Pallet loading optimization considering storage time and relative humidity

Purpose: This paper studies a 3-dimensional pallet loading problem considering interlock stacking pattern, box dimensions, humidity, and storage time, where overlapping and overhanging are not allowed. Despite the importance of this problem in the literature, our work provides the first method that considers the environmental conditions such as 1) storage time and 2) humidity, and their tremendous impacts on the strength of the boxes, as has been observed widely in the DHL supply chain.Design/methodology/approach: This paper proposes a two-phase heuristic algorithm to solve a 3-dimensional pallet loading problem under real conditions (relative humidity, and storage time) considering interlock stacking patterns, where overlapping and overhanging are not allowed. In phase 1, the horizontal layer configuration is determined by block techniques. Three types of horizontal layers are created based on box dimensions perpendicular to the base. In phase 2, a novel mathematical model is propounded to improve the pallet volume utilization, and stability considering the pallet's maximum allowable height and weight, and the dynamic compression strength of boxes. The dynamic compression strength of boxes is calculated by the modified McKee formula. Two performance measures, pallet volume utilization and stability (load height), are utilized to evaluate the performance of the proposed heuristic algorithm in real-world instances (DHL Supply Chain). Findings: The results illustrated that the dynamic compression strength of boxes decreases as the relative humidity and storage time increase. The load height changes dynamically along with box dimensions, box alignment, direction, relative humidity, and storage time. Increasing relative humidity and storage time and applying an interlock stacking pattern reduce the pallet utilization, however, enhance the pallet stability. Finally, the proposed heuristic algorithm's efficacy increases as the identical boxes dimensions' heterogeneity increases.Originality/value: It is believed in the supply chain where these characteristics are observed, the implementation of the heuristic algorithm will help them improve the pallet volume utilization and stability.