Two-Stage Robust Programming Modeling for Continuous Berth Allocation with Uncertain Vessel Arrival Time

Abstract

In order to mitigate the environmental pollution caused by sea freight, we focused on optimizing carbon emissions in container terminal operations. This paper establishes a mixed integer programming (MIP) model for a continuous berth allocation problem (CBAP) considering the tide time window. We aimed to minimize the total carbon emissions caused by the waiting time, consumption time and deviation to berth preference. In order to overcome the influence of an uncertain arrival time, the proposed MIP model was extended to mixed integer robust programming (MIRP) models, which applied a two-stage robust optimization (TSRO) approach to the optimal solution. We introduced an uncertainty set and scenarios to describe the uncertain arrival time. Due to the complexity of the resulting models, we proposed three particle swarm optimization (PSO) algorithms and made two novelties. The numerical experiment revealed that the robust models yielded a smaller variation in the objective function values, and the improved algorithms demonstrated a shorter solution time in solving the optimization problem. The results show the robustness of the constructed models and the efficiency of the proposed algorithms.