We present a new method for solving bin packing problems, including two-constraint variants, based on an arc flow formulation with side constraints. Conventional formu- lations for bin packing problems are usually highly symmetric and provide very weak lower bounds. The arc flow formulation proposed provides a very strong lower bound, and is able to break symmetry completely.
The proposed formulation is usable with various variants of this problem, such as bin packing, cutting stock, cardinality constrained bin packing, and 2D-vector bin packing. We report computational results obtained with standard benchmarks, all of them showing a large advantage of this formulation with respect to the traditional ones.
Keywords: bin packing, cutting stock, integer programming, arc flow formulation, cardinality constrained bin packing, 2D-vector bin packing.