Dynamic Demand Prediction in Cross-Docking Operations Using Differential Equation Models

Cross-docking has emerged as an important logistics strategy within Just-in-Time (JIT) inventory systems because it minimizes warehousing activities, reduces inventory holding costs, and improves supply chain responsiveness. However, the success of cross-docking operations largely depends upon accurate demand prediction. Traditional forecasting approaches often fail to capture the dynamic and time-dependent nature of demand fluctuations, leading to inefficiencies in inventory allocation and vehicle scheduling. Therefore, this study develops a differential equation-based demand forecasting model for cross-docking environments. The proposed framework employs ordinary differential equations (ODEs) to represent the rate of change in customer demand over time and integrates demand dynamics with cross-docking decision-making processes. The model enables continuous monitoring of demand variations and facilitates proactive inventory adjustments. A simulation-based analysis demonstrates that the proposed forecasting framework improves forecast accuracy, reduces stockouts, minimizes inventory carrying costs, and enhances order fulfillment performance. Findings indicate that differential equation modeling provides a robust mathematical foundation for real-time demand prediction in JIT cross-docking systems. The study contributes to the growing body of research on mathematical supply chain modeling and offers practical implications for logistics managers seeking data-driven forecasting solutions. Keywords: Cross-Docking, Demand Forecasting, Differential Equations, Just-in-Time Inventory, Supply Chain Optimization, Mathematical Modeling.