# Research on Fleet Size of Demand Response Shuttle Bus Based on Minimum Cost Method
## 5 Conclusions  
In this paper, based on the operating characteristics of DRC, the parameter models of passenger waiting time, vehicle operating cycle and passenger in-vehicle time are theoretically derived, and the fleet size optimization model is constructed with the objective of minimizing time cost and operating cost. The influence of travel demand and vehicle type on fleet size and total cost is analyzed through simulation, and on this basis, the influence law of fleet size, vehicle capacity type and demand density on passenger average waiting time, average in-vehicle time and vehicle travel distance is analyzed. The results show that passenger average waiting time, average in-vehicle time, and vehicle travel distance all increase with the increase in demand density, and decrease with the increase in fleet size. When using single-vehicle or double-vehicle operation, the average waiting time, average in-vehicle time, and vehicle travel distance all decrease significantly with the increase in fleet size; when the fleet size is larger than two/vehicles, the average waiting time, average in-vehicle time, and vehicle travel distance gradually tends to level off. The decline gradually levelled off. The primary contributions of this study are as follows:  
1. The study introduces a hybrid optimization approach that integrates both user costs and operational costs, offering an enhancement over traditional fleet allocation strategies, which typically consider only a single perspective. 2. The study reveals a linear relationship between the optimal fleet size and demand density, while also examining the effect of vehicle capacity variations on this relationship. These findings possess notable generality and practical applicability. 3. The developed model is highly adaptable to various operational scenarios and serves as an effective decision support tool for Demand-Responsive Transit (DRT) systems. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mode Type** & **Key Features** & **Advantages** & **Limitations** & **Suitable Scenarios** \\ \hline \multirow{3}{*}{order-bus} & Passengers reserve & \multirow{3}{*}{Reduces idle} & \multirow{3}{*}{Poor responsiveness} & Medium- to low-density areas with regular commuting demand \\  & departure time and stop in advance & & & \\ \cline{1-1} \cline{3-5}  & Passengers request & \multirow{3}{*}{High flexibility} & High dispatching cost & Medical trips, elderly communities, small zones \\ \cline{1-1} \cline{3-5}  & door-to-door service & & & \\ \cline{1-1} \cline{3-5}  & via phone or app & & & \\ \hline \multirow{3}{*}{microtransit} & Small vehicles with flexible routing; complements transit & Urban supplement to conventional transit & Limited capacity & Urban sub-centers and transit hub catchment areas \\ \cline{1-1} \cline{3-5}  & & & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of different DRC. It provides quantitative insights that can assist public transportation operators and urban transportation planners in formulating effective scheduling strategies. Future research could incorporate real-world traffic networks and dynamic demand data to extend the model's structure. This would involve considering the integration of multiple vehicle types and the implementation of spatiotemporal scheduling mechanisms. Additionally, exploring data-driven optimization methods could enhance the model's feasibility and intelligence in practical systems. In summary, the research in this paper provides a useful exploration of the scheduling and planning of demand response bus services in terms of theory and methodology, and lays the foundation for the realization of an efficient, low-cost, and high-service-level public transportation system. Conceptualization, Y.Z. ; methodology, X.S. ; software, X.S. ; validation, X.S. ; formal analysis, Y.Z. ; investigation, Y.Z. ; resources, X.S. ; data curation, X.S. ; writing--original draft preparation, X.S.