Recent approaches to the berth allocation problem under uncertainty

The Berth Allocation Problem (BAP) arises when a set of incoming vessels has to be berthed along the quay of a maritime terminal for container discharge-loading operations. In a deterministic framework, the consolidated mathematical programming formulation relies upon rectangular packing formulations, where the quay is viewed as a continuous long segment with the second continuous dimension being represented by the length of the time horizon. Some recent papers focus on the problem of managing the uncertainty in vessel arrival times and operation times by resorting to basic ideas from stochastic programming and robust optimization. Uncertainty is usually considered in the general case where no probability distributions can be inferred from real data pertaining to vessel arrivals and operation times. On the other hand, whenever uncertainty can be modeled by probability distributions, the problem could be tackled by resorting to discrete-event simulation. Hence, following a different conception, the BAP could be suitably viewed at both a tactical and operational level, in an integrated way, but by two separate models: a mathematical programming model at the tactical level and a simulation model at the operational level, where complex operations have to be simulated. Alternative ideas for reformulating the BAP by i) considering multiple scenarios or ii) inserting time buffers into linear constraints related to activities duration or iii) using Monte Carlo simulation to represent berth planning events and activities are critically discussed. Numerical results for comparing the effective capability of tolerating disruptions in resource availability and disturbances in activity duration across different week schedules are presented.