Interactive integer linear programming procedures for stacking optimization for the 3D palletization problem

The paper describes the development of interactive integer linear programming (ILP) procedures for stacking optimization for the 3D palletization problem. The proposed model is an extension of the authors' recent development of the 3D volumetric pallet optimization algorithm. It deals with different complexity levels of the 3D stacking palletization, i.e. the pallet volume is optimized using different stacking columns of rectangular and/or square boxes of multiple dimensions. The interactive ILP procedures consider the exact location of boxes to be stacked on the pallet and incorporate two successive models with different objectives: the first one is the optimization of the base area of the pallet, and the second is the optimization of each stacking height for the different sub-areas generated from the first model. The resulting optimum solution is only of the column stacking type. Two case studies of different characteristics are presented and the results are compared with those in the literature.