## 1 Introduction  
There is a significant increase in the number of vehicles on the road due to the growing urban population. According to the World Health Organization (WHO), more than 55% of the world's population lives in urban areas, and this figure is expected to rise to 68% by 2050 [1]. An analysis of recent research reports shows that the number of vehicles on the road has increased by 95.7% compared to March of the previous year [2]. This increase not only causes traffic congestion but also brings many negative effects, such as environmental and economic impacts. Currently, the transport sector is the second most responsible sector for greenhouse gas emissions released in a year, and 74% of greenhouse gas emissions are caused by road transport [3]. The employment opportunities offered by cities are an important reason for the increase in traffic density that accompanies population growth. There are millions of workers in countries who have to commute every working day of the week to their jobs in the city center or far from the city center. As the distance to work increases, the increase in the rate of commuting by private car leads to an increase in traffic density, especially during the commuting hours [4]. At this point, it is assumed that the provision of a staff shuttle service to facilitate the commuting of employees of institutions and companies to work will both provide more comfortable, safer and cheaper transport by relieving employees from the stress of traffic and reduce the tendency to use private cars. In large public institutions, companies and factories, the provision of shuttle services for employees is seen as a serious cost. These costs can include expenses such as vehicle purchase or rental, fuel, insurance, maintenance and repair and driver salaries. The aim of the organizations is to create their own efficient and fast service networks at minimum cost. For this reason, different objectives can be adopted, such as minimizing the distance and the number of vehicles to be used during the service on the route created to minimize costs and the optimal use of capacity [5]. Achieving these objectives is a major problem because it depends on many different parameters. This is where the concept of optimization comes into play and is of great importance to service providers. Optimization studies, carried out according to the defined purpose in systems constrained by different parameters, play a role in solving the complexity of the system and achieving the most appropriate result. To minimize these operational costs and improve efficiency, companies must strategically optimize their shuttle service networks. This requires balancing various constraints, such as fleet composition, scheduling, demand fluctuations and environmental considerations. In this context, optimization techniques play a crucial role in enhancing mobility solutions by streamlining operations, improving service reliability and reducing financial burdens on organizations. Dynamic optimization models can help mitigate inefficiencies by minimizing redundant trips, allocating resources effectively and responding to varying demand patterns. First of all, the management of heterogeneous transport fleets requires the application of complex models and algorithms to ensure optimal service quality and resource allocation. The autonomous intersection management model proposed by [PERSON] et al. [6], although focused on pedestrian and vehicle movement at autonomous intersections, reveals the possibilities of applying spatiotemporal network models to other situations, such as employee transportation services. The advantage of this model lies in its ability to reduce waiting times and optimize traffic flows. But such a solution calls for specialized algorithms, such as the shuttle-by-shuttle planning (SBSP) method, which partitions and iteratively finds suboptimal solutions by means of computer resources.