Hybrid Statistical–Metaheuristic Inventory Modeling: Integrating SARIMAX with Skew-Normal and Zero-Inflated Errors in Clinical Laboratory Demand Forecasting

<jats:p>Clinical laboratories require accurate forecasting and efficient inventory management to balance service quality and cost under uncertain demand. In this study, we propose a hybrid forecasting–optimization framework tailored to hospital clinical determinations with highly irregular, zero-inflated, and asymmetric consumption patterns. Demand series for 34 items were modeled using Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors (SARIMAX) structures combined with skew-normal (SN) and zero-inflated skew-normal (ZISN) residuals, with residual centering, truncation, and lambda regularization applied to ensure stable estimation. Model performance was benchmarked against Gaussian SARIMA and non-linear MLP forecasts. The SN/ZISN models achieved improved forecasting accuracy while preserving interpretability and explainability of residual behavior. Forecast outputs were integrated into a Particle Swarm Optimization (PSO) layer to determine cost-minimizing order quantities subject to packaging and budget constraints. The proposed end-to-end framework demonstrated a potential 89% reduction in inventory costs relative to the hospital’s historical policy while maintaining service levels above 85% for high-volume determinations. This hybrid approach provides a transparent, domain-adapted decision support system for supply chain governance in healthcare settings. Beyond the specific case of Chilean hospitals, the framework is adaptable to broader healthcare supply chains, supporting generalizable applications in diverse institutional contexts.</jats:p>