Robust Out-of-Order Retrieval for Grid-Based Storage at Maximum Capacity

• URL: http://arxiv.org/abs/2601.19144v1
• Date: Tue, 27 Jan 2026 03:19:50 GMT
• Title: Robust Out-of-Order Retrieval for Grid-Based Storage at Maximum Capacity
• Abstract summary: The paper proposes a framework for improving the operational efficiency of automated storage systems under uncertainty.<n>It considers a 2D grid-based storage for uniform-sized loads, which are moved by a robot along a collision-free path in the grid.<n>The objective is to minimize the load relocations to ensure efficient retrieval.
• Score: 14.759453430635034
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $50\%+$.

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