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

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Cherri, LH (Author) Other; Mundim, LR (Author) Other; Mundim, LR (Author) Other; Andretta, M (Author) Other; Andretta, M (Author) Other; Toledo, FMB (Author) Other; Toledo, FMB (Author) Other; José Fernando Oliveira (Author) FEUP; José Fernando Oliveira (Author) FEUP; Maria Antónia Carravilla (Author) FEUP; Maria Antónia Carravilla (Author) FEUP

Journal

Title: European Journal of Operational Research

Vol. 253

Pages: 570-583

ISSN: 0377-2217

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 30 Citations

Scopus - 35 Citations

Other information

Authenticus ID: P-00K-9S2

DOI: 10.1016/j.ejor.2016.03.009

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14