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.

Maritime decarbonization and strict international regulations have forced liner companies to find new solutions for reducing fuel consumption and greenhouse gas emissions in recent years. Green technology is regarded as one of the most promising alternatives to achieve environmental benefits despite its high initial investment costs. Therefore, a scientific method is required to assess the possibility of green technology adoption for liner companies. This study formulates a mixed-integer nonlinear programming model to determine whether to retrofit their ship fleets with green technology and how to deploy ships while taking maritime decarbonization into account. To convert the nonlinear model into a linear model that can be solved directly by off-the-shelf solvers, several linearization techniques are applied in this study. Sensitivity analyses involving the influences of the initial investment cost, fuel consumption reduction rate of green technology, unit fuel cost, and fixed operating cost of a ship on operation decisions are conducted. Green technology may become more competitive when modern technology development makes it efficient and economical. As fuel and fixed operating costs increase, more ships retrofitted with green technology will be deployed on all shipping routes.

Maritime transport serves as the backbone of international trade, accounting for more than 90% of global trade. Although maritime transport is cheaper and safer than other modes of transport, it often means long sailing distances, which often results in substantial fuel consumption and emissions. Liner shipping, a vital component of maritime transport, plays an important role in achieving sustainable maritime operations, necessitating the implementation of green liner shipping practices. Therefore, this study formulates a nonlinear integer programming model for a multi-fuel engine selection optimization problem to optimally determine ship order choice in terms of the fuel engine type, fleet deployment, fuel selection, and speed optimization, with the aim of minimizing the total weekly cost containing the weekly investment cost for ship orders and the weekly fuel cost. Given the complexity of solving nonlinear models, several linearization techniques are applied to transform the nonlinear model into a linear model that can be directly solved by Gurobi. To evaluate the performance of the linear model, 20 sets of numerical instances with, at most, seven routes are conducted. The results show that among 20 numerical instances, 16 sets of numerical instances are solved to optimality within two hours. The average gap value of the remaining four sets of numerical instances that cannot be solved to optimality within two hours is 0.51%. Additionally, sensitivity analyses are performed to examine crucial parameters, such as the weekly investment cost for ordering ships, the ship ordering budget, and the potential application of new fuel engine types, thereby exploring managerial insights. In conclusion, our findings indicate that equipping ships with low-sulfur fuel oil engines proves to be the most economical advantageous option in the selected scenarios. Furthermore, ordering ships with low-sulfur fuel, oil + methanol + liquefied natural gas engines, is beneficial when the weekly investment cost for such engines does not exceed $13,000, under the current parameter value setting.

As a relatively clean energy source, liquefied natural gas (LNG) is experiencing a growing demand. The uneven global distribution of LNG often compels residents in regions without local sources to import it, underscoring the need to optimize the global LNG transportation network. Therefore, this study formulates a nonlinear mixed-integer programming model for a multimodal transport and storage problem to optimize LNG carrier allocation, LNG storage planning, and LNG transport planning, aiming to minimize the total cost of multimodal transport, minus the rewards offered by ports. In order to facilitate the solving of the model, some linearization methods are used to transform the nonlinear model into a linear model. To assess the efficiency of the linear model, we conduct computational experiments on small-scale instances with five inland cities, medium-scale instances with 15 inland cities, and large-scale instances with 60 inland cities. The results show that all small- and medium-scale instances can be solved to optimality within 427.50 s. Feasible solutions with a maximum gap value of 0.03% for large-scale instances can be obtained within 1 h. In addition, sensitivity analyses are conducted to identify the impacts of the cost of transporting LNG by vehicles, the charter cost of LNG carriers, and the rewards for shipping LNG. In general, higher cost of transporting LNG by vehicles and higher charter cost of LNG carriers lead to a higher objective value. It is also found that when the rewards for shipping LNG increase to a certain extent, such that the additional rewards exceed the additional multimodal transport cost incurred, the amount of LNG unloaded at the subsidized port increases.

Countries around the world have tightened their border controls in response to the spread of COVID-19. Consequently, seafarers are prohibited from boarding or leaving ships at most ports, with few exceptions. This situation means that seafarers are highly likely to serve onboard vessels beyond their contracted shifts. Most seafarers are prone to depression because they have to spend long periods at sea away from family and friends, and, thus, banning crew changes will put their mental health further at risk. This will increase the likelihood of maritime accidents, thus jeopardizing global supply chains and ultimately exacerbating current hardships. To tackle this emergency, the International Maritime Organization and the European Commission have called on governments to coordinate efforts to designate ports for crew changes during the pandemic. This study aims to solve the crew change problem by using an integer linear programming model. In the sensitivity analysis section, we find that the number of opening ports for crew changes and the cost of crew changes decrease when the cost of opening ports increases. The results show governments will not invest in opening more ports when the cost of opening ports increases. However, the penalty increases when the number of open ports decreases, and the cost of opening ports increases. As the number of crew changes is decreasing, this leads to the penalty increasing, when the number of open ports decreases.

The greenhouse effect caused by carbon dioxide (${\mathrm{C}\mathrm{O}}_2$) emissions has forced the shipping industry to actively reduce the amount of ${\mathrm{C}\mathrm{O}}_2$ emissions emitted directly into the atmosphere over the past few years. Carbon capture, utilization, and storage (CCUS) is one of the main technological methods for reducing the amount of ${\mathrm{C}\mathrm{O}}_2$ emissions emitted directly into the atmosphere. ${\mathrm{C}\mathrm{O}}_2$ transport, i.e., shipping ${\mathrm{C}\mathrm{O}}_2$ to permanent or temporary storage sites, is a critical intermediate step in the CCUS chain. This study formulates a mixed-integer programming model for a carbon storage and transport problem in the CCUS chain to optimally determine ship allocation, ship departure scheduling, and ${\mathrm{C}\mathrm{O}}_2$ storage and transport. Taking advantage of the structure of the problem, we transform the mixed-integer programming model into a simpler model that can be computed efficiently. To evaluate the performance of the simpler model, numerous computational experiments are conducted. The results show that all small-scale instances (each with 10 power plants) and medium-scale instances (each with 30 power plants) can be solved optimality by Gurobi within 14.33 s. For large-scale instances with 60 and 65 power plants, feasible solutions with average gap values of 0.06% and 6.93% can be obtained by Gurobi within one hour, which indicates that the proposed methodology can be efficiently applied to practical problems. In addition, important parameters, including the unit fuel price, the time-charter cost, and the ship sailing speed, are examined in sensitivity analyses to investigate the impacts of these factors on operations decisions. In summary, a lower fuel price, a lower charter cost, or a higher ship sailing speed can increase the profit of the CCUS chain.