# Research on Fleet Size of Demand Response Shuttle Bus Based on Minimum Cost Method
## 1 Introduction
A prominent example of DRC implementation in Japan is the \"Himawari Bus\" service in the Fukutsu region, which operates using an advanced algorithm that adjusts routes based on real-time user demand. [PERSON] et al. (2007) [34] studied the effectiveness of such systems, concluding that they provide a more sustainable alternative to traditional bus services in sparsely populated areas. In Europe, DRC systems have been adopted and tested in various cities to enhance public transport efficiency, particularly in regions facing similar challenges of underutilized services. Countries like the Netherlands and the UK have pioneered the development and implementation of DRC technologies, focusing on both environmental sustainability and social inclusivity. In the Netherlands, the \"OV-bus\" system has been extensively studied. Research by [PERSON] et al. (2018) [35] analyzed the performance of DRC systems in Dutch cities, emphasizing the role of real-time data and demand forecasting in optimizing service routes. The findings indicate that DRCs, when integrated with smart city technologies, can reduce emissions and improve operational efficiency while maintaining or even increasing passenger satisfaction. The UK has seen similar success with DRCs, particularly in areas like Manchester and London. The TFL Go app, which provides on-demand shuttle services, has been the subject of multiple studies, including [PERSON] et al. (2018) [36] who examined the integration of DRCs with traditional bus and rail networks. Their research highlights that DRCs can offer a cost-effective solution for filling gaps in transit coverage while contributing to the decarbonization goals set by the European Union. Both Japan and European countries have demonstrated the potential of demand-responsive connectors to revolutionize transportation systems. In Japan, DRCs have been especially useful in rural and aging-population areas, while European research has focused on integrating these systems into urban transport networks to reduce emissions and congestion. The studies reviewed highlight that, while challenges remain in terms of technological integration and user adoption, the future of DRCs holds promise for creating more sustainable and flexible transport solutions. Further research and pilot programs will be essential in refining the efficiency and scalability of these systems  
Current research gaps include the absence of fleet optimization models balancing passenger and operator interests for DRC services. To address this, our study introduces a cost-minimization framework that optimizes fleet size by harmonizing user experience (e.g., wait times) with operational efficiency (e.g., vehicle utilization). The model construction relies on the dynamic variables of travel demand decisions, such as operating cycle, slack time, waiting time, in-vehicle time and vehicle travel distance, etc., and then uses numerical simulation to further study the relationship between fleet size, demand density, vehicle capacity and the above dynamic variables, and finally simulates the total system cost of DRC buses under different scenarios of different demands through simulation, so as to analyze and obtain the optimal fleet cost under different demands and different vehicle types. The optimal fleet size under different demands and different vehicle types is analyzed [37]. Conventional models often assume single-vehicle operations within partitioned service zones, disregarding interdependencies between zones. This oversimplification fails to account for cross-zone demand patterns or operational constraints, leading to sub-optimal fleet allocation. Therefore, it is necessary to take into account the distribution of passenger flow, vehicle capacity constraints, operating time limitations and other factors between the various service areas, to establish a model of the number of vehicles allocated to the line, and to coordinate and optimize the allocation of vehicles on the line.