A mixed‐integer model for two‐dimensional polyominoes strip packing and tiling problems

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.