Integrated scheduling for ore terminals under cargo flow uncertainty

This paper addresses the integrated scheduling problem of berth allocation and terminal equipment in ore terminal. In the berth allocation aspect, we consider vessels with varying cargo demands and berth occupancy requirements. In the equipment aspect, we focus on the matching relationship between hoppers and vessels, accounting for the uncertainty in hopper flow rates driven by spraying dust suppression systems. The core objective is to minimize the total costs arising from hopper flow uncertainty, including both loading costs and vessel waiting costs. We adopt a robust formulation and propose a mixed-integer linear programming (MILP) model, followed by a custom solution method rooted in a logic-based Benders decomposition (LBBD) framework. Computational experiments reveal that our method, which requires an average of 50 seconds of CPU time, significantly outperforms Gurobi, which needs 3600 seconds to reach comparable solutions, confirming the computational efficiency of our method. Further experimental analysis includes a cost coefficient sensitivity study, confirming trade-offs between berth allocation and hopper assignment. This analysis further confirms our method’s effectiveness in reducing vessel waiting times and loading costs under uncertainty, while demonstrating that our study provides both theoretical guidance and practical recommendations for improving terminal operations.