The social amenities allocation problem is a challenge in urban planning, requiring an optimal distribution of their locations to accommodate demand while ensuring accessibility. This paper presents a novel approach to solving this problem using Constraint Programming (CP). The constraint modeling language MiniZinc is used to formulate the problem, and the Gecode and Chuffed solvers are utilized to identify feasible allocations. To improve computational efficiency, a bounding strategy is applied, determining upper and lower limits on the number of required kindergartens, leveraging a 0/1 knapsack model and combinatorial search techniques. In addition, a clustering-based preprocessing step is introduced that enhances the selection of candidate kindergartens.
The proposed approach is evaluated on real-world data from Sofia, Bulgaria, demonstrating its ability to produce optimal allocations for kindergartens while maintaining computational feasibility. It is implemented within the urban planning use case of the Urban Digital Twin pilot project of the city. The results highlight the advantages of CP for solving complex spatial allocation problems, offering a scalable framework for future applications in urban infrastructure planning.