Stochastic dynamic programming model for liner international scheduling optimization under ECA policies

The implementation of Emission Control Area (ECA) policies has directly impacted international liner shipping activities, manifesting itself in widening fuel price differentials and regional fuel compliance restrictions. To address this complex challenge, we propose a comprehensive framework for optimizing international liner scheduling, encompassing decisions such as liner deployment, bunkering port selection, bunkering method, bunkering quantity, and speed optimization. To handle the uncertainty in multi-stage of dynamic decision-making, we establish a stochastic dynamic programming model and design a customized stochastic Monte Carlo optimization algorithm. Based on simulation experiment with Asia-Europe route, we find that a dynamic bunkering strategy can effectively improve transportation efficiency compared to traditional bunkering methods. Furthermore, fuel price fluctuations have incentivize liner operators to adopt offshore bunkering strategies. Active participation in offshore bunkering not only helps reduce sulfur emissions but also provides practical guidance for shipping companies' transformation under the regular implementation of ECA regulations.