• This paper investigates a shipping service design problem for wind-assisted ships. • The problem is formulated as a two-stage stochastic mixed integer programming model. • A Benders decomposition algorithm is designed to solve the stochastic model. • Comparative analysis indicates the superiority of wind-assisted ships. Wind-assisted propulsion systems (WAPS) have emerged as a promising technology in the shipping industry. The utilization of wind energy can provide auxiliary thrust and hence reduce the fuel consumption as well as carbon emissions of wind-assisted ships. However, the rigid structure of a traditional shipping service is often suboptimal for harnessing wind energy effectively. This paper explores a shipping service design problem for wind-assisted ships, which is formulated as a two-stage stochastic mixed-integer programming model. The first-stage decisions determine the optimal port visit sequence of all ports, while the second-stage decisions adapt the ship’s schedule under a set of wind scenarios to minimize expected total voyage costs, including fuel, operational, and delay-related expenses. A Benders decomposition algorithm is utilized to solve the stochastic model. The model is applied to a realistic trans -Pacific case study. The results of a comparative analysis against a conventional shipping case indicate the superiority of wind-assisted ships in reducing both costs and carbon emissions. Furthermore, a comprehensive sensitivity analysis reveals that the economic advantage of the integration of WAPS technology and stochastic optimization is robust, providing shipping companies with a practical and profitable strategy towards sustainable operations.
Zhang et al. (Tue,) studied this question.