A three-dimensional bin packing problem with item fragmentation and its application in the storage location assignment problem

This paper introduces the three-dimensional bin packing problem with item fragmentation (3D-BPPIF) and explores its application in the storage location assignment problem (SLAP) to efficiently allocate warehouse spaces to product groups. Based on real-world constraints, the aim is to find an effective 3D-packing of the product groups into warehouse storage spaces to minimize the total distance. Given the internal limitations present in many warehouses, the storage spaces are not homogeneous, making the allocation to product groups a challenging task that can reduce space utilization efficiency. Accordingly, to effectively utilize warehouse storage spaces, we developed a MILP formulation incorporating the concepts of shape changeability and item fragmentation, significantly enhancing the flexibility of the arrangements. Due to the NP-hard nature of the problem, we proposed a simulated annealing-based meta-heuristic to solve large-scale real-world problems. Numerous computational experiments prove the validity of the proposed model and illustrate that the proposed algorithm can provide appropriate 3D assignments.