Clustering-based column generation and heuristic methods for the container loading problem with practical constraints : a case study

Purpose: This study addresses a real-world container loading problem (CLP) encountered in a logistics company in Turkey, filling a gap in the literature by solving practical constraints using a state-of-the-art algorithm. The problem involves constraints such as rotations, stackability, loading priorities, and mixed loading constraints.Design/methodology/approach: To overcome the computational challenges posed by large-scale instances, a novel three-step approach is proposed. First, the K-Means clustering algorithm is applied to group objects with similar dimensions. Then, each group is allocated to containers using a Column Generation (CG) method combined with a 3D-Best Fit Decreasing with Orientation (3D-BFDO) algorithm. Additionally, the CG process is enhanced by integrating a machine learning (ML) model to predict reduced-cost columns, improving computational efficiency and solution quality.Findings: Extensive experiments demonstrate that the proposed approach significantly improves container space utilization while reducing operational costs. The results highlight the effectiveness of ML and K-Means in enhancing traditional optimization techniques.Research limitations/implications: The study focuses on a specific set of practical constraints relevant to real-world logistics applications. Further research could explore additional constraints and scalability to different logistics environments.Practical implications: The approach offers a practical solution for logistics companies dealing with a large-scale CLP by optimizing space utilization and reducing operational costs. The integration of ML into CG presents a viable method for improving decision-making in logistics.Originality/value: The study bridges the gap between theoretical models and real-world logistics challenges by introducing a data-driven enhancement to traditional optimization techniques. The proposed integration of K-Means clustering and ML into CG represents an innovative contribution to container loading optimization.