A Simple and Effective Decomposition for the Multidimensional Binpacking Constraint

Stefano Gualandi, Michele Lombardi

Abstract: The multibin_packing constraint captures a fundamental substructure of many assignment problems, where a set of items, each with a fixed number of dimensions, must be assigned to a number of bins with limited capacities. In this work we propose a simple decomposition for multibin_packing that uses a bin_packing constraint for each dimension, a set of all_different constraints automatically derived from a conflict graph, plus two alternative symmetry breaking approaches. Despite its simplicity, the proposed decomposition is very effective on a number of instances recently proposed in the literature.