Abstract: The hinterland area after port integration often intersects and overlaps due to the characteristics of fuzzy and uncertain boundaries, and is widely present in public hinterland in reality. For shipping companies, the transportation network of empty containers has been updated due to the intersecting hinterland, and the direction of empty container repositioning also has more possibilities. The process of empty container repositioning has the characteristics of randomness and periodicity. During different decision-making cycles, the shipping company may be an empty container supply port, i.e. a surplus container port, but in the next stage, it may become an empty container demand port, i.e. a shortage container port. The uncertainty of empty container supply and demand makes shipping companies face the situation of empty containers transported from the port of shortage to the port of surplus. Reverse unreasonable transportation will exacerbate the imbalance between empty container supply and demand, and further affect the shipping company’s heavy container transportation plan, reducing service levels. At the same time, based on the dual attributes of containers as carriers and transporting goods, any single optimization cannot fully depict the practical problems brought by empty containers. Therefore, in the context of the development trend of port clusters, it is of great significance to carry out joint optimization of empty container repositioning and storage in an environment with uncertain empty container demand for the empty container repositioning network that links port clusters and landward hinterland.
This paper aims to minimize the total cost of all decision-making cycles, taking into account constraints such as the balance of empty container inflow and outflow at each port node, the balance of transportation volume between ports and public hinterlands, exclusive hinterland terminals, the balance of transportation volume between public hinterland terminals, storage capacity limitations, and transportation capacity limitations. At the same time, a periodic inventory control strategy is introduced to reasonably control the empty container inventory of each port within the port group, thereby optimizing the cost of empty container inventory that changes due to empty container transportation operations. With distributed robust optimization, random constraints are processed and transformed into deterministic problems by introducing probability distribution sets. The combination design of dynamic programming and simulated annealing algorithm is used to solve the problem, and the numerical experiments are conducted to verify the superiority of the joint optimization and the effectiveness of the periodic inventory control strategy. The results indicate that the empty container repositioning network model linked by port groups and landward hinterlands is more efficient than the round-trip transportation model between ports and their hinterlands. The joint optimization of empty container repositioning and inventory control can reduce the total container management costs for shipping companies, including empty container repositioning and storage. Given the periodicity of liner transportation, the periodic inventory control strategy is more effective under uncertain demand for empty containers.
The further research direction is to explore the combined optimization schemes of container repositioning, storage, and leasing among different port groups by shipping companies, while also exploring the effectiveness of other inventory control strategies in reducing empty container management costs in uncertain environments.

Key words: port group, empty container repositioning, inventory control, demand uncertainty, robust optimization

摘要： 针对空箱需求不确定性的特点,综合考虑港口群内各港口间、港口与内陆腹地场站间以及内陆腹地场站之间的多方向空箱调运,引入定期库存控制策略,选取辽宁沿海港口群—东北腹地中的部分港口与腹地作为研究对象,建立了港口群空箱调运与存储联合优化模型,采用分布式鲁棒优化对随机优化模型进行确定性转化,并设计了动态规划与模拟退火的组合算法对模型进行求解。结果表明:港口群与陆向腹地联动的空箱调运网络模式较之于港口及其腹地之间往返调运模式更为高效;空箱调运与库存控制的联合优化可以为船公司降低包括空箱运输与存储的总箱管费用;鉴于班轮运输的周期性,定期库存控制策略在空箱需求不确定条件下更有效。

关键词: 港口群, 空箱调运, 库存控制, 需求不确定性, 鲁棒优化