## 1 Introduction
Due to the decentralization of the retrieval operation of import containers, the operation process for retrieving all the import containers in the bay requires multiple independent operation rounds (also referred to as \"operation stages\" in other studies). The pickup order and operation plan are determined within each operation round based on the EIs' arrival information. Between two neighboring operation rounds, the bay layout at the end of the previous operation round will be the basis for the next round. Therefore, in this paper, we propose a method that gradually optimizes the pickup operations during each operation round instead of optimizing the overall operation process for retrieving all the containers in a bay. In this method, the problem size of the SCRP is significantly reduced. This method is referred to as _Real-time Batch Optimization_, which focuses on the real-time operation round (or the current operation round). The \"real-time\" means that the current operation round is subject to the instant generation of an operation plan based on the arrival of ETs rather than execution based on a predetermined operation plan. The real-time operation scenario has three characteristics: first, a batch of ETs has arrived at the yard; second, a batch of target containers is known, and the number of target containers depends on the arrived ETs; third, the pickup sequence of ETs is adjustable. In the new approach, we first categorize the ETs into batches (groups) based on their reservation information from the TAS and the arrival information from terminal gates. Of course, the retrieval sequence of the ETs belonging to different batches is precise, and the retrieval sequence of the ETs within the same batch is still being determined. Then, based on this grouping, all the arrived ETs within the real-time operation round are defined as a specific batch (group) whose retrieval priories are set to zero, representing the highest pickup priority. Correspondingly, the target containers within the real-time operation round are a batch with a retrieval priority of 0, which may only be part of the containers booked in the current time window. Moreover, their pickup service order of all arrived ETs is adjustable (no longer following the first-come-first-served principle), and the optimal pickup order is determined based on the bay layout to minimize the number of relocations. The contributions of this paper are as follows:  
* Based on the dynamic programming (DP) model of the SCRP, we derive a dynamic upper bound of its optimal solution. Thus, we transform the optimization objective into minimizing this dynamic upper bound, significantly reducing the size of the solution process. * We propose a new heuristic relocation strategy, namely Least-relocations-and-Lowest-precedence-gap (LL), which learns from the expected relocation index (ERI) heuristic presented by [6] and the expected min-max (EM) heuristic proposed by [5]. * We introduce two novel relocation rules: moving ahead for a sequential-placed slot (MSS) and freeing up for a sequential-placed slot (FSS). The former rule assigns, as far as possible, a sequential placement for the potential blocking containers in the future in advance. The latter rule tries to find a stack that can free its topmost container to satisfy a sequential placement for the current blocking container. * A novel heuristic algorithm, called the sequential-placement first heuristic (\(SPFH\)), is devised. It takes advantage of the properties of the two relocation rules mentioned above. The rest of the paper is structured as follows: In Section 2, we quickly survey the recent literature on the CRP. Section 3 gives a detailed description of the real-time CRP and the formulation of the improved DP model. Section 4 describes the proposed \(SPFH\) algorithm in detail. We report the results of our computational experiments with the methods discussed in this paper in Section 5. Finally, Section 6 concludes the study and suggests future research directions.