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Irregular packing: MILP model based on a polygonal enclosure

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  • Miguel Santoro
  • Felipe Lemos

Abstract

This paper addresses the two-dimensional irregular packing problem, also known as the nesting problem. This is a subset of cutting and packing problems of renowned practical and theoretical relevance. A mixed integer-linear programming formulation is proposed to optimize the packing of particular polygonal shapes, convex forms with 3–8 sides, since their opposite sides are parallel. The model can be used to pack enclosures of general irregular shapes, generating upper bounds to the optimal solutions. The model was tested with 270 mass generated instances of small dimensions. Copyright Springer Science+Business Media New York 2015

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  • Miguel Santoro & Felipe Lemos, 2015. "Irregular packing: MILP model based on a polygonal enclosure," Annals of Operations Research, Springer, vol. 235(1), pages 693-707, December.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:693-707:10.1007/s10479-015-1971-9
    DOI: 10.1007/s10479-015-1971-9
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    Cited by:

    1. Germán Pantoja-Benavides & David Álvarez-Martínez & Francisco Parreño Torres, 2024. "The Normalized Direct Trigonometry Model for the Two-Dimensional Irregular Strip Packing Problem," Mathematics, MDPI, vol. 12(15), pages 1-25, August.
    2. Leao, Aline A.S. & Toledo, Franklina M.B. & Oliveira, José Fernando & Carravilla, Maria Antónia & Alvarez-Valdés, Ramón, 2020. "Irregular packing problems: A review of mathematical models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 803-822.
    3. Lastra-Díaz, Juan J. & Ortuño, M. Teresa, 2024. "Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts," European Journal of Operational Research, Elsevier, vol. 313(1), pages 69-91.

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