Matheuristic approaches for multi-product 3-dimensional container loading problem

The problem of packing cases in three-dimensional space in a space-efficient manner is a challenging optimization problem that has wide application in supply-chain and logistics planning across various industries where physical products must be loaded and packed for storage and/or shipped to different destination locations. This work explores the use of matheuristic approaches to solve the 3D container loading problem to obtain high-quality loading plans in reasonable computation time for different levels of heterogeneity in the product mix. In our problem of interest, cuboidal cases must be arranged in a large cuboidal container, such as a shipper or gaylord box, allowing for two different case orientations around the vertical axis. We use a number of synergistic objectives to maximize space utilization while ensuring that items belonging to the same product SKU are preferentially placed together. We test and compare different solution methods, including full-space and decomposition-based ones, for placing items in 2D or 3D space. The decomposition methods use mathematical programming models in combination with embedded heuristics and construct a complete solution in three-dimensional space in an iterative manner. Results indicate that the 2D successive layer packing method is the most viable approach when considering solution quality and computational efficiency.