An expanded robust optimisation approach for the berth allocation problem considering uncertain operation time

•This paper considers tactical berth allocation problem with uncertain operation time.•We proposed an expanded robust optimisation model by employing K-means clustering technique.•A column-and-constraint-generation algorithm is proposed.•Computational experiments are conducted to verify the effectiveness of the algorithm and models. Container terminals play a vital role as representative logistic facilities for contemporary trade by handling outbound, inbound, and transshipment containers to and from the sea and hinterland. The increasing number of containers and vessels poses new challenges to port management and resource scheduling, because of scarce land, high labour cost, and limited technical equipment. This study investigates the berth allocation planning problem at a tactical level considering uncertain operation time. Based on the historical data, we formulate a data-driven expanded robust optimisation model to minimise the total cost of deviations between the planned and expected berthing time of the vessel. To solve the model, we firstly use K-means clustering to construct the uncertainty set. Secondly, we present a column-and-constraint generation algorithm to solve the model. Extensive computational experiments are conducted to verify the effectiveness of the proposed model and algorithm. Experiment results show that the proposed model can not only guarantee the out-of-sample performance, which overcomes the vulnerability of the sample average approximation approach but also avoid the over-conservatism of the traditional robust optimisation model.