Redrawing boundaries for balance: A population-based regional division model

Balancing the span of management across administrative divisions is a persistent challenge in urban and regional spatial governance. This study adapts a spatial optimization model originally developed for electoral districting to partition a given region into contiguous and compact divisions while satisfying explicit balance constraints for a chosen target variable, such as population. The model combines an enumeration–recursion search strategy to generate all feasible divisions with a binary programming problem that minimizes deviations from the target balance. Using population as the illustrative variable, we apply the model to redraw prefecture, urban district, and subdistrict boundaries in three respective cases in China—Anhui Province, the urban area of Chengdu, and Shijingshan District, Beijing—and compare the optimization results with the status quo. The results show substantial reductions in population disparity between divisions relative to existing administrative boundaries, indicating a more balanced distribution of population, and therefore a more equal span of management. The model can be extended to various spatial governance tasks, including school districting, police districting, and infrastructure catchment area planning.