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

Clinical laboratories require accurate forecasting and efficient inventory manage- ment to balance service quality and cost under uncertain demand. In this study, we propose a hybrid forecasting-optimisation framework tailored to hospital clinical determinations with highly irregular, zero-inflated, and asymmetric consumption patterns. Demand series for 34 items were modelled using SARIMAX structures combined with Skew-Normal (SN) and Zero-Inflated Skew-Normal (ZISN) residuals, with residual centering, truncation, and lambda regularisation 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 behaviour. Forecast outputs were integrated into a Particle Swarm Optimisation (PSO) layer to determine cost-minimising 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.