Mathematical model of on-demand route formation for public transport based on individual passenger requests in low-density population area

Background. The organization of public transport routes based on individual passenger requests (on-demand routes) using small-class buses in areas with low population density has become a pressing issue due to the necessity of improving the efficiency of transport systems under limited financial and material resources. Traditional regular route schemes often prove unprofitable and insufficiently convenient for residents of such territories, leading to decreased transport accessibility and deterioration of population living standards. Modern technologies and mathematical modeling enable the development of flexible and cost-effective solutions capable of adapting to the characteristics of low-density regions and minimizing costs associated with organizing transport services.

The need for optimizing transport flows acquires particular significance in light of global sustainable development and environmental trends. Developing models that reduce operational expenses and decrease the carbon footprint of transport operations corresponds to modern requirements for rational natural resource utilization and energy efficiency.

Creating effective mechanisms for managing on-demand routes holds high social significance, contributing to ensuring equal opportunities for all segments of the population regardless of their geographical location and financial status.

Purpose. To develop a mathematical model for organizing on-demand routes for passenger transportation using small-class buses in populated areas with low population density, ensuring maximum efficiency and economic viability of transport services.

Materials and methods. This study employed a comprehensive approach to developing a mathematical model for organizing on-demand routes. The research was based on analyzing real conditions of bus service operation in regions with low population density. The model considered the following parameters: number of populated areas and their geographic location, passenger flow volume, technical specifications of small-class buses, time constraints, and financial performance indicators of transport enterprises. Route optimization was performed using dynamic programming algorithms that accounted for variable demand structure and resource limitations. Practical testing of the model was conducted using data from a specific region with low population density, enabling the collection of reliable results and drawing conclusions about the effectiveness of the proposed approach to organizing transport services.

Results. A comprehensive analysis of existing approaches to organizing on-demand routes was conducted, and key factors determining their effectiveness were identified. A mathematical model was developed that accounts for the specifics of populated areas with low population density, including uneven distribution of demand, large distances between populated areas, and limited financial resources. Various route optimization algorithms were investigated, and the most suitable method was selected for solving the stated problem. Numerical simulation of the proposed model was performed using a specific regional example, and its effectiveness was evaluated compared to existing transportation schemes. Recommendations were developed for implementing the proposed model in the practical activities of transport organizations operating in conditions of low population density.