# Combining Optimization and Simulation for Designing a Robust Short-Sea Feeder Network
## 1 Introduction
[PERSON] and [PERSON] [13] consider more advanced route structures, such as butterfly routes, because they allow for better use of vessel resources. [PERSON] et al. [11] study one of the largest networks operated by a major liner-shipping company, where cargo can be transshipped several times to take more than one route to be delivered. [PERSON] et al. [14] extend this problem to include transit time restrictions. [PERSON] and [PERSON] [15] incorporate limitations on number of transshipments for the cargo. For the short-sea shipping, [PERSON] et al. [16] study the impact of different network designs for a local liner shipping company. [PERSON] et al. [17] address the problem of a roll-on roll-off liner service that operates using a hub-and-spoke network design. [PERSON] et al. [18] provide an economic analysis of introducing autonomous vessels in short-sea shipping. For a more detailed overview of the literature on liner shipping network design, please also see the surveys by [PERSON] et al. [19], [PERSON] et al. [1] and [PERSON] et al. [20]. Synchronization has received relatively little attention in the literature on maritime transportation. Cargo is usually transshipped in ports, often requiring a sequence of arrivals or specifying a time window. The work of [PERSON] and [PERSON] [21] is one of the fewest papers to address synchronization directly. The problem considers a combined vessel scheduling and cargo routing problem, where transshipment of cargo is only possible when two routes meet at the same port on the same day. In another work, [PERSON] et al. [22] study a problem from project shipping where different cargoes may require a synchronized delivery. In land-based transportation, synchronization issues are more common. The reader is referred to [PERSON] [23] for an overview of the literature on VRPs with multiple synchronization constraints. The research on uncertainty in maritime service networks mainly distinguishes between two types of uncertainty. The first type is uncertainty in service times, usually port times or sailing times, whereas the second type considers uncertainty in demand. When considering uncertainty in operations, the research focuses on keeping a designed schedule, i.e., satisfy frequency requirements or pickup and delivery time windows. As an example of this work line, the problem examined by [PERSON] and [PERSON] [24] of designing liner vessel routes with uncertainty in port operation times. The uncertainty is related to sailing times as a consequence of making up for the delays. In [PERSON] et al. [25], a multi-objective liner shipping service problem with uncertain port times is studied. One of the objectives is to minimize schedule unreliability, which is the probability of the vessels arriving after the scheduled time windows. Conversely, [PERSON] et al. [26] study how vessels can recover from delays caused by regular uncertainties and unexpected disruptions. In their work, regular uncertainties may happen both at sea and in port, and their characteristics can be estimated using historical data. When it comes to demand uncertainty, the research usually focuses on designing a maritime transportation system such that demand can be served. For example, [PERSON] and [PERSON] [27] study the problem of fleet deployment under incomplete demand information. [PERSON] et al. [28] present a model for designing a ferry network given uncertain demand. [PERSON] and [PERSON] [29] study the design of more general transit networks under uncertain demand. However, none of these studies consider uncertainty in service times. One approach to deal with the uncertainty is to combine simulation and optimization models to provide robust solutions. [PERSON] et al. (2018) use simulation and optimization to evaluate the robustness of tactical fleet deployment plans for roll-on roll-off liner shipping with respect to random disruptions at the operational level. [PERSON] et al.