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We present a branch-cut-and-price framework to solve Cutting Stock Problemswith strong relaxations using Set Covering (Packing) Formulations, which aresolved by column generation. The main contributions of this paper include anextended Ryan-Foster scheme, which allows us to use this powerful branchingscheme even in non-binary problems by using a conflict propagation lemma; afast column generation process based on a diversification strategy; customprimal heuristics, enabling us to find optimal solutions for several openinstances; and a technique to use a smaller feasibility tolerance infloating-point linear programming solvers, combined with numerically safemethods to produce stronger and safer lower bounds. Additionalperformance-improving strategies include a technique that controls the heightof the branch-and-bound tree; a variable selection algorithm based on branchinghistory; a new set of dual inequalities; insights to obtain a lean model; andthe subset-row inequalities. By employing this comprehensive framework, weovercame the current state-of-the-art concerning the following problems:Cutting Stock, Skiving Stock, Ordered Open-End Bin Packing, Class-ConstrainedBin Packing, and Identical Parallel Machines Scheduling with Minimum Makespan.Additionally, a new challenging benchmark for Cutting Stock is introduced.

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