Comparative analysis of mathematical formulations for the two‐dimensional guillotine cutting problem

Abstract

About 15 years ago, a paper proposed the first integer linear programming formulation for the constrained two‐dimensional guillotine cutting problem (with unlimited cutting stages). Since then, eight other formulations followed, seven of them in the last four 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 mistake in the generation of the T instances, which should have the same optima with or without guillotine cuts. We also propose hybridising a 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.

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“…These algorithms apply a series of predetermined rules to dictate the layout and specifications of drainage systems, with the goal of enhancing efficiency and reducing material waste. In particular, Integer Programming (IP) has been used to address the Cutting Stock Problem (CSP) which optimizes material usage in manufacturing [15,16]. However, the interdisciplinary nature of these developments has resulted in a focus on enhancing explainability.…”