One-dimensional multi-period cutting stock problem with two stages applied to lattice slab production

This study looks at a real-world production planning problem that arises in a Brazilian lattice slab factory. Based on its production, which comprises a process in two stages, the main concerns of the factory are the waste of steel trusses in the first stage, setups and inventory costs in the second stage. The proposed mathematical model is based on the one-dimensional multi-period cutting stock problem with two stages and aims at the minimization of setup, production and inventory costs, subject to capacity and demand balance constraints. To solve this model, different strategies based on the column generation procedure are implemented, where two sets of subproblems are used to provide cutting patterns for each stage. Then, different rounding strategies and the relax-and-fix heuristics are applied to identify integer solutions. We based the data set on real information from a specific factory and also from specialized websites. Computational results are used to evaluate the application of the proposed model in a realistic context.