The container relocation problem (CRP) is an important factor affecting the operation efficiency of container terminal yards, and it has attracted much attention for decades. The CRP during the pickup operations of import containers is still an intractable problem for two reasons: the first is that the solution efficiency of the algorithms developed in the existing literature cannot meet the real-time operation requirements; the second is that the pre-optimized operation plan cannot cope with the changes in the real-time operation scenarios caused by the uncertainty of the arrival time of external trucks. This paper proposes an optimization method for the real-time operation scenario which aims to solve the most reasonable operation plan quickly according to the arrivals of external trucks, in which a dynamic upper bound of the optimal solution is derived based on the dynamic programming model of the import containers’ CRP, and an approximate optimal solution can be obtained by minimizing this dynamic upper bound. A heuristic algorithm based on three relocation rules is developed to implement this method, considering the adjustment of the pickup sequence of the target containers. Numerical experiments show that (1) when the number of a batch of target containers is less than 10 (excluding target containers that can be directly picked up), the method proposed in this paper can solve the problem quickly to meet the demand of optimizing real-time pickup operations; (2) compared with other outstanding algorithms, the quality of the solutions obtained by this method is also improved; and (3) this method can be applied to the most container terminals for optimizing real-time pickup operations.

The container relocation problem (CRP) is one of the important topics in container terminals, which aims to find the optimal sequence of movements to minimize the total number of relocations needed to retrieve all the containers within a bay according to a given specific layout and retrieval order. However, determining such an order may be difficult due to uncertainty. Various CRP solution methods proposed so far show a common pitfall concerning the complexity of the solving process, whose scale grows exponentially with the number of containers. Considering the retrieval operation process of the inbound containers in a bay consists of several operation rounds, this paper focuses on the real-time operation scenario of each round to minimize the actual number of relocations during the pick-up process, i.e., starting from the initial layout of the bay, we minimize the sum of the incremental number of blocking containers due to the layout change and the number of reallocated containers unrelated to the target container. We present a heuristic algorithm (called SPFH) based on the three rules (LL, MSS, and FSS), considering the adjustment of the pick-up order of containers. Numerical experiments on a set of instances generated from the literature are performed. The proposed methodology excels in both execution efficiency and solution quality and is capable of solving instances that were impossible to solve before. This also makes our methods appealing for being applied in practice. The source codes are available at https://github.com/zhou-sf/rt-scrp.