# Optimal Fleet Transition Modeling for Sustainable Inland Waterways Transport
## 2 Materials and Methods  
The optimization model developed in this study aims to determine the minimum number of electric vessels required to replace the existing diesel-based fleet in Orta lake. The model is based on a comprehensive market analysis of available electric vessel models and their technical characteristics, including capacity, range, charging time, and costs. The model operates in discrete timesteps, with each timestep representing a specific duration (e.g., one hour). For each timestep and each route, the model checks if there is any available vessel with enough battery charge to make the entire trip of the considered route. If this is not the case, the model adds a new vessel. Figure 1 shows the basic steps that compose the greedy heuristic algorithm. The algorithm follows a specific procedure to determine the minimum electric fleet requirements. First, the necessary inputs are gathered, including technical details on the lake, routes, timetables, and vessel specifications. With this critical information in hand, the model can then begin its analysis. The evaluation occurs on a timestep basis, incrementing through the entire planning horizon. At each timestep, the model checks the schedule to see if any vessels are due to depart on their routes from the ports. If a departure is scheduled, the model then looks to see if there is an electric vessel available at that port with enough charge to make the full trip. Availability is determined based on the current status of each vessel already in the system and its own state of charge. The state of charge should be enough to cover the scheduled travel. If no satisfactory electric vessel can be found, this signals the need to add another electric boat to the fleet. Once any necessary vessels are added, the model updates the status of all vessels to reflect their new positions and charges. This sequential process is repeated for every timestep as the model iterates through the schedule. By methodically stepping through each timestep, checking vessel availability against scheduled departures, and adding new vessels only when required, the model can determine the minimum fleet size to fully replace the diesel boats. The key output of the model is the minimum number of electric vessels required to entirely replace the current diesel fleet by maintaining unchanged the time schedule of vessels arrivals and departures. This reveals how many electric vessels would be needed if making a full transition to a sustainable vessels fleet. In addition, the model outputs the status, position, and state of charge of each individual vessel through time. This provides further critical information:  
* Status indicates whether each vessel is \"available\", \"traveling\", or \"charging\" at each timestep. This shows how the vessels are assigned to routes over the schedule. * Position tracks where each vessel is located on the lake at each moment. This illustrates how the vessels move across the different routes. * State of charge shows the remaining battery capacity of each vessel through time. This helps identify charging needs and ensures battery levels are sufficient. The full set of outputs gives a detailed picture of how an optimal electric fleet could be configured and scheduled, delivering key insights into the feasibility and logistics of transitioning away from diesel vessels. Figure 1: Diagram of the model. The status and state of charge of each vessel are updated for each timestep and each route. The status of a vessel can be \"available\", \"traveling\", or \"charging\", and the state of charge represents the remaining battery capacity of the vessel. The model evaluates the minimum number of electric vessels necessary to completely cover the routes that are currently covered by diesel vessels. For each vessel, the model calculates the position, state of charge, and other relevant parameters. The objective function of the model is presented in Equation (1).