Warehouse storage and retrieval optimization via clustering, dynamical systems modeling, and GPU-accelerated routing

• A mathematical framework models order region formation and routing dynamics • Warehouse order clustering reduces pick surface area and improves efficiency • Refill operations are guided toward cluster centers to minimize travel time • Real-time route optimization is achieved using CUDA C implementation of Bellman-Ford • Sub-route segmentation ensures scalability under combinatorial complexity 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. The procedure is formulated as a dynamic mathematical model 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 in large-scale warehouse environments.