A predict-then-optimize framework for Just-In-Time arrival of vessels with probabilistic berth-availability forecasts

Just-In-Time (JIT) arrival is a state-of-the-art operational strategy that aligns inbound vessel arrivals with berth availability to reduce fuel consumption and anchorage waiting without sacrificing service reliability. However, while ship operators could adjust the inbound vessel’s arrival time through en-route speed planning, target-berth availability remains an exogenous and uncertain port-side factor. To address this coordination problem, this study develops a predict-then-optimize framework that probabilistically models berth availability and evaluates the value of probabilistic forecasts for en-route speed planning in a scenario-based JIT planning setting. First, in the forecasting stage, berth availability is proxied by the remaining time to departure (RTD) of the vessel currently scheduled ahead at the target berth. This quantity is predicted probabilistically using conformalized quantile regression with gradient boosting. Then, in the speed-planning stage, the resulting predictive distribution is incorporated into a risk-aware speed-planning model that captures the asymmetric operational consequences of early and late arrivals. Based on 5,418 vessel-reported estimated time of departure (ETD) records for container vessels at the Port of Hong Kong in 2025, the forecasting results demonstrate that the proposed method materially improves predictive accuracy relative to vessel-reported ETD and provides well-calibrated uncertainty estimates for an operational use. Computational experiments further show that speed-planning decisions based on the full predictive distribution achieve lower and more robust cost outcomes than those based solely on vessel-reported ETD or on a single predicted departure time, with these advantages becoming more pronounced when late arrival may cause severe downstream disruptions.