Solving a 3D bin packing problem with stacking constraints

Abstract

We consider a novel variant of the three-dimensional bin packing problem (3DBPP) arising from a maritime shipping port. Unlike the classical bin packing problem, our 3DBPP requires all items to be stacked vertically during the packing process. To tackle this problem effectively, we divide it into two subproblems: the stack packing problem (SPP) and the two-dimensional bin packing problem (2DBPP). We first formulate the SPP as an integer programming model to minimize the total bottom area of the stacks, which is further solved by a branch-and-price method. Then, in the 2DBPP, to pack all stacks into a minimum number of bins, we follow the left-down most extreme point placement strategy. An encoder–decoder model was developed to optimize the packing sequence and orientation of the stacks simultaneously. Industrial instances from shipping ports were collected and extended. The computational results show that our two-stage algorithm performs well in solving the stacking-constrained 3DBPP.