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An exact algorithm for fleet co-deployment and slot co-chartering in a sustainable shipping alliance under emissions trading system
European Journal of Operational Research ( IF 6.0 ) Pub Date : 2025-05-20 , DOI: 10.1016/j.ejor.2025.05.021
Yadong Wang, Shenghui Zhu, Çağatay Iris

Shipping alliances have emerged as a cooperation platform between independent shipping companies, aiming to enhance customer satisfaction and exploit the economies of scale through capacity and information sharing. A sustainable shipping alliance should operate in a profitable, fair and environmentally friendly way under emerging Emissions Trading System (ETS). A non-convex mixed-integer nonlinear programming model is suggested to jointly optimize the fleet co-deployment in the network, sailing speed in each shipping leg, schedule design for each shipping service, and the slot allocation and co-chartering for each alliance member. These decisions ultimately determine each company’s carbon emissions. Under the ETS, companies are charged for emissions that exceed their allowances, while any surplus allowances can be traded for revenue in carbon markets. In addition to maximizing the alliance’s total profit, this study minimizes profit margin variation among members in proportion to their investment, promoting fairness in a novel way. A tailored spatial branch-and-bound (SB&B) algorithm is developed to deliver the global optimal solution for the problem. Novel problem relaxation and branching strategies are suggested based on the structure of the programming model. The SB&B algorithm significantly outperforms an existing non-convex nonlinear solver. Compared to case which do not consider slot co-chartering and fairness, our study improves total profit by 3.13 %, meets 0.52 % more freight demand, and ensures a fairer profit distribution on average. Under the ETS, carbon emissions can be reduced by up to 54.3 %, with smaller ships being used and average sailing speeds decreasing as the emission trading price rises from $0/tonne to $300/tonne.

中文翻译:

在排放交易系统下,在可持续航运联盟中实现船队共同部署和船位共同租船的精确算法

航运联盟已成为独立航运公司之间的合作平台,旨在通过容量和信息共享提高客户满意度并利用规模经济。在新兴的排放交易体系 (ETS) 下,可持续的航运联盟应以有利可图、公平和环保的方式运作。建议采用非凸混合整数非线性规划模型,共同优化船队在网络中协同部署、各航段航速、各航次船期设计、各联盟成员船位分配与租船。这些决策最终决定了每家公司的碳排放量。根据 ETS,公司需要为超过其配额的排放量付费,而任何盈余配额都可以在碳市场上交易收入。除了最大化联盟的总利润外,本研究还最大限度地减少了成员之间与其投资成比例的利润率差异,以一种新颖的方式促进了公平。开发了一种定制的空间分支定界 (SB&B) 算法,以提供问题的全局最优解。根据规划模型的结构提出了新颖的问题松弛和分支策略。SB&B 算法的性能明显优于现有的非凸非线性求解器。与不考虑货位共同租船和公平性的情况相比,我们的研究将总利润提高了 3.13%,满足了 0.52% 的运费需求,并确保了平均更公平的利润分配。根据 ETS,随着排放交易价格从 0 美元/吨上涨到 300 美元/吨,使用较小的船舶和平均航行速度可以减少高达 54.3% 的碳排放量。
更新日期:2025-05-20
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