Simulated Annealing Integrated with Discrete-Event Simulation for Berth Allocation in Bulk Ports Under Demurrage Constraints

Efficient berth allocation remains a critical challenge in bulk port operations due to the stochastic nature of vessel arrivals and the complex interaction among loading resources. This study proposes an integrated optimisation–simulation framework to minimise total demurrage costs under uncertainty. The mathematical model was formulated as a mixed-integer linear program (MILP) to determine the optimal assignment and sequencing of vessels to berths and shiploaders, subject to time-window and capacity constraints. The MILP was solved using a Simulated Annealing (SA) metaheuristic to improve computational efficiency for large-scale instances. Subsequently, the optimised berth plans were evaluated in FlexSim, a discrete-event simulation environment, to assess the operational variability arising from stochastic factors, including vessel arrival times, service durations, and loader availability. System performance was measured through vessel waiting time, berth utilisation rate, and demurrage cost variability across multiple replications. Results indicate that the proposed SA–FlexSim framework reduced average demurrage costs by 28.7% compared to the deterministic MILP and by 21.3% relative to standalone SA, confirming its effectiveness and robustness under uncertain operating conditions. The hybrid methodology provides a practical decision-support tool for terminal operators seeking to enhance scheduling reliability and cost efficiency in bulk port environments.