Conformal prediction-based sequential scheduling for container terminal operations under uncertainty

Container terminal scheduling requires coordinated berth allocation and quay crane assignment decisions under uncertainty in vessel arrivals and cargo handling times. Deterministic scheduling approaches often produce fragile plans, while stochastic methods can be computationally demanding and rely on distributional assumptions. This paper proposes a Conformal Prediction-Augmented Sequential Scheduling Framework that integrates distribution-free prediction intervals into a sequential mixed-integer optimisation pipeline for uncertainty-aware scheduling. Two Extreme Gradient Boosting models predict arrival delays and handling times, wrapped with split conformal intervals calibrated at 90% coverage. These intervals are propagated through berth allocation and crane assignment models under three operational modes (optimistic, nominal, pessimistic), with a final calibrated makespan estimate. Evaluation on 241 vessel calls at Durban Container Terminal demonstrates 13–31 × speedups relative to a 50-scenario stochastic heuristic, statistically significant scheduling improvements over deterministic baselines, and the result that 98% of scheduling gains are attributable to conformal uncertainty quantification rather than prediction accuracy alone. The framework additionally provides infeasibility diagnostics absent from conventional approaches, and is distribution-free and structurally non-invasive.