Building an effective carsharing system and organizing an excellent carsharing service is an urgent task for both the user and the owner. From the owner’s point of view, such a system can be profitable, given the dynamics of market development in this direction in recent years. Also, the potential profitability of the system is determined by the peculiarities of the region in which it is implemented and the client’s needs from the carsharing service. From the customer’s point of view, such a system is an excellent alternative to personal transport, taxi services, and public transport. The functioning of the carsharing system within a specific region has a positive effect on reducing traffic jams, reducing air pollution, increasing revenues to the regional budget, etc. [5]. This obviously has a positive effect on improving the comfort of the region’s residents.

Building an optimization model of profit maximization for carsharing services must be completed and requires a separate study. The creation of such a model is closely related to the requests of the system’s owner. Therefore, parameters that affect the owner’s profit should be reflected in the model, considering regional characteristics, demand, and customer needs. Also, the maximization model depends on the type of carsharing, which exerts influence and profitability of the system in different regional and geographical conditions. In particular, [6] describes the system of carsharing using electric cars. This study found that such a system still needs to be fixed since electric cars need a long time to charge. This leads to a decrease in the profitability of such a system over time compared to a traditional carsharing system. The paper [7] describes a model of electric carsharing and micro-mobility, as well as the potential impacts of these types of carsharing. However, the problem of maximizing the profitability of such systems needs to be described. The positive impact on the development of city infrastructure and the improvement of the quality of life of city residents is determined by the effective functioning of such a carsharing system, which is beneficial to the system’s owner. Otherwise, there is no point in investing in developing this type of service.

For the effective functioning of the carsharing system, operational decisions must be made constantly. Some of them require solving relevant optimization problems. In particular, Ref. [4] describes a profit maximization model of a carsharing system and a mathematical programming method for finding its solution. In this model, cars do not move without the participation of customers. In [8], a simulation model for evaluating options for such movements was developed. However, the specified model is static and does not consider the change in demand for cars in different parts of the region and times of day. This is important for a rational calculation of the potential profit of the system, taking into account the built-in restrictions. The paper [9] describes a mixed integer programming model for establishing the sequence of actions for moving cars in a carsharing system. In works [10,11], systems for optimizing the movement of vehicles are considered.

Work [12] describes the problem of maximizing the profit of the carsharing system, which considers car maintenance costs. Integer programming was used to solve the problem. The problem of linear programming for maximizing the profits of the carsharing system is described in [13]. An overview of scientific studies on modeling and optimization for the carsharing system is described in [14], where the authors classify the literature into three categories: strategic, tactical, and operational, according to the level of decisions made in optimization tasks. Optimization models and solution methods proposed in existing studies are considered for each category. In particular, in the category of studies on state strategic planning, [15,16,17] are critical publications that aim to maximize profits. Other works discuss the category of making operational decisions on managing the carsharing system to optimize profits [18,19,20]. The problem of profit maximization related to the relocation of cars is described in works [21,22,23]. Related problems must also be solved, such as user verification [24,25,26] and the problem of managing a complex transport system [27].

Study [28] carried out a systematic review of the literature in the field of vehicle sharing, in particular carsharing. A meta-analysis of studies showed that dynamic carsharing services reduce travel costs and demand for parking and improve the ecology of the city. The development of carsharing and micro-sharing services contributes to the urban development of cities. The development of carsharing systems can contribute to sustainability as well as social and transport justice. The authors of study [28] advocate for the consolidation of urban transport policy to achieve the desired results for solving the problems of urban mobility. The study also shows that the field of urban mobility is not sufficiently studied.

Study [29] shows that the carsharing market is not sufficiently developed in the Republic of Kazakhstan. Since the country’s population is growing fast, the implementation of such systems will make the quality of living in large cities and towns of this country more comfortable and convenient.

In [30], it is shown that optimal planning of the location of the infrastructure of charging stations and the distribution of the car fleet and the operation of moving vehicles in a city contribute to increasing profits. The importance of taking into account the uncertain time-varying demand in the input parameters of the profit maximization model is also shown. This significantly increases the efficiency of carsharing systems by 5.3%. Study [30] was conducted on the case of New York City. A similar study is necessary for other large cities with dense transport infrastructure. However, unlike the New York City, data on other cities (for example, Astana) are missing or access is restricted. This complicates research in this direction. There are few studies that take into account the dynamics in the functioning models of carsharing systems. This study is a development in the direction of urban science in terms of filling the gap in the use of dynamic models for maximizing the profit of carsharing systems, in particular in the Central Asian region. This study considers building a profit maximization model for a carsharing service for the capital of the Republic of Kazakhstan, Astana. Regional aspects and needs of customers in this region have determined the need to develop this type of service. Moreover, it is about the development of carsharing services. Micro-services in this region may be less popular due to the significant distances that city residents travel daily, which is related to the vastness of the city and the peculiarity of the location of urban infrastructure facilities.