📝 SummarXiv

Abstract

Inventory management in dynamic and competitive business environments presents multidimensional challenges, particularly in the face of demand uncertainty and logistical and financial constraints. In this context, accurate demand forecasting is critical for optimizing resources and anticipating market fluctuations. However, the isolated use of traditional metrics such as Mean Absolute Error (MAE) or Root Mean Squared Error (RMSE) can lead to biased evaluations and limit model robustness. To address this limitation, we propose the Hierarchical Evaluation Function (HEF), a composite function that integrates R2, MAE, and RMSE under a hierarchical and dynamic framework, complemented by adaptive penalties. The study implements HEF in the optimization of multiple prediction models, applying Grid Search, Particle Swarm Optimization (PSO), and Optuna, and evaluating their performance on reference databases (Walmart, M3, M4, and M5). The results, validated using statistical tests, confirm that HEF consistently outperforms the MAE used as the evaluation function in global metrics such as R2, Global Relative Precision, RMSE, and RMSSE, improving explanatory power and stability against extreme errors. In contrast, the MAE retains advantages in simplicity and computational efficiency. In summary, HEF constitutes a robust and adaptive alternative for highly variable environments, providing a solid framework for model selection and hyperparameter optimization.