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

•Two new nesting MIP models are proposed, compared and assessed.•Direct geometry and no-fit-polygon convex decomposition are used.•General models as they easily support pieces with complex geometries.•Easier to implement than previous models in the literature.•Outperform the best exact approach know...

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Vydané v:European journal of operational research Ročník 253; číslo 3; s. 570 - 583
Hlavní autori: Cherri, Luiz H., Mundim, Leandro R., Andretta, Marina, Toledo, Franklina M.B., Oliveira, José F., Carravilla, Maria Antónia
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 16.09.2016
Elsevier Sequoia S.A
Predmet:
Algorithms
Cutting
Cutting stock problem
Geometry
Handling
Heuristic
Integer programming
Linear programming
Mathematical models
MIP models
Nesting
Operational research
Optimization algorithms
Packing
Packing problem
Polygons
Strip
Studies
Nesting
Cutting
Packing
MIP models
ISSN:0377-2217, 1872-6860
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Shrnutí:•Two new nesting MIP models are proposed, compared and assessed.•Direct geometry and no-fit-polygon convex decomposition are used.•General models as they easily support pieces with complex geometries.•Easier to implement than previous models in the literature.•Outperform the best exact approach known in the literature. 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.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2016.03.009