Mathematical models for a cutting problem in the glass manufacturing industry

Abstract

The glass cutting problem proposed for the ROADEF 2018 challenge is a two-dimensional, three-stage guillotine cutting process, with an additional cut to obtain pieces in some specific situations. However, it is not a standard problem because it includes specific constraints. The sheets produced in the glass manufacturing process have defects that make them different and have to be used in order. The pieces to be cut are grouped into subsets and the pieces from each subset must be cut in order.We approach the problem by developing and solving integer linear models. We start with the basic model, which includes the essential features of the problem, as a classical three-stage cutting problem. Then, we progressively add new conditions to consider the order in the stacks, the minimum waste produced by guillotine cuts, and the possibility of trimming in some specific cases. Finally, we deal with the existence of defects in the sheets. We propose the first integer linear model capable of working with trimming and defects. The results show that in most cases it is possible to obtain the optimal solution for small problems taking into account all the constraints of the real problem and that good feasible solutions are obtained for larger instances.