# Combining Optimization and Simulation for Designing a Robust Short-Sea Feeder Network
## 1 Introduction
(2019) study the quay crane scheduling problem in a port terminal and consider the uncertainty from the availability of some delivery vehicles and disruptions in quay crane operations. The authors use simulation-optimization to produce robust quay crane schedules. [PERSON] et al. (2019) develop a simulation-optimization method for multimodal freight transportation systems where the uncertainty is related to demand and travel times. [PERSON] et al. (2019) combine a metaheuristic with a discrete-event simulation to provide robust solutions at the operational level in parcel transshipment terminals. This paper considers the first type of uncertainty, more specifically uncertain sailing times due to harsh weather conditions. However, in contrast to the papers mentioned above, it studies a short-sea liner network instead of a deep-sea network. A common assumption in papers on deep-sea liner network design with uncertain port times is that vessels can make up for delays by increasing their speed between ports (see, e.g., [PERSON] and [PERSON] (2019)). This can be reasonable when legs between ports are long. However, for short-sea networks, the sailing legs are short, and weather conditions may prevent the vessel from reducing or even eliminating a delay. The problem presented in this paper is an extension to the deterministic Short-sea Liner Network Design Problem with Transshipment at Sea (SLNDP-TS) introduced by [PERSON] et al. (2018). It contributes to the research literature on liner shipping network design in three ways. Firstly, we take into account uncertain sailing times due to harsh weather in the network design problem. Secondly, we consider transshipments at sea, which requires that the synchronization of routes to ensure that mother and daughter vessels are at the same location at the same time. Thirdly, we apply an iterative solution approach combining optimization with discrete event simulation to handle both uncertainties in sailing times and synchronization requirements. Our solution method is based on the hybrid optimization-simulation method proposed by [PERSON] et al. (2019) with the difference of using a discrete-event model instead of an optimization model for the simulations. Unlike commonly used probabilistic models, we use wave height from historical weather data to adequately capture the effect of harsh weather conditions on sailing speed. The simulation model links wave height to vessel speed and evaluates the impact on the synchronization operations. The simulation results are returned to the optimization model to select routes that are less likely to generate delays. Additionally, we develop and test different performance-improving strategies to enhance the solutions' robustness to possible delays. The computational study results show that our approach provides more robust solutions than deterministic ones without a significant increase in costs. The remainder of this paper is structured as follows. In Section 2, the problem is described in more detail. Section 3 outlines the solution approach. The optimization and simulation models are presented in more detail in Section 4. Results from the computational study are presented in Section 5. We conclude in Section 6.