The two-dimensional cutting stock problem with usable leftovers: mathematical modelling and heuristic approaches

Different variations of the classic cutting stock problem (CSP) have emerged and presented increasingly complex challenges for scientists and researchers. One of these variations, which is the central subject of this work, is the two-dimensional cutting stock problem with usable leftovers (2D-CSPUL). In these problems, leftovers can be generated to reduce waste. This technique has great practical importance for many companies, with a strong economic and environmental impact. In this paper, a non-linear mathematical model and its linearization are proposed to represent the 2D-CSPUL. Due to the complexity of the model, a heuristic procedure was also proposed. Computational tests were performed with instances from the literature and randomly generated instances. The results demonstrate that the proposed model and the heuristic procedure satisfactorily solve the problem, proving to be adequate and beneficial tools when applied to real situations.