Cutting Stock with Binary Patterns: Arc-flow Formulation with Graph Compression

TL;DR

This paper introduces an exact arc-flow formulation with graph compression for solving the binary cutting stock problem, offering a compact representation of patterns and comparing it to traditional column generation methods.

Contribution

The paper proposes a novel arc-flow formulation with graph compression for 0-1 CSP, providing an efficient exact solution approach and a computational comparison with Gilmore-Gomory's method.

Findings

Arc-flow approach yields a compact graph representation.

Computational results show competitive performance with Gilmore-Gomory's approach.

The method effectively solves 0-1 CSP instances.

Abstract

The cutting stock problem with binary patterns (0-1 CSP) is a variant of CSP that usually appears as a relaxation of 2D and 3D packing problems. We present an exact method, based on an arc-flow formulation with side constraints, for solving 0-1 CSP by simply representing all the patterns in a very compact graph. Gilmore-Gomory's column generation approach is usually used to compute strong lower bounds for 0-1 CSP. We report a computational comparison between the arc-flow approach and the Gilmore-Gomory's approach.