This paper introduces a warehouse optimization procedure aimed at enhancing the efficiency of product storage and retrieval. By representing product locations and order flows within a time-evolving graph structure, we employ unsupervised clustering to define and refine compact order regions, effectively reducing picking distances. We describe the procedure using a dynamic mathematical model formulated using tools from random dynamical systems theory, enabling a principled analysis of the system's behavior over time even under random operational variations. For routing within this framework, we implement a parallelized Bellman-Ford algorithm, utilizing GPU acceleration to evaluate path segments efficiently. To address scalability challenges inherent in large routing graphs, we introduce a segmentation strategy that preserves performance while maintaining tractable memory requirements. Our results demonstrate significant improvements in both operational efficiency and computational feasibility for large-scale warehouse environments.
@article{arxiv.2504.20655,
title = {Warehouse storage and retrieval optimization via clustering, dynamical systems modeling, and GPU-accelerated routing},
author = {Magnus Bengtsson and Jens Wittsten and Jonas Waidringer},
journal= {arXiv preprint arXiv:2504.20655},
year = {2025}
}