Ship refueling optimization for dual-fuel ships considering carbon intensity indicator rating limit and uncertain fuel prices

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.