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Refueling decisions of liner ships are facing challenges from both fuel price fluctuations and carbon emission constraints. This paper proposes a multistage stochastic programming model to tackle the refueling problem for dual-fuel ships under carbon intensity indicator (CII) rating limit and carbon tax costs. The model also takes into account various factors, including fuel consumption of main and auxiliary engines, fuel availability at ports of call, and fuel price fluctuations. The proposed model is solved using scenario size selection and moment matching methods, and a greedy heuristic algorithm is adopted to speed up the process. Managerial insights are obtained from multinomial logistic regression and sensitivity analyses. Our numerical results reveal that low sulfur fuel oil (LSFO) refueling decisions are closely linked to the difference of LSFO and liquefied natural gas (LNG) fuel prices and that LSFO becomes more attractive when the variance of LSFO fuel price or the LNG availability decreases. Besides, carbon emission costs are found to become a true consideration when carbon taxes exceed a certain threshold. These insights can help practitioners better understand the coupling influence of carbon emissions and fuel price fluctuations on the ship refueling problem.

Ships are traditionally powered by fossil fuels such as heavy fuel oil (HFO) and marine diesel oil (MDO), where the emissions, such as particulates, hydrocarbons (HC), carbon monoxide (CO), nitrogen oxides (NOX) and carbon dioxide (CO2), negatively affect the environment and human health. The International Maritime Organization (IMO) encourages shipping companies to use liquefied natural gas (LNG), which is a green fuel source to power shipping activities and is easy to store, to replace traditional marine fuels. There are three common methods of LNG bunkering: ship-to-ship, truck-to-ship, and port-to-ship. The objective of this study is to determine the optimal bunkering method at a port using an integer linear programming (ILP) model considering three kinds of costs: fixed, variable, and extra. To find the optimal bunkering method, the three methods and their related constraints are modeled into the ILP model. The results indicate that ship-to-ship is the optimal bunkering method for LNG under the scenario of the port considered. Numerical experiments are conducted to validate model performance and generate managerial insights.

Ship air emissions are recognized as one of the key concerns of the maritime industry. Competent authorities have issued various regulations to manage air emissions from ships. Although the authorities are policy makers, the effectiveness of policies is up to the shipping industry who operates the vessels and terminals to fulfill maritime transportation works. Given this characteristic, bi-level optimization model has been widely adopted in studies that optimize policy design or evaluate its effectiveness. The framework of a typical bi-level optimization model for ship emission management problem is given to show the basic structure of similar issues. A series of applications of bi-level optimization model in managing ship emissions is reviewed, including cases of Energy Efficiency Design Index, Emissions Control Area, Market Based Measure, Carbon Intensity Indicator, and Vessel Speed Reduction Incentive Program. We hope this paper can enlighten scholars interested in this area and provide help for them.

The 76th session of the Marine Environment Committee (MEPC 76) of the International Maritime Organization adopted several mandatory measures in June 2021 to reduce carbon emissions from ships. One of the measures is the carbon intensity indicator (CII), which is the carbon emissions per unit transport work for each ship. Several options of CIIs are available and none of them is chosen to be applied yet. We prove that, at least in theory, requiring the attained annual CII of a ship to be less than a reference value, no matter which CII option is applied, may increase its carbon emissions. Therefore, more elaborate models, combined with real data, should be developed to analyze the effectiveness of each CII option and possibly to design a new CII.