A mixed-integer model for two-dimensional polyominoes strip packing and tiling problems Online publication date: Sun, 11-Jan-2015
by Mohamed N. Kashkoush; Mohamed A. Shalaby; Ehab A. Abdelhafiez
International Journal of Operational Research (IJOR), Vol. 15, No. 4, 2012
Abstract: Two-dimensional irregular strip packing problem is one of the common cutting and packing problems, where it is required to assign (cut or pack) a set of 2D irregular-shaped items to a rectangular sheet. The sheet width is fixed, while its length is extendable and has to be minimised. In this paper, a new mixed-integer programming (MIP) model is introduced to optimally solve a special case of the problem, where item shapes are polygons with orthogonal edges, named polyominoes. Polyominoes strip packing may be classified as polyominoes tiling; a problem that can also be handled by the proposed model. Reasonable problem sizes (e.g. 45 polyominoes inside a 10 × 25 sheet) are solvable using an ordinary PC. Larger problem sizes are expected to be solvable when using state-of-the-art computational facilities. The model is also verified via a set of benchmark problems that are collected from the literature and provided optimal solution for all cases.
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