A Simulation-Driven Hybrid SPN–Machine Learning Framework for Container Freight Rate Forecasting under Uncertainty

Abstract In a market where the business environment is unstable and uncertain, forecasting container freight rates is crucial for effective supply chain planning, cost control, and risk avoidance. This paper proposes a hybrid forecasting model that predicts container freight rates more accurately by clearly considering operational uncertainty. The model integrates machine learning (ML) and stochastic petri nets (SPNs). The simulation covers key logistic operations, such as port congestion, vessel queues, capacity usage, and equipment availability. It uses monthly route-level data from the Ningbo Containerized Freight Index (NCFI). To learn complex Machine Learning models like Prophet, LSTM, Random Forest, and XGBoost, the stochastic operational states are transformed into structures features. These features are combined with historical market data. The model’s performance is measured by RMSE, MAE, MAPE, and í µí±… 2. The results show that the hybrid SPN-ML model outperforms benchmark ML models. It produces fewer predication errors and offers greater explanatory power, especially during periods of market uncertainty. Simulations enhance the learning processes. Sensitivity analysis confirms a clear correction between forecast accuracy and the realism of the simulation layer. The results suggest combining machine learning with stochastic simulation improves predictive robustness, interpretability, and generalizability compared to models based solely on real data. The proposed methodology provides a practical basis for freight rate prediction amid uncertainty in global shipping markets. It offers a useful decision-making tool for carriers and shippers on the Ningbo-Middel East route.