Three-dimensional bin packing problem with variable bin length Application in industrial storage problem

We treat a practical application of packing problem in supply chain management. This study was motivated by a real situation encountered in the storage problem of a foam industry in Tunisia. The storage problem consists in allocating, without overlapping, a given set of rectangular items (mattresses) to the minimum number of three dimensional bins with the different bins (rack) dimensions as input variables. Storage problem is a variable - sized bin packing problem that consists in finding an arrangement of set of items that cannot be rotated into the minimum number of variables bins. We develop a new heuristic method and we propose an integer programming model for the storage problem. The algorithm was applied in the case of unlimited number of bins. Numerical results on real-life test instances are reported.