An Optimization Model and Algorithms for Loading Combined Container Units Used in Multimodal Transport System with Automotive Parts

To meet the packaging and loading requirements of irregular-shaped parts within automotive components in multi-modal container transport, a novel combined unit container is designed. The loading optimization model and algorithm for the proposed container are presented. This addresses challenges pertaining to internal division of the container unit, packing of irregular-shaped items, and multi-layer stacking requirements. The focus is on pallet selection for items to be packed, the positioning of loaded pallets within the container unit, and the effective alignment of goods, pallets, and the internal container space. Considering the above differences, the decision variables are redefined for pallet selection, stacking positioning for loaded pallets within the container unit, and positioning of dual pallets on the same layer. The constraints such as the selection of pallet types, the uniformity of pallet sizes within a single loading unit and its neighboring units are considered as well. A 0-1 integer programming model, Container Loading Model (CLM), is constructed to maximize the utilization of the effective space inside the container. To achieve efficient optimization, a heuristic algorithm, Fast-packing Algorithm (FPA), is presented encompassing cargo grouping, sorting, and packing. The experiments results show that both the proposed CLM and FPA provide high-quality loading solutions. The average effective space utilization rates achieved by CLM and FPA across all instances are 84.52% and 83.57%, respectively. For the instances involving packing goods selection, the average results attain 91.00% and 89.84%, respectively. Notably, the CLM requires a long solution time with an average of 473.57 s, with marginal improvements in solution quality with increased time. In contrast, the FPA exhibits the fastest solution time with an average of 0.20 s and an average deviation from upper bounds of 1.52%. Compared with the genetic algorithm and evolutionary strategy algorithm, the proposed FPA achieves best results within 1 s for all instances.