A Branch-and-Cut-and-Price Algorithm for Cutting Stock and Related Problems

Abstract

In this project, we introduce a branch-and-cut-and-price framework to solve the Cutting Stock Problems with strong relaxations using the Set Covering (Packing) Formulations, which are solved through column generation. We propose an extended Ryan-Foster branching scheme tailored to non-binary models, a pricing algorithm that produces convergence in a few iterations, and a variable selection technique based on branching history. These strategies are combined with subset-row cuts and custom primal heuristics to create a framework that overcomes the current state-of-the-art of Cutting Stock Problem, Skiving Stock Problem, and other related problems, being at least twice faster in the first problem and at least 60% faster in the second one.