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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Robust mixed-integer linear programming models for the irregular strip packing problem

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Cherri, Luiz H. [1] ; Mundim, Leandro R. [1] ; Andretta, Marina [1] ; Toledo, Franklina M. B. [1] ; Oliveira, Jose F. [2] ; Carravilla, Maria Antonia [2]
Total Authors: 6
[1] Univ Sao Paulo, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil
[2] Univ Porto, Fac Ingn, INESC TEC, Rua Dr Roberto Frias, P-4200465 Oporto - Portugal
Total Affiliations: 2
Document type: Journal article
Source: European Journal of Operational Research; v. 253, n. 3, p. 570-583, SEP 16 2016.
Web of Science Citations: 19

Two-dimensional irregular strip packing problems are cutting and packing problems where small pieces have to be cut from a larger object, involving a non-trivial handling of geometry. Increasingly sophisticated and complex heuristic approaches have been developed to address these problems but, despite the apparently good quality of the solutions, there is no guarantee of optimality. Therefore, mixed-integer linear programming (MIP) models started to be developed. However, these models are heavily limited by the complexity of the geometry handling algorithms needed for the piece non-overlapping constraints. This led to pieces simplifications to specialize the developed mathematical models. In this paper, to overcome these limitations, two robust MIP models are proposed. In the first model (DTM) the non-overlapping constraints are stated based on direct trigonometry, while in the second model (NFP - CM) pieces are first decomposed into convex parts and then the non-overlapping constraints are written based on nofit polygons of the convex parts. Both approaches are robust in terms of the type of geometries they can address, considering any kind of non-convex polygon with or without holes. They are also simpler to implement than previous models. This simplicity allowed to consider, for the first time, a variant of the models that deals with piece rotations. Computational experiments with benchmark instances show that NFP CM outperforms both DTM and the best exact model published in the literature. New real-world based instances with more complex geometries are proposed and used to verify the robustness of the new models. (C) 2016 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 10/10133-0 - Cutting, packing, lot-sizing and scheduling problems and their integration in industrial and logistics settings
Grantee:Reinaldo Morabito Neto
Support type: Research Projects - Thematic Grants
FAPESP's process: 12/18653-8 - Nesting Problem
Grantee:Luiz Henrique Cherri
Support type: Scholarships in Brazil - Doctorate
FAPESP's process: 14/10740-4 - Nesting Problem
Grantee:Luiz Henrique Cherri
Support type: Scholarships abroad - Research Internship - Doctorate
FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:José Alberto Cuminato
Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC