# Optimal Fleet Transition Modeling for Sustainable Inland Waterways Transport
## 1 Introduction
This study primarily considered the impact of traffic intensity, as the slope variation in the case study was low. Another study [22] proposed an optimization approach using a mixed-integer linear model for the electrification of a bus route in Singapore, considering factors such as partial charging and battery degradation. [PERSON] et al. (2018) [23], [PERSON] and [PERSON] (2017) [24], and [PERSON] et al. (2021) [25], have considered aspects such as vehicle scheduling for electric and hybrid buses, optimal charging, and the assignment of electric buses to predefined routes. Lastly, [PERSON] et al. [26] explored the feasibility of transitioning an entire regional bus fleet in an Alpine region of Italy to zero-emission buses, specifically battery electric buses (BEBs) and fuel cell electric buses (FCEBs). They developed a model based on the vehicle's energy balance, taking into account factors such as distance, altitude, and climate conditions. In the topic of sustainable transitions for maritime transport routes, while different studies have addressed the network design and vehicle scheduling problem [27; 28; 29], few studies have specifically addressed the optimization of passenger vessel services with a focus on zero-emission vessels. [PERSON] and [PERSON] (2018) [30] examined the design and feasibility of zero-emission hydrogen-fuel-cell-powered ferries through case studies of five different passenger vessel types. A key finding is that larger, lower speed ferry designs are the most cost-effective starting point for deploying currently available hydrogen fuel cell technology, resulting in lower emissions, capital costs, and operating costs per passenger mile compared to higher speed designs. [PERSON] et al. (2021) [31] focused on the potential for replacing high-speed passenger vessels in Norway with zero-emission solutions such as compressed hydrogen or battery electric zero-emission vessels. They highlight the necessity of route optimization studies to properly support decision makers in choosing the best sustainable maritime solutions. [PERSON] et al. (2022) [32] focused on the Zero-Emission Vessel Route Planning Problem for planning routes serviced by battery electric vessels. For this scope, they present a mixed-integer programming optimization model which jointly minimizes operator and passenger costs. This model is used to evaluate technology replacement potential and associated costs for two routes in Norway. The results show that transitioning to zero-emission technology increases operational costs due to battery range and charging time constraints, which may require more vessels and result in reduced frequency and increased passenger discomfort. [PERSON] and [PERSON] (2023) [33] presented a simulation-driven robust optimization approach for the design of zero-emission vessels powered by ammonia. Theirmethodology uses dynamic voyage simulation integrated with a holistic vessel design model to optimize the design for economic and environmental performance. The approach presented in this study differs from the ones mentioned above in that it specifically addresses the transition of a diesel-based fleet to an electric one in a local lake setting. The model takes into account various characteristics of the lake, the boats, and the routes, and it updates the status and state of charge of each vessel for each timestep and each route. This allows the model to evaluate the minimum number of electric vessels necessary to completely cover the routes and their timetables that are currently covered by diesel boats. In order to achieve this, a greedy heuristic algorithm is adopted to solve the optimization problem. The literature applying optimization models specifically to study the transition from diesel-based passenger vessel fleets to electric fleets is very recent and limited. This work provides an original contribution by implementing a greedy heuristic algorithm to determine the minimum number of vessels required and analyzes charging infrastructure needs for a full diesel to electric fleet transition.