Hierarchical Evaluation Function: A Multi-Metric Approach for Optimizing Demand Forecasting Models

Accurate demand forecasting is crucial for effective inventory management in dynamic and competitive environments, where decisions are influenced by uncertainty, financial constraints, and logistical limitations. Traditional evaluation metrics such as Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) provide complementary perspectives but may lead to biased assessments when applied individually. To address this limitation, we propose the Hierarchical Evaluation Function (HEF), a composite function that integrates R2, MAE, and RMSE within a hierarchical and adaptive framework. The function incorporates dynamic weights, tolerance thresholds derived from the statistical properties of the series, and progressive penalty mechanisms to ensure robustness against extreme errors and invalid predictions. HEF was implemented to optimize multiple forecasting models using Grid Search, Particle Swarm Optimization (PSO), and Optuna, and tested on benchmark datasets including Walmart, M3, M4, and M5. Experimental results, validated through statistical tests, demonstrate that HEF consistently outperforms MAE as an evaluation function in global metrics such as R2, Global Relative Accuracy (GRA), RMSE, and RMSSE, thereby providing greater explanatory power, adaptability, and stability. While MAE retains advantages in simplicity and efficiency, HEF proves more effective for long-term planning and complex contexts. Overall, HEF constitutes a robust and adaptive alternative for model selection and hyperparameter optimization in highly variable demand forecasting environments.