A Grid-Based Spatial Representation of Logistics Warehouses Using 3rd-Order Tensors

Zine El Abidine Falouti

Warehouse Spatial Modeling, Third-Order Tensors, Spatial Discretization, Logistics Automation, Smart Warehousing.

The digital representation of a logistics warehouse within Enterprise Resource Planning (ERP) systems, particularly Warehouse Management Systems (WMS), is mainly based on operational data and warehouse activities. While these systems help improve inventory management, reduce operational costs, shorten delivery times, and increase distribution efficiency, they do not provide a mathematical representation of the warehouse's physical space. As a result, researchers have limited support for developing and testing optimization methods that depend on the spatial organization of the warehouse. This research proposes a mathematical three-dimensional (3D) grid model in which each storage cell is represented by its spatial coordinates and an associated weight. The proposed model provides a simple and generic digital representation of a logistics warehouse that can be used as a basis for research on warehouse optimization, including storage allocation, routing, robot navigation, and space utilization.

Received: 05 Jul 2026, Received in revised form: 03 Aug 2026, Accepted: 07 Aug 2026, Available online: 12 Aug 2026

10.22161/ijaers.138.3