Accurate forecasting in the forest industry is crucial to understanding future market dynamics and supporting policy decisions. This study introduces the Quantum Red Fox Optimisation Algorithm (QRN) and evaluates its performance in forest supply chain forecasting against a traditional Deep Recurrent Learning model (DRN). QRN integrates quantum mechanics into the Red Fox optimisation Algorithm, enhancing its search capabilities. Using dataset simulating supply chain aspects in emerging, developed, and global producers, QRN consistently outperforms DRN. The results showed the superiority of QRN, achieving an average classification accuracy of 87.12%, compared to DRN's 84.25%. In multistep forecasting, QRN exhibits higher accuracy across all categories, with an average improvement of 2.15%. Furthermore, QRN yields lower root mean square error (RMSE) values, highlighting its precision and stability.