# Data-Driven Modular Vehicle Scheduling in Scenic Areas
## 4 Experimental Results and Analysis
### Sensitivity Analysis of M2 in Different Scenarios  
Since the number of departures is jointly determined by the number of passengers and the vehicle capacity, the vehicle capacity is an essential factor affecting the fleet scheduling strategy. In addition, as the number of visitors to tourist attractions is characterized by high peaks and flat peaks in a day, waiting at different times of the day will, in practice, have different effects on the tourist experience. Therefore, the impact of changes in penalties on the model is also a consideration. To investigate the impact of vehicle capacity and waiting penalty on the overall cost in each model, we define vehicle capacity with three cases: \(c=6\), \(c=12\), and \(c=18\), and consider two types of waiting penalties: variable and fixed. For the variable waiting penalty, the random value at each time step follows a normal distribution with a mean of {1, 2, 3,..,10} and a variance of {3, 4, 5, 6}. These two parameters are combined to create six distinct scenarios, and a sensitivity analysis is conducted across them. All experimental parameters remain unchanged except for vehicle capacity and waiting penalties. First, to clarify the cost differences between M2 and M1, we plotted the cost savings achieved by M2 over M1 at each time step during the T2 decision period. These values are aggregated from 30 simulation runs, with box plots illustrating the distribution of cost savings across simulations for each time step and line plots showing the average cost savings from the 30 simulations at each step. The results are displayed in Figure 7.  
As shown in Figure 7, increasing vehicle capacity consistently enhances the average cost savings of M2 over M1, regardless of penalty changes, while also reducing the volatility of M2's cost savings at each time step as the vehicle load grows. This may be attributed to the fact that, in M1, a vehicle must be dispatched as soon as passengers are present. When vehicle capacity is larger, even a smaller group of passengers necessitates a dispatch, inevitably raising transport costs. In contrast, M2 can assess dispatch decisions based on the current penalties and transport costs, enabling it to achieve superior cost savings by reducing the frequency of dispatches. Regarding penalties, for the same load, the average cost savings of M2 are approximately USD 10 when penalties fluctuate, compared to about USD 5 when penalties remain constant. This indicates that variable penalties have a more favorable optimization effect than fixed penalties. However, the volatility in M2's average cost savings is relatively high with changing penalties, likely due to the increased complexity in balancing penalties with transport costs, which leads to a less stable optimization effect. To examine the overall optimization trend of M2 relative to M1, the cumulative cost savings of M2 over M1 across 30 simulations are calculated at each time step. The results are presented in Figure 8.  
In Figure 8, each time step displays the distribution of cumulative cost differences across 30 simulations for that specific time, represented by box plots, with the orange dashed line marking the average cumulative cost difference at each point. All plots show a consistent increase in the cumulative cost savings of M2 over M1 over time, highlighting that M2's cost advantage over M1 becomes progressively more pronounced as time advances. Regarding vehicle loads, there is minimal difference in the cumulative cost savings with changes in vehicle load when penalties are varied. However, when penalties remain constant, the cumulative cost savings increase at a faster rate as the vehicle load increases. The wider spread of the box plots with raised vehicle loads suggests that, while the relative efficiency of cost savings improves as vehicle capacity increases, the cumulative savings also become more volatile, indicating greater potential for optimization.