# Research on Fleet Size of Demand Response Shuttle Bus Based on Minimum Cost Method
## 1 Introduction
While existing studies address fare optimization through factors like congestion, subsidies, and passenger demographics, they often overlook vehicle-related parameters, such as fleet size and capacity. A holistic approach integrating passenger needs with operational constraints--including long-term economic and environmental impacts--remains underexplored [25]. Recent studies on fleet sizing span diverse vehicle types. For example, [PERSON] [26] developed a hybrid bus allocation model incorporating constraints like fleet size, passenger flow, express stop frequency, emissions, and electric bus range. Genetic algorithms were employed to assess how electric vehicle adoption impacts total operational costs. [PERSON], based on the travel trajectory and travel demand of some new energy vehicles in Shanghai, used genetic algorithms to solve for the fleet size of small-scale self-driving shared vehicles (SAVs), and finally determined that the optimal scenario occurs when one SAV replaces 2.4 private cars on average [27]. [PERSON] considered vehicle scheduling and dispatcher allocation, and constructed a hybrid fleet size optimization model for shared vehicles with profit maximization of the operator as the objective, CO2 emission and road congestion levels as the constraints, and solved the degree of influence of different factors on the fleet size by using Gurobi in Matlab R2022b [28]. [PERSON] proposed a planning method for the minimum fleet for reservation carpooling, by constructing a topological relationship graph of journeys between carpooling passengers and solving the minimum path in this topological relationship, and then calculating the minimum fleet size [29]. [PERSON] proposed a two-layer model based on IC card swipe data for regional schedule optimization and fleet size constraints based on the station influence degree, and the optimized results showed that the number of buses allocated was reduced while meeting the base passenger demand, and a reasonable trip chain and travel plan were further constructed [30]. [PERSON] proposed a minimum fleet size adjustment method for a demand-aware dynamic carpooling system, and the minimum fleet size is calculated by the Hopcroft-Karp algorithm based on the trip diagram [31]. In addition to the above methods of constructing fleet sizes for different vehicle types, some authors have also proposed fleet models based on the minimization of transit operating costs [32]. [PERSON] conducted field simulations for an automated demand-responsive transportation system and showed that when the travel cost of the total operating cost is minimized and the maximum passenger waiting time requirement is met, the optimal fleet model for shuttle services can be determined [33]. It was also shown that the most effective ways to reduce system costs to passengers are to increase the level of demand, increase the proportion of independently arriving passengers, and use adequate vehicle sizes and shorter vehicle dwell times. Among them, [PERSON] et al. established a model for optimizing and adjusting the operating efficiency parameters of the bus system by analyzing the key parameters of the flexible bus system, and carried out simulation and verification analyses to correct the parameters of the model with regard to the design of the system routes and the scheduling problems established in the previous stage. [PERSON] considered that people make this trip by car, shuttle bus, bike, or walking modes. Cars and shuttle buses, which share the same road network, constitute about 76% of the total trips. As road congestion is expected to grow in the future, it is prudent to look for other modes that can fulfill the travel demand. In Japan, DRCs have primarily been explored in the context of public transportation in both urban and rural settings. The Japanese government has shown significant interest in integrating DRC systems to address challenges posed by an aging population and declining ridership on conventional public transport systems.