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About

About

Tiago Silveira has been working as a Researcher at the Federal University of Alfenas, Brazil. He has received his Ph.D. in Information Technologies at the University of Parma, Italy, working on Optimization field with cutting and packing problems.

Interest
Topics
Details

Details

  • Name

    Tiago Silveira
  • Role

    External Research Collaborator
  • Since

    11th June 2021
  • Nationality

    Itália
  • Contacts

    +351222094000
    tiago.silveira@inesctec.pt
Publications

2023

The Floating-Cuts model: a general and flexible mixed-integer programming model for non-guillotine and guillotine rectangular cutting problems

Authors
Silva, E; Oliveira, JF; Silveira, T; Mundim, L; Carravilla, MA;

Publication
OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE

Abstract
Cutting and packing problems are challenging combinatorial optimization problems that have many rel-evant industrial applications and arise whenever a raw material has to be cut into smaller parts while minimizing waste, or products have to be packed, minimizing the empty space. Thus, the optimal solution to these problems has a positive economic and environmental impact. In many practical applications, both the raw material and the cut parts have a rectangular shape, and cut-ting plans are generated for one raw material rectangle (also known as plate) at a time. This is known in the literature as the (two-dimensional) rectangular cutting problem. Many variants of this problem may arise, led by cutting technology constraints, raw-material characteristics, and different planning goals, the most relevant of which are the guillotine cuts. The absence of the guillotine cuts imposition makes the problem harder to solve to optimality.Based on the Floating-Cuts paradigm, a general and flexible mixed-integer programming model for the general rectangular cutting problem is proposed. To the best of our knowledge, it is the first mixed inte-ger linear programming model in the literature for both non-guillotine and guillotine problems. The basic idea of this model is a tree search where branching occurs by successive first-order non-guillotine-type cuts. The exact position of the cuts is not fixed, but instead remains floating until a concrete small rect-angle (also known as item) is assigned to a child node. This model does not include decision variables either for the position coordinates of the items or for the coordinates of the cuts. Under this framework, it was possible to address various different variants of the problem.Extensive computational experiments were run to evaluate the model's performance considering 16 dif-ferent problem variants, and to compare it with the state-of-the-art formulations of each variant. The results confirm the power of this flexible model, as, for some variants, it outperforms the state-of-the-art approaches and, for the other variants, it presents results fairly close to the best approaches. But, even more importantly, this is a new way of looking at these problems which may trigger even better approaches, with the consequent economic and environmental benefits.