The reliable ship fleet planning problem for liner shipping services

This paper investigates a reliable ship fleet planning problem with the uncertainties of container shipping demand, transport costs and freight rates in liner shipping services, and this problem is formulated as a two-stage robust optimization model. In our model, the first-stage decision is to determine the types and quantities of ships, as well as their allocation to different routes, and the second-stage is to fulfill container shipping demand after uncertain information is revealed. Compared to the models proposed in existing researches, our model involves multiple uncertainties aforementioned, and it can also capture the correlation between demand and freight rates. Due to the difficulty of directly solving the two-stage robust optimization model, the column-and-constraint generation algorithm and the benders-dual cutting plane algorithm are developed to address this model. Based on a real shipping network case, extensive computational experiments are conducted to test the practical significance of the presented model and the applicability of our algorithm. The computational results indicate that considering multiple uncertainties simultaneously can significantly save the worst-case costs, demonstrating that the developed two-stage robust optimization model provides a valuable decision-making reference for liner companies seeking to enhance the reliability of ship fleet planning.