Measuring the Service Capacity of Public Facilities Based on a Dynamic Voronoi Diagram

The supply–demand relationship of urban public service facilities is the key to measuring a city’s service level and quality, and a balanced supply–demand relationship is an important indicator that reflects the optimal allocation of resources. To address the problem presented by the unbalanced distribution of educational resources, this paper proposes a dynamic Voronoi diagram algorithm with conditional constraints (CCDV). The CCDV method uses the Voronoi diagram to divide the plane so that the distance from any position in each polygon to the point is shorter than the distance from the polygon to the other points. In addition, it can overcome the disadvantage presented by the Voronoi diagram’s inability to use the nonspatial attributes of the point set to precisely constrain the boundary range; the CCDV method can dynamically plan and allocate according to the school’s capacity and the number of students in the coverage area to maintain a balance between supply and demand and achieve the optimal distribution effect. By taking the division of school districts in the Bao’an District, Shenzhen, as an example, the method is used to obtain a school district that matches the capacity of each school, and the relative error between supply and demand fluctuates only from −0.1~0.15. According to the spatial distribution relationship between schools and residential areas in the division results, the schools in the Bao’an District currently have an unbalanced distribution in some areas. A comparison with the existing school district division results shows that the school district division method proposed in this paper has advantages. Through a comprehensive analysis of the accessibility of public facilities and of the balance of supply and demand, it is shown that school districts based on the CCDV method can provide a reference for the optimal layout of schools and school districts.