Solving Cutting Stock Problems via an Extended Ryan-Foster Branching Scheme and Fast Column Generation

We present a branch-cut-and-price framework to solve cutting stock problems with strong relaxations using set covering (packing) formulations, which are solved by column generation. The main contributions of this paper include an extended Ryan-Foster scheme, which allows us to use this powerful branching scheme even in nonbinary problems by using a conflict propagation lemma; a fast column generation process based on a diversification strategy; custom primal heuristics, enabling us to find optimal solutions for several open instances; and a technique to use a smaller feasibility tolerance in floating-point linear programming solvers, combined with numerically safe methods to produce stronger and safer lower bounds. Additional performance-improving strategies include a technique that controls the height of the branch-and-bound tree; a variable selection algorithm based on branching history; a new set of dual inequalities; insights to obtain a lean model; and the subset-row inequalities. By employing this comprehensive framework, we overcame the current state-of-the-art concerning the following problems: cutting stock, skiving stock, ordered open-end bin packing, class-constrained bin packing, and identical parallel machines scheduling with minimum makespan. Additionally, a new challenging benchmark for cutting stock is introduced. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 312345/2023-2], the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 2015/11937-9 and 2022/05803-3], and the Fundo de Apoio ao Ensino, à Pesquisa e Extensão, Universidade Estadual de Campinas [Grant 2372/23]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0399 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0399 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .