Spatial Allocation of Veterinary Healthcare Facilities in Beijing Using Random Forest and Priority-Constrained Covering Optimisation

Veterinary hospitals are increasingly important neighborhood services, but citywide evidence on their strategic allocation remains limited. Existing GIS-based suitability studies identify favorable areas, but do not determine which limited set of planning nodes to prioritise when existing supply is clustered and underserved areas require explicit protection. This study develops a transparent allocation framework for Beijing by integrating Random Forest (RF)-based observed clinic-location probability, E2SFCA-derived service-gap indicators, and a priority-constrained covering optimisation model. The RF output is interpreted as a proxy for location attractiveness, rather than a direct estimate of demand for veterinary healthcare. The optimisation then protects predefined priority areas and maximises weighted coverage under alternative facility budget scenarios. Additional analyses include a threshold-derived priority set, class-imbalance metrics, catchment-radius sensitivity, key-area-count sensitivity, systematic candidate/key-score coefficient perturbation, district-grouped spatial validation, raw versus calibrated RF allocation sensitivity, and pet-service endogeneity checks. Under the main 5 km catchment and P = 40 scenario, the model achieved complete priority-area coverage and weighted coverage of 0.656. Coverage increased further at higher budgets, so P = 40 is not regarded as a practical optimum, but rather as a diminishing-return scenario. At P = 20 and P = 40, priority-area coverage increased by 5.0 and 2.5 percentage points relative to MCLP, respectively, while aggregate weighted coverage remained comparable. The framework supports strategic planning priority analysis, not direct commercial site selection.