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

TL;DR

This paper develops a robust framework for grid-based storage systems that minimizes load relocations under uncertain retrieval sequences, especially effective for bounded perturbations up to half the grid width.

Contribution

It introduces a novel approach to handle retrieval sequence uncertainties in maximum capacity grid storage, proving necessary grid widths and providing an efficient solver.

Findings

Relocations are nearly eliminated for perturbations up to half the grid width.

Relocations are reduced by over 50% for perturbations up to the full grid width.

The framework is effective in practical logistics scenarios with uncertain retrieval orders.

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 $50\%+$.