Mathematical optimisation in the honeycomb cardboard industry: A model for the two-dimensional variable-sized cutting stock problem

Abstract

This paper presents a mixed-integer linear programming model for a two-dimensional variable-sized cutting stock problem with guillotine cuts that arises in the honeycomb cardboard sector. This research is developed in collaboration with a company based in Spain. The aim is not only to define the cutting patterns but also to establish the dimensions (width and length) of the panels to be produced, in such a way that the amount of material used is minimised. This particular problem belongs to the family of Cutting Stock Problems involving a Variable-Sized Stock, where the size of the panels in stock is not known in advance and is determined by the model itself. Cutting Stock Problems with Variable Sized Stock have recently been introduced in two papers, one of them in the textile sector and the other in the cardboard sector. This paper proposes a model for the latter sector that allows cutting patterns with more than one type of item, a feature that has not been considered beforehand. This, therefore, provides considerable flexibility to the model and broadens its range of applications. Moreover, the model has been validated on real data with high variability in its characteristics. The results indicate that the material used can be drastically reduced compared to the company’s current operation.