Joint Planning of Fleet Deployment, Ship Refueling, and Speed Optimization for Dual-Fuel Ships Considering Methane Slip

Reducing air pollution and greenhouse gas emissions has become one of the primary tasks for the shipping industry over the past few years. Among alternative marine fuels, liquefied natural gas (LNG) is regarded as one of the most popular alternative marine fuels because it is one of the cleanest fossil marine fuels. Therefore, a practical way to implement green shipping is to deploy dual-fuel ships that can burn conventional fuel oil and LNG on various ship routes. However, a severe problem faced by dual-fuel ships is methane slip from the engines of ships. Therefore, this study formulates a nonlinear mixed-integer programming model for an integrated optimization problem of fleet deployment, ship refueling, and speed optimization for dual-fuel ships, with the consideration of fuel consumption of both main and auxiliary engines, ship carbon emissions, availability of LNG at different ports of call, and methane slip from the main engines of ships. Several linearization techniques are applied to transform the nonlinear model into a linear model that can be directly solved by off-the-shelf solvers. A large number of computational experiments are carried out to assess the model performance. The proposed linearized model can be solved quickly by Gurobi, namely shorter than 0.12 s, which implies the possibility of applying the proposed model to practical problems to help decision-makers of shipping liners make operational decisions. In addition, sensitivity analyses with essential parameters, such as the price difference between the conventional fuel oil and LNG, carbon tax, and methane slip amount, are conducted to investigate the influences of these factors on operational decisions to seek managerial insights. For example, even under the existing strictest carbon tax policy, shipping liners do not need to deploy more ships and slow steaming to reduce the total weekly cost.