Multiple-choice Vector Bin Packing: Arc-flow Formulation with Graph Compression

The vector bin packing problem (VBP) is a generalization of bin packing with multiple constraints. In this problem we are required to pack items, represented by p-dimensional vectors, into as few bins as possible. The multiple-choice vector bin packing (MVBP) is a variant of the VBP in which bins have several types and items have … Read more

Bin Packing and Related Problems: General Arc-flow Formulation with Graph Compression

We present an exact method, based on an arc-flow formulation with side constraints, for solving bin packing and cutting stock problems — including multi-constraint variants — by simply representing all the patterns in a very compact graph. Our method includes a graph compression algorithm that usually reduces the size of the underlying graph substantially without … Read more

Solving Bin Packing Related Problems Using an Arc Flow Formulation

We present a new method for solving bin packing problems, including two-constraint variants, based on an arc flow formulation with side constraints. Conventional formulations 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 … Read more