School network reorganization under educational and spatial constraints using classical and quantum optimization

As demographic decline and fiscal pressures force governments to consolidate public services, school network reorganization has become a critical policy challenge. The authors address the problem of how to reorganize school networks—specifically by merging autonomous administrative units—while balancing the competing needs for administrative efficiency, equitable access to education, and the preservation of schools as vital community infrastructure in fragile or isolated territories.

The researchers propose a novel Integer Linear Programming (ILP) model that integrates geographical, administrative, and educational criteria. Unlike previous models that often focus on a single objective, this framework incorporates road-network travel times, institutional compatibility, and territorial fragility indicators. To test the model, the authors created a synthetic benchmark generator to evaluate computational performance and applied the framework to a real-world case study of the public school network in the Calabria region of Italy. Additionally, the model was reformulated as a constrained quadratic model to test its compatibility with hybrid quantum optimization environments.

The study demonstrates that the proposed optimization framework can effectively identify optimal aggregation plans that satisfy complex policy requirements while maintaining the structural integrity of the educational system. The results confirm that the model is robust enough to handle real-world data from diverse territorial contexts, such as the varied geography of Calabria. Furthermore, the successful implementation of the model within a hybrid quantum-classical environment serves as a proof-of-concept, showing that emerging quantum technologies can be applied to large-scale public-service planning, even if current hardware limitations necessitate further maturation for widespread operational use.