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.

中文翻译：

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蜂窝纸板行业的数学优化：二维可变尺寸切割材料问题的模型


本文提出了一种混合整数线性规划模型，用于解决蜂窝纸板行业中出现的带有断头台切割的二维可变尺寸切割坯料问题。这项研究是与一家位于西班牙的公司合作开发的。目的不仅是确定切割图案，还确定要生产的面板的尺寸（宽度和长度），从而最大限度地减少材料的使用量。这个特殊问题属于涉及可变尺寸库存的切割库存问题系列，其中库存面板的尺寸事先未知，并且由模型本身确定。最近有两篇论文介绍了可变尺寸库存的裁剪问题，其中一篇针对纺织行业，另一篇针对纸板行业。本文提出了后一个领域的模型，该模型允许切割具有多种类型的物品的图案，这是事先未考虑到的功能。因此，这为模型提供了相当大的灵活性并扩大了其应用范围。此外，该模型已在其特征具有高度可变性的真实数据上得到验证。结果表明，与公司当前的运营相比，所使用的材料可以大幅减少。