Abstract: With the continuous development of global trade, maritime greenhouse gas emission control has become one of the most challenging environmental issues, which has attracted great attention from all walks of life. Currently, the International Maritime Organization (IMO) has designated four Emission Control Areas (ECA) in the North Sea, the Baltic Sea, the English Channel and the Caribbean coast of North America and the U.S. China has also established three ECAs in the waters of the Pearl River Delta, the Yangtze River Delta and the Bohai Sea Rim. In addition, considering the availability of container terminal resources, liner companies usually have to sign cooperation agreements with ports in order to provide multiple time windows at the ports. In a circular route consisting of multiple ports, the liner companies deploy multiple ships to call at each port in a regular sequence according to a certain departure frequency (usually weekly) to provide customers with round-trip scheduled liner shipping services from week to week. Under the new situation of the implementation of ECA rules and deep integration of port and shipping supply chain, liners need to use MGO in ECA and LSFO outside ECA, and adopt different speed in different leg. On the one hand, this leads to profound changes in liner’s arrival/departure schedule, refueling port selection and refueling volume strategy, and on the other hand, it also leads to changes in container cargo loading strategy between port pairs, which in turn will affect the changes in voyage cargo revenue. Therefore, it is of great practical significance to study the problem of optimizing the refueling and cargo revenue of liner shipping considering ECA under the situation of drastic fluctuation of freight and fuel prices.
This paper extends the study of refueling and cargo revenue optimization based on the background of multi-window cooperation agreements signed between liner companies and ports, in order to provide reference for liner shipping operation optimization decisions under the new situation of maritime greenhouse gas emission control and deep supply chain integration. The impact of fuel switching on ECA internal/external routes on fuel consumption is analyzed. Combining the differentiation factors of fuel price at each port of call and freight demand from origin to destination and freight rate, a mixed integer non-linear programming model is established, where the total liner shipping route freight revenue is maximized. Then, a piecewise linear secant approximation algorithm is designed. The method is applied to transform the original model into a mixed-integer linear programming model that can be solved directly using commercial software (e.g., CPLEX, etc.). The problem contains the following decision elements: (1)Determining the ship sailing speed of ECA internal/external routes; (2)Selecting the arrival/departure time of ship; (3)Determining the number of ships deployed on the route; (4)Determining the refueling ports and refueling volume of LSFO and MGO; (5)Determining the loading strategy of each O-D pair.
Taking the MEX route of China COSCO Shipping Group Co., Ltd. as an example, the applicability and effectiveness of the model and algorithm are verified. The results of the numerical example show that the joint optimization of refueling and cargo loading can increase the voyage revenue of liner shipping by 4.21% under the consideration of ECA and multiple time windows. As the length of port time window increases, the possibility of liner being late to the port decreases, and the liner can adjust its speed more flexibly, better choose the port with low fuel price, and more reasonably balance the loading and refueling strategies, thus improving the voyage revenue. The study shows that the signing of multi-window cooperation agreements between liner companies and ports, as well as the deployment of new types of ships with lower fuel consumption coefficients, not only facilitate liner companies to flexibly adjust sailing speed and arrival/departure time, but also effectively reduce fuel consumption and improve the voyage revenue. Liner companies should sign win-win cooperation agreements with ports, so as to obtain a larger length of available time window at ports without increasing container terminal resources (i.e., without increasing loading and unloading operation time). In addition, liner companies should take into account the fuel consumption coefficients of different ship types according to the actual demand of liner shipping, and match the advanced and suitable ship types to ensure the maximum profit of liner shipping. The research conclusions can provide a useful reference for liner companies to make liner operation decisions with ECA rules.
This paper investigates the problem of optimizing liner refueling and cargo revenue considering ECA when liner companies deploy the same type of ship on a single route. The study yields a series of important conclusions and management opinions. However, liner companies also deploy heterogeneous ships on some routes, and the next study can consider the optimization problem of liner refueling and cargo revenue for multiple ship types on multiple routes. In addition, robust optimization of liner refueling and cargo revenue is also an interesting direction due to weather, sea conditions and natural disasters that may cause delayed ship arrivals and port disruptions.

Key words: liner shipping, emission control area, multi-time windows, refueling and cargo shipping strategy, mixed integer non-linear programing model

摘要： 针对考虑排放控制区(Emission Control Area,ECA)和多时间窗的班轮加油与货运收益优化问题,通过分析ECA内/外航路班轮燃油切换对燃油消耗的影响,结合各港口油价、各起讫港口对货运需求量及运费率差异,以班轮运输航次收益最大化为目标,构建了混合整数非线性规划模型,并设计了分段线性割线逼近求解算法。以中国远洋海运集团有限公司的MEX航线为例,验证了模型和算法的适用性和有效性,算例结果显示,在考虑ECA和多时间窗的情况下,加油与货物装运联合优化可使班轮航次收益提高4.21%。研究表明:班轮公司与港口签署多时间窗合作协议,以及配置燃油消耗系数更小的新型班轮,不仅有利于班轮公司灵活地调整班轮航速和到/离港时间,且能够有效地降低燃油消耗,提高班轮航次货运收益。研究结论可为班轮公司制订ECA规则下的班轮运营决策提供有益的参考。

关键词: 班轮运输, 排放控制区, 多时间窗, 加油与货物装运策略, 混合整数非线性规划模型