A MIP-CP based approach for two- and three-dimensional cutting problems with staged guillotine cuts

  • Oliviana Xavier do NascimentoEmail author
  • Thiago Alves de Queiroz
  • Leonardo Junqueira
S.I. : CLAIO 2018


This work presents guillotine constraints for two- and three-dimensional cutting problems. These problems look for a subset of rectangular items of maximum value that can be cut from a single rectangular container. Guillotine constraints seek to ensure that items are arranged in such a way that cuts from one edge of the container to the opposite edge completely separate them. In particular, we consider the possibility of 2, 3, and 4 cutting stages in a predefined sequence. These constraints are considered within a two-level iterative approach that combines the resolution of integer linear programming and constraint programming models. Experiments with instances of the literature are carried out, and the results show that the proposed approach can solve in less than 500 s approximately 60% and 50% of the instances for the two- and three-dimensional cases, respectively. For the two-dimensional case, in comparison with the recent literature, it was possible to improve the upper bound for 16% of the instances.


Two- and three-dimensional cutting problems Guillotine cutting stage constraints Integer linear programming Constraint programming 



The authors would like to thank the Coordination for the Improvement of Higher Education Personnel (CAPES), the National Counsel of Technological and Scientific Development (CNPq - Grant 308312/2016-3), the State of Goiás Research Foundation (FAPEG), and the State of São Paulo Research Foundation (FAPESP).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Institute of Mathematics and TechnologyFederal University of GoiásCatalãoBrazil
  2. 2.Department of Production Engineering, Polytechnic SchoolUniversity of São PauloSão PauloBrazil

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