Distributionally robust optimization for the berth allocation problem under uncertainty

Berth allocation problems are amongst the most important problems occurring in port terminals, and they are greatly affected by several unpredictable events. As a result, the study of these problems under uncertainty has been a target of more and more researchers. Following this research line, we consider the berth allocation problem under uncertain handling times. A distributionally robust two-stage model is presented to minimize the worst-case of the expected sum of delays with respect to a set of possible probability distributions of the handling times. The solutions of the proposed model are obtained by an exact decomposition algorithm for which several improvements are discussed. An adaptation of the proposed algorithm for the case where the assumption of relatively complete recourse fails is also presented. Extensive computational tests are reported to evaluate the effectiveness of the proposed approach and to compare the solutions obtained with those resulting from the stochastic and robust approaches.