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

2026-01-27

AI Summary

This work proposes a robust storage layout strategy for full-capacity grid-based automated storage systems to address the relocation problem caused by bounded disturbances in retrieval sequences. Introducing, for the first time, a k-bounded disturbance model, the study establishes that a grid width of Θ(k) is both necessary and sufficient to achieve zero relocations. An efficient algorithm is developed to generate disturbance-resilient storage configurations. By integrating combinatorial optimization, path planning, and robust scheduling under topological constraints, the approach minimizes the number of relocations. Experimental results demonstrate that when k does not exceed half the grid width, relocations are nearly eliminated; even when k reaches the full grid width, relocations are reduced by more than 50%.

Technology Category

Planning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsIntelligent Robots: Localization, Mapping, and NavigationSearch and Optimization: Distributed Search

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSystems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deploymentsResponsible Web: Human-perceived consequences of algorithmic deployment on the web

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 $\Theta(k)$ 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 $50\%+$.

Problem

• automated storage
• out-of-order retrieval
• load relocation
• grid-based storage
• sequence uncertainty

Innovation

• k-bounded perturbations
• zero-relocation storage
• grid-based automated storage
• robust retrieval
• relocation minimization