The Three-dimensional Bin Packing Problem for Deformable Items

The three-dimensional bin packing problem(3D-BPP) for deformable items is quite common and essential in real-world city logistics and manufacturing environments, for example, fresh food supply chain. However, no published literature has addressed this problem from an exact point of view. In order to further increase loading efficiency and reduce operating costs for related firms, we examine a 3D-BPP variation in this work that takes into account the compressibility factor of deformable items. We formulate the studied problem as a mixed integer programming model in which several groups of unique decisions and constraints are introduced. A series of numerical experiments are conducted over several randomly generated benchmarks with various parameter settings. Results reveal that the total volume of packed items and the space utilization are significantly enhanced after considering the compressibility factor since the actual room occupied by packed items are estimated in a more accurate and practical way. In particular, the improvement in the space utilization reaches 8%$\sim$ 28% compared with the case without compressibility issue. These benefits show that there is a large potential in reducing packaging and delivering costs by estimating the actual occupied space under the dynamic volume change assumption.