# Optimal Fleet Transition Modeling for Sustainable Inland Waterways Transport
## 3 Case Study  
The case study for this research is Orta lake, a lake in the Piemonte region, which is in the north of Italy. The lake spans an area of approximately 18.2 square kilometers, with a maximum depth of 143 m, making it the ideal location for short route inland waterways transport. The current inland waterways operations on the lake are primarily supported by three diesel-powered vessels with capacity for 100 people, which provide essential transportation for both locals and tourists alike. The lake currently operates a fleet of three diesel-powered vessels for inland waterway transport, and the objective of this study is to strategize the transition towards an electric-powered fleet. The first route, as illustrated in Figure 2, commences from Omegana (port 0) in the north of the lake, moving towards the Island of San Giulio before arriving to Orta Piazza (port 1). This route serves as a critical link between different towns and the Island of San Giulio, which hosts a renowned ancient monastery that is a significant attraction for tourists. The second route is a shorter one, running in a circular pattern around the lake, stopping at several small villages and tourist spots along the perimeter. The round-trip journey serves not only as a means of transport but also offers scenic tours around the lake. The vessels operate on a scheduled timetable, with increased frequency during the tourist season. For this reason, this study focuses on the summer touristic season. This decision is rooted in the understanding that the summer months represent a period of significantly heightened inland waterways activity due to an influx of tourists, making it the most critical time of the year in terms of the volume and frequency of connections. By modeling the most demanding scenario in terms of vessel usage, the study seeks to ensure that the proposed sustainable transition not only serves the requirements of the off-peak periods but is also capable of effectively managing the heightened demand during the peak tourist season. Figure 2: Orta lake with the two vessels’ routes. The model operates in discrete timesteps of 5 min. The lake has two main ports, and the distances between these ports are defined as follows (shown in Figure 3):  
* The distance between Port 0 (Omega) and Port 1 (Orta piazza) is 15 km (green line). * The distance for the round trip at Port 1 (Orta piazza) is 7 km (red line). The connections between the ports, along with their departure times, are defined as follows:  
* The connections from Port 0 to Port 1 are at 09:00 and 14:15. * The connections from Port 1 to Port 0 are at 12:35 and 18:00. * The round trip connections at Port 1 (red route) are at various times throughout the day, from 10:00 to 18:45. The electric vessels considered for the transition have the following technical characteristics, taken from the manufacturer website, Fjellstrand [37], and Baird Maritime:  
* Battery capacity: 1524 kWh. * Maximum speed: 42.5 km/h. * Specific energy consumption: 35.78 kWh/km (this number given by the manufacturer already accounts for the resistance of wind and waves). * Passenger capacity: 147. The model uses these inputs to evaluate the minimum number of electric vessels necessary to completely cover the routes and timetables that are currently covered by diesel boats. The results of this evaluation are presented in the next section. The overall modeling approach of representing the fleet transition challenge as a mixed-integer linear optimization model solved using a greedy heuristic algorithm has precedent from other transportation contexts such as electric buses [26]. Specifically, [PERSON] et al. [26] developed a model to evaluate scenarios for transitioning a regional bus fleet to zero-emission options, utilizing a greedy algorithm similar to our approach. Their work provides validation that a greedy heuristic can effectively solve optimization problems related to sustainable fleet transition.