Online integrated allocation of berths and quay cranes in container terminals with 1-lookahead

This paper studies an online over-list model of the integrated allocation of berths and quay cranes (QCs) in container terminals with 1-lookahead ability. The objective is to minimize the maximum completion time of container vessels, i.e., the makespan. We focus on two different types of vessels, three berths and a small number of QCs in the hybrid berth layout, with 1-lookahead ability. We propose a $${{(1 + \sqrt{2} )/2}}$$ -competitive algorithm for the case with four cranes, a 5/4-competitive algorithm for the case with five cranes and a 4/3-competitive algorithm for the case with six cranes, respectively. All of the algorithms are proved to be optimal.