The berth allocation problem in bulk terminals under uncertainty

Uncertainty is critical in bulk terminals because it is inherent to many operations. In particular, the berth allocation problem (BAP) is greatly affected by the uncertain arrival times of the vessels. In this paper, we propose the first distributionally robust optimization (DRO) model for the BAP in bulk terminals, where the probability distribution of the arrival times is assumed to be unknown but belongs to an ambiguity set. To solve the model, we use an exact decomposition algorithm (DA) in which the probability distribution information is iteratively included in the master problem through optimal dual cuts. The DA is then enhanced with two improvement strategies to reduce the associated computational time; however, with these strategies, the DA may no longer be exact and is still inefficient for solving large-scale instances. To overcome these issues, we propose a modified exact DA where the dual cuts used in the original DA are replaced by powerful primal cuts that drastically reduce the time required to solve the DRO model, making it possible to handle large-scale instances. The reported computational experiments also show clear benefits of using DRO to tackle uncertainty compared to stochastic programming and robust optimization.