A top-down cutting approach for modeling the constrained two- and three-dimensional guillotine cutting problems

Abstract

In this article, we address the Constrained Two-dimensional Guillotine Cutting Problem (C2GCP) and the Constrained Three-dimensional Guillotine Cutting Problem (C3GCP). These problems consist of cutting a rectangular two-/three-dimensional object with orthogonal guillotine cuts to produce ordered rectangular two-/three-dimensional items seeking the most valuable subset of items cut. They often appear in manufacturing settings that cut objects to produce item types of low demand, such as in the cutting of flat glass in the glass industry, rocks in the granite and marble industries and steel blocks in the metallurgical industry. To model and solve these problems, we propose a novel top-down cutting approach that leads to effective mixed integer linear programming models for the C2GCP and the C3GCP. The insight of the proposed approach is to represent the cutting pattern as a binary tree, in which the root node is the object, and branches correspond to guillotine cuts. The results of computational experiments with a general-purpose optimization solver and using three sets of benchmark instances showed that the proposed models are competitive with state-of-the-art formulations of the C2GCP and the C3GCP in quality of solution and processing times, particularly when the number of items in an optimal solution is moderate.

Keywords:

• Cutting and packing
• 2D and 3D guillotine cutting
• non-staged patterns
• mixed-integer linear programming models
• top-down cutting

Acknowledgements

The authors would like to thank the National Council for Scientific and Technological Development (CNPq-Brazil) [grant number 200745/2018-2] and the São Paulo Research Foundation (FAPESP-Brazil) [grant numbers 16/08039-1, 16/01860-1] for the financial support. This study was financed in part by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. Research carried out using the computational resources of the Center for Mathematical Sciences Applied to Industry (CeMEAI) funded by FAPESP-Brazil [grant number 13/07375-0]. The authors are grateful to the two anonymous reviewers for their valuable comments and suggestions of revisions.

Disclosure statement

No potential conflict of interest was reported by the authors.