Algorithm Design for an Online Berth Allocation Problem

In this paper, we investigate an online berth allocation problem, where vessels arrive one by one and their information is revealed upon arrival. Our objective is to design online algorithms to minimize the maximum load of all berths (makespan). We first demonstrate that the widely used Greedy algorithm has a very poor theoretical guarantee; specifically, the competitive ratio of the Greedy algorithm for this problem is lower bounded by Ω(log⁡m/log⁡log⁡m), which increases with the number of berths m. On account of this, we borrow an idea from algorithms for the online strip packing problem and provide a comprehensive theoretical analysis of the Revised Shelf (RS) algorithm as applied to our berth allocation problem. We prove that the competitive ratio of RS for our problem is 5, improving on the original competitive ratio of 6.66 for the online strip packing problem. Through numerical studies, we examine the RS algorithm and Greedy algorithm in an average case. The numerical simulation of competitive ratios reveals distinct advantages for different algorithms depending on job size. For smaller job sizes, the Greedy algorithm emerges as the most efficient, while for medium-sized jobs, the RS algorithm proves to be the most effective.