The dataset presented is part of the one used in the paper "A heuristic algorithm to improving the coil slitting process in the steel industry" by Óscar Soto-Sánchez, María Sierra-Paradinas, Micael Gallego, Antonio Alonso-Ayuso, Francisco Gortázar submitted for publication (2024). This paper, which is currently under review, proposes a heuristic algorithm for a cutting stock problem in the steel industry. This problem occurs in a Spanish company and the proposed algorithm is currently in production after being validated on real company data and compared with an exact mixed integer linear optimization model (MILO). The dataset presented here includes twenty instances used in the paper (the rest cannot be presented for confidentiality reasons). For each instance, the order and coil characteristics are provided, as well as the compatibility between these two. Finally, for each instance, the solution of the model, the heuristic algorithm, and the hybrid algorithm are provided. The content of the zenodo repository consists of a Dataset.zip file and a README.pdf file (this file explains the entire content of the dataset). The Dataset.zip file contains the instances, the solutions and the README.md and README.pdf files. Therefore, it is only necessary to download the Dataset.zip file.