The Normalized Direct Trigonometry Model for the Two-Dimensional Irregular Strip Packing Problem

Germán Pantoja-Benavides, David Álvarez-Martínez () and Francisco Parreño Torres
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Germán Pantoja-Benavides: School of Engineering, Los Andes University, Bogota 111711, Colombia
David Álvarez-Martínez: School of Engineering, Los Andes University, Bogota 111711, Colombia
Francisco Parreño Torres: Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, Spain

Mathematics, 2024, vol. 12, issue 15, 1-25

Abstract: Background: The Irregular Strip Packing Problem (ISPP) involves packing a set of irregularly shaped items within a strip while minimizing its length. Methods: This study introduces the Normalized Direct Trigonometry Model (NDTM), an innovative enhancement of the Direct Trigonometry Model (DTM). The NDTM incorporates a distance function that supports the integration of the separation constraint, which mandates a minimum separation distance between items. Additionally, the paper proposes a new set of constraints based on the bounding boxes of the pieces aimed at improving the non-overlapping condition. Results: Comparative computational experiments were performed using a comprehensive set of 90 instances. Results show that the NDTM finds more feasible and optimal solutions than the DTM. While the NDTM allows for the implementation of the separation constraint, the number of feasible and optimal solutions tends to decrease as more separation among the items is considered, despite not increasing the number of variables or constraints. Conclusions: The NDTM outperforms the DTM. Moreover, the results indicate that the new set of non-overlapping constraints facilitates the exploration of feasible solutions at the expense of optimality in some cases.

Keywords: Irregular Strip Packing Problem; mixed-integer linear programming; separation constraint (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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