This paper proposes a framework for improving the operational efficiency of automated storage systems under uncertainty. It considers a 2D grid-based storage for uniform-sized loads (e.g., containers, pallets, or totes), which are moved by a robot (or other manipulator) along a collision-free path in the grid. The loads are labeled (i.e., unique) and must be stored in a given sequence, and later be retrieved in a different sequence -- an operational pattern that arises in logistics applications, such as last-mile distribution centers and shipyards. The objective is to minimize the load relocations to ensure efficient retrieval. A previous result guarantees a zero-relocation solution for known storage and retrieval sequences, even for storage at full capacity, provided that the side of the grid through which loads are stored/retrieved is at least 3 cells wide. However, in practice, the retrieval sequence can change after the storage phase. To address such uncertainty, this work investigates \emph{$k$-bounded perturbations} during retrieval, under which any two loads may depart out of order if they are originally at most $k$ positions apart. We prove that a $Θ(k)$ grid width is necessary and sufficient for eliminating relocations at maximum capacity. We also provide an efficient solver for computing a storage arrangement that is robust to such perturbations. To address the higher-uncertainty case where perturbations exceed $k$, a strategy is introduced to effectively minimize relocations. Extensive experiments show that, for $k$ up to half the grid width, the proposed storage-retrieval framework essentially eliminates relocations. For $k$ values up to the full grid width, relocations are reduced by $50\%+$.

翻译：本文提出了一种在不确定性条件下提升自动化仓储系统运行效率的框架。该框架研究用于存放统一规格货物（如集装箱、托盘或周转箱）的二维网格化存储系统，货物由机器人（或其他操纵装置）沿网格中无碰撞路径移动。货物带有标签（即具有唯一性），必须按给定序列存入，之后需按不同序列取出——这种操作模式常见于物流应用场景，如末端配送中心和造船厂。目标是最小化货物移库操作以确保高效检索。已有研究证明，当存储/检索所用网格边界宽度至少为3个单元格时，即使存储达到满容量，对于已知的存储与检索序列，仍可保证零移库解决方案。然而在实际应用中，检索序列可能在存储阶段结束后发生变化。为应对此类不确定性，本研究探讨检索过程中的\emph{$k$有界扰动}，在此扰动下，任意两个货物若原始位置间隔不超过$k$个位次，则可能发生乱序出库。我们证明，为实现满容量下的零移库操作，网格宽度需满足$Θ(k)$的必要充分条件。同时，我们提供了一种高效求解器，用于计算能抵御此类扰动的鲁棒存储布局。针对扰动超过$k$的高不确定性场景，本文引入了一种有效最小化移库的策略。大量实验表明：当$k$值不超过网格宽度一半时，所提存储-检索框架基本能消除移库操作；当$k$值达到网格全宽时，移库次数可减少$50\%$以上。