that harsh weather does not affect the transshipment operation. An example is illustrated in Figure 1.  
While potentially having considerable economic benefits, transshipment at sea also raises many technical challenges. Among others, the system requires synchronizing the main route sailed by the mother vessel with all routes sailed by the daughter vessels. Conversely, Weather conditions are known  
Figure 1: An example of the short sea pioneer (SSP) logistics system [10] composed of one main route and three daughter routes. The main route serves the continental port, Maasvlakte, a large Norwegian port in Bergen, and three ocean hubs. All daughter routes depart from ocean hubs and serve local Norwegian ports. to impact sailing times and can cause considerable delays [2]. Thus, the synchronization operation can be subject to disruptions that may cause additional waiting times at the transshipment location and can propagate through the system for the subsequent periods. To function correctly, the routes for both mother and daughter vessels need to be robust to potential delays, i.e., they have to account for uncertainty in weather conditions. Traditionally, the literature on liner shipping network design problems has been focusing on deterministic deep-sea (long-haul) shipping networks. These problems usually determine the optimal set of routes to be served by a heterogeneous fleet of vessels while satisfying demand, transshipment, and frequency requirements (see, e.g., [PERSON] et al. [11] ). The following publications are recent examples, discussing different variants of the traditional liner network design problem. [PERSON] and [PERSON] [12] include the repositioning of empty containers in the shipping operations when determining the optimal network design.