Appointment-Based Lock Scheduling for Inland Vessels Under Arrival Time Uncertainty

Appointment-based lock scheduling can mitigate congestion at inland ship locks, but the inherent uncertainty in vessel arrivals frequently causes severe schedule degradation, disrupting the original lockage plans. To address this challenge, we develop an optimization framework that quantifies arrival-time uncertainty using a deep ensemble to generate generates reliable prediction intervals, and embeds a rescheduling mechanism for missed appointments within a multi-objective model. The model is solved with a hybrid heuristic that combines Differential Evolution, Variable Neighborhood Search, and Non-dominated Sorting Genetic Algorithm II (DE–VNS–NSGA-II). Compared to conventional evolutionary techniques, hybrid Particle Swarm Optimization (PSO) approaches, and recent advanced algorithms (GSAA-RL and ADEA-KC), the proposed algorithm effectively overcomes premature convergence in highly constrained discrete scheduling spaces by leveraging DE for robust global exploration and VNS for deep local refinement. In simulations with 143 vessels, the approach reduced average waiting time by 18.51% (28.63 h to 23.33 h), lowered the schedule adjustment rate by 9.02% (0.331 to 0.301), and decreased lock-utilization loss by 5.06% (0.413 to 0.392) relative to a standard baseline. The results demonstrate more stable schedules and more efficient use of lock capacity under uncertainty, providing a data-driven decision-support tool for lock operators to dynamically mitigate disruptions and reallocate passage quotas at inland navigation hubs.