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.

为ROADEF 2018挑战赛提出的玻璃切割问题是二维，三阶段断头台切割工艺，在某些特定情况下需要额外切割才能获得碎片。但是，这不是标准问题，因为它包括特定的约束。在玻璃制造过程中生产的板材具有使它们与众不同的缺陷，必须按顺序使用。要切割的片段被分组为子集，每个子​​集的片段都必须按顺序切割。

我们通过开发和求解整数线性模型来解决该问题。我们从基本模型开始，该模型包括问题的基本特征，作为经典的三阶段切割问题。然后，我们逐步添加新的条件来考虑堆叠中的顺序，断头台切割产生的最小浪费以及在某些特定情况下修边的可能性。最后，我们处理薄板中存在的缺陷。我们提出了第一个能够处理修整和缺陷的整数线性模型。结果表明，在大多数情况下，考虑到实际问题的所有约束条件，可以获得针对小问题的最佳解决方案，并且对于较大的实例，可以获得良好的可行解决方案。