A mixed integer programming formulation for the three-dimensional bin packing problem deriving from an air cargo application

The present paper discusses the problem of optimizing the loading of boxes into containers. The goal is to minimize the unused volume. This type of problem belongs to the family of multiple bin size bin packing problems (MBSBPP). The approach includes an extensive set of constraints encountered in real-world applications in the three-dimensional case: the stability, the fragility of the items, the weight distribution, and the possibility to rotate the boxes. It also includes the specific situation in which containers are truncated parallelepipeds. This is typical in the field of air transportation. While most papers on cutting and packing problems describe ad hoc procedures, this paper proposes a mixed integer linear program. The validity of this model is tested on small instances.