About ten years ago, a paper proposed the first integer linear programming formulation for the constrained two-dimensional guillotine cutting problem (with unlimited cutting stages). Since, six other formulations followed, five of them in the last two years. This spike of interest gave no opportunity for a comprehensive comparison between the formulations. We review each formulation and compare their empirical results over instance datasets of the literature. We adapt most formulations to allow for piece rotation. The possibility of adaptation was already predicted but not realized by the prior work. The results show the dominance of pseudo-polynomial formulations until the point instances become intractable by them, while more compact formulations keep achieving good primal solutions. Our study also reveals a small but consistent advantage of the Gurobi solver over the CPLEX solver in our context; that the choice of solver hardly benefits one formulation over another; and a mistake in the generation of the T instances, which should have the same optima with or without guillotine cuts. Our study also proposes hybridising the most recent formulation with a prior formulation for a restricted version of the problem. The hybridisations show a reduction of about 20% of the branch-and-bound time thanks to the symmetries broken by the hybridisation.

翻译：约十年前，一篇论文首次提出了带约束的二维断头台切割问题（无限切割阶段）的整数线性规划模型。此后又涌现出六个新模型，其中五个发表于近两年。这一研究热点的迅速升温导致各模型之间缺乏全面比较。本文对每个模型进行综述，并在文献实例数据集上比较其实验结果。我们调整了多数模型以支持零件旋转——这种调整的可能性虽被前期工作预判但未实现。结果表明，伪多项式模型在实例规模可解范围内表现优越，而更紧凑的模型在实例规模超出其处理能力时仍能获得优质原始解。研究还发现：在我们的实验环境下，Gurobi求解器相对CPLEX求解器具有微小但稳定优势；求解器选择对不同模型的性能影响差异极小；此外发现了T实例生成过程中的错误——该实例集在有无断头台切割约束时应具有相同最优解。本研究还提出将最新模型与早期受限版本模型混合的策略。混合方法通过打破对称性，使分支定界时间降低了约20%。