An exact algorithm for fleet co-deployment and slot co-chartering in a sustainable shipping alliance under emissions trading system

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.