Integrated green technology adoption, ship speed optimization and slot management for shipping alliance under emission limits and uncertain fuel prices

Due to newly adopted global sulfur emission limits and designated sulfur emission control areas (SECAs), liner shipping companies invest in green technologies, such as retrofitting vessels with sulfur scrubbers or fuel-switching equipment. Sulfur scrubbers require significant initial investment but allow the use of cheaper heavy fuel oil (HFO) both inside and outside SECAs. Conversely, fuel-switching equipment has lower initial costs but higher fuel costs, as vessels use very low sulfur fuel oil (VLSFO) outside SECAs and marine gas oil (MGO) within SECAs to comply with emission limits. Liner shipping companies optimize sailing speeds both inside and outside SECAs considering fuel consumption costs and initial investment costs. Typically, liner shipping companies form alliances and choose the optimal green technology, optimize sailing speed, and manage ship slots within the alliance, considering sulfur emission restrictions and uncertain fuel prices. A mixed-integer nonlinear robust optimization model is formulated to solve this problem, using a polyhedral uncertainty set to represent the uncertain fuel prices. The suggested robust counterpart reformulation method creates a tractable model to obtain optimal solutions. Numerical experiments demonstrate that, compared to deterministic and stochastic models, our robust model significantly reduces profit variation with only a slight decrease in the mean profit value. Moreover, adopting green technologies within a shipping alliance results in a substantial increase in total profit and a notable reduction in sulfur emissions compared to operating independently.