Abstract: According to the World Economic Outlook released by the International Monetary Fund (IMF), the global GDP growth rate would reach 4.4% in 2022. World economic growth will inevitably result in an increase in global trade transportation demand. At present, global trade transportation mainly relies on container liner transportation. Thus, the demand for container liner shipping will grow significantly. However, in the case of limited capacity in the shipping market, the sharp increase in demand for liner transportation has led to a series of difficulties in the shipping market, such as soaring container prices and difficult booking of container slots. Therefore, in the face of strong demand and fierce competition in the shipping market, liner companies should allocate the container slots reasonably and effectively, on the basis of meeting the needs of shippers and their own operations, to maximize the transportation benefits.
At the same time, empty container repositioning has become a key problem affecting the operation of container liner companies in recent 10 years. So, it is necessary to consider the collaborative optimization of empty container reposition in the allocation of container slots. Furthermore, “Internet+shipping” has gradually become the key research direction of the shipping industry. A series of shipping e-commerce platforms have emerged in the shipping market. They have many obvious advantages. Firstly, the shipping e-commerce online platforms enrich the booking channels of shippers. Secondly, they have the advantages of real-time information interaction and dynamic allocation. Last but not least, online booking is an important way to improve the competitiveness of liner companies. In summary, to maximize the revenue of shipping liner companies and promote the long-term development of the shipping industry, the study of collaborative optimization of container slot allocation and empty container repositioning under the environment of shipping e-commerce has important practical significance.
Although some literature considers the empty container repositioning while studying the container slot allocation problem, most of them don’t consider the empty container operation needs of liner companies. They just regard empty containers as a type of container classification. Therefore, the research on the container slot allocation considering the shipper’s loaded container transportation demand and the empty container operation demand of liner companies has not yet been done. In addition, as the “online booking” mode has just emerged, the academic research on container slot allocation in the online booking mode is very few. To the best of our knowledge, this study is the first attempt to comprehensively consider the shipper’s demand for loaded container transportation and the empty container operation demand of liner companies based on the overbooking theory. To some extent, this study fills up this gap.
The container slot allocation problem is a multi-stage dynamic resource allocation problem, and the empty container repositioning problem is a multi-cycle inventory scheduling problem. Both are revenue management decision-making problems that the shipping industry needs to face. The former focuses on current interests, while the latter on the future. In this study, the above two problems are collaboratively optimized. Based on the overbooking strategy in revenue management, in accordance with booking online mode, this paper compares the collaborative optimization scenario with the traditional container slot allocation optimization scenario.
Two mixed-integer programming models are established for the different scenarios respectively. Scenario 1 model is a mixed integer programming model for slot allocation based on the overbooking strategy in the e-commerce environment. The objective function is to maximize the benefits of liner companies in multiple voyages and cycles, which consists of container slot booking benefits, container transportation costs, customer churn costs, and ship operating fixed costs. Likewise, the scenario 2 model is a mixed integer programming model for collaborative optimization. The objective function consists of seven parts, namely, the booking income of loaded container slots, the income of empty container slots which are required to meet the daily operation of liner companies, the loaded container transportation costs, the empty container transportation costs, the empty container storage costs, and the ship operation fixed costs.
The two models are linearized to obtain exact solutions. And the exact solution is obtained by using the commercial software named CPLEX. In this paper, the PCN route of a liner company is taken as an example for the numerical experiment. The following conclusions can be drawn from numerical experiments. First of all, the total revenue of scenario 2 is significantly higher than scenario 1. In the second place, the utilization ratio of scenario 2 is significantly higher than scenario 1, and the distribution shows a uniform trend. Finally, under scenario 1 and scenario 2, the volume of loaded container booking is higher than the volume of transportation, which is the inevitable result of the overbooking strategy. The validity and practicability of the models are verified by numerical experiments. The results show that collaborative optimization can improve the utilization of liner slots and improve the operating revenue of liner companies. Further research will focus on the collaborative optimization of empty and loaded container conversion and transportation system within the port cluster.

Key words: collaborative optimization, slot allocation, empty container reposition, overbooking strategy, booking online

摘要： 舱位分配问题是多阶段的动态资源分配问题,空箱调运问题是多周期的库存调度问题,二者均为航运业需要面对的收益管理决策问题,前者着眼于当期利益,后者着眼于未来收益,本研究将二者进行协同优化。基于收益管理理论中的超额预订策略,在满足托运人的重箱以及班轮公司空箱运输需求的基础上,针对在线订舱模式下的集装箱舱位分配与空箱调运协同优化问题展开研究。针对在线订舱模式下的舱位分配与空箱调运协同优化情景与传统的单一的舱位分配优化情景进行对比,构建了双混合整数规划模型,利用CPLEX处理器求得精确解,通过算例分析验证了模型的有效性和实用性。研究结果表明舱位分配与空箱调运协同优化可以提升集装箱班轮的舱位利用率,提高班轮公司运营收益。

关键词: 协同优化, 舱位分配, 空箱调运, 超额预订策略, 在线订舱