A particular approach for the Three-dimensional Packing Problem with additional constraints

This paper focuses on a restrained concretization of the general NP-hard Container Loading Problem that arises from a real world application. This particular problem can be informally described as: given different sets of bins and boxes, find the packing of the boxes into the smallest number of bins obeying some additional restrictions on the placement. The mathematical programming formulation that appears to better model this application is the Three-dimensional Bin-Packing Problem (3D-BPP) which is no more than an extension of the classic Bin-Packing Problem to the orthogonal packing of solid objects. We present an alternative non-linear formulation for the 3D-BPP version as well as new designed heuristic algorithms (CPBOX and BOXCP) for the approximation of the optimal solution using boxes and bins of heterogeneous dimensions. Moreover, we also present a heuristic specifically designed to work under very particular storage application restrictions. The numerical results indicate that all of these new heuristics have good performance standards especially when applied to replications of real input data.