An MDD Approach to Multidimensional Bin Packing

We investigate the application of multivalued decision dia- grams (MDDs) to multidimensional bin packing problems. In these problems, each bin has a multidimensional capacity and each item has an associated multidimensional size. We develop several MDD representations for this problem, and explore different MDD construction methods including a new heuristic-driven depth-first compilation scheme. We also derive MDD restrictions and relaxations, using a novel application of a clustering algorithm to identify approximate equivalence classes among MDD nodes. Our experimental results show that these techniques can significantly outperform current CP and MIP solvers.