Optimizing carbon emission allocation for liner shipping companies

Maritime shipping accounts for approximately 3% of all annual carbon dioxide (${\text{CO}}_2$) emissions worldwide. To address this, the EU Emissions Trading System (ETS) mandates that shipping companies pay for every ton of ${\text{CO}}_2$ they emit. In response to this regulation, liner shipping companies have passed the cost of carbon emissions onto their customers. These companies typically levy an emissions surcharge per twenty-foot equivalent unit (TEU) container and calculate the surcharge based on individual trades, which typically encompass multiple origin–destination (od) pairs within a region. However, this surcharge structure fails to account for variations in distance between od pairs within the same trade. To address this limitation, we propose a carbon emissions allocation policy using an optimization method to allocate emissions per TEU for each od pair. This method incorporates both the shortest sailing distance and the actual traveling distance of the od pair, combining these into a harmonic distance. The harmonic factor represents the chosen carbon emissions allocation policy. Considering that carbon emission allocation should be tailored to specific shipping routes, this study constructs an augmented shipping network of multiple routes. Based on this network, we develop two od-link-based models: one with transshipment and the other without transshipment. Both models aim to maximize the profits of liner shipping companies. The models are validated through experiments conducted using real-world and synthetic shipping networks. The results show that the model with transshipment yields higher profits than the model without. In the model without transshipment, the carbon emission allocation policy has little impact on the profits of shipping companies. However, in the model with transshipment, selecting an appropriate carbon emission allocation policy is critical.