The optimization of loading utilization for heterogeneous cargo in a single vehicle model under complex physical constraints

Abstract

Addressing the challenge of arranging large-scale heterogeneous cargo in modern logistics distribution, this paper constructs a static loading optimization model that integrates spatial, mechanical, and safety constraints, using a single vehicle type as the research context. By analyzing the physical properties of 3,000 cargo items, the study first identifies that this scenario exhibits significant volume constraints, with an average spatial density of only approximately 143 kg/m³, far below the vehicle's rated load capacity. The model employs a mixed-integer nonlinear programming approach, utilizing Big-M techniques to linearize complex spatial non-overlap constraints, while integrating stringent physical rules such as top safety clearance, protection against crushing of fragile items, and lower load-bearing limits. At the algorithmic level, this study developed a 3D-FFD heuristic engine based on 3D extreme point generation, achieving rapid convergence in interference detection through vectorized bounding box techniques. The solution results indicate that, while ensuring 100% physical compliance, the medium-sized vehicle scheme achieves a full-load capacity of 68.99%. The study effectively determines the minimum dispatch volume for each vehicle configuration, providing high-precision algorithmic support for logistics enterprises to maximize the utilization of redundant cargo space.