A three-stage layer-based heuristic to solve the 3D bin-packing problem under balancing constraint

This research investigates the Three Dimensional-Single Bin-Size Bin-Packing Problem (3D-SBSPP). The aim is to pack n boxes of different dimensions and weights into a minimum number of equally balanced bins. The boxes can be rotated according to six possible orientations. Balancing the bins, volume and weight wise, is of high importance. To achieve this goal, a three-stage heuristic was developed. In the first stage, the different possible layers are generated. Each layer is formed by boxes of same type packed according to a common given orientation. The second stage generates solution candidates using the layers formed in stage 1. In stage 3, the boxes to be shipped are placed in the bins following the solution candidates of stage 2 that give the best volumetric and/or weight utilization. The proposed heuristic was successfully validated through an exhaustive experimental study using a variety of problem instances and involving comparisons with other existing heuristics.