The Three-Dimensional Bin Packing Problem and Its Practical Algorithm

The three-dimensional bin packing problem (3DBPP) is orthogonally to pack a given set of rectangular-shaped items into the minimum number of three-dimensional rectangular bins. It is formulated as a mixed integer program (MIP) that can solve small-sized instances to optimum. For large scale of instances, a composite algorithm, aimed at solving the 3DBPP with several practical constraints, is proposed and evaluated by the lower bound and the test instances available on website. It should be noted that although the computational tests are conducted for the 3DBPP with identical bins, the proposed approach is designed for a general case with heterogeneous bins.