The Two Dimensional Bin Packing Problem with Side Constraints

Abstract

We propose a new variant of Bin Packing Problem, where rectangular items of different types need to be placed on a two-dimensional surface. This new problem type is denoted as two-dimensional Bin Packing with side constraints. Each bin may consist of different two-dimensional sides, and items of different types may not overlap on different sides of the same bin. By different parameter settings, our model may be reduced to either a two- or three-dimensional Bin Packing Problem. We propose practical applications of this problem in production and logistics. We further introduce lower bounds, and heuristics for upper bounds. We can demonstrate for a variety of instance classes proposed in literature that the GAP between those bounds is rather low. Additionally, we introduce a Column-Generation based algorithm that is able to further improve the lower bounds and comes up with good solutions. For a total of 400 instances, extended from previous literature, the final relative gap was just 6.8%.