Int. J. Operational Research, Vol. 15, No. 4, 2012 391 Copyright © 2012 Inderscience Enterprises Ltd. A mixed-integer model for two-dimensional polyominoes strip packing and tiling problems Mohamed N. Kashkoush*, Mohamed A. Shalaby and Ehab A. Abdelhafiez Department of Mechanical Design and Production, Cairo University, Giza 12613, Egypt E-mail: kashkou@uwindsor.ca E-mail: mashalaby@aucegypt.edu E-mail: ehabaty@ksu.edu.sa *Corresponding author 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. Keywords: strip packing; tiling; polyominoes; 2D polygons; mixed-integer model; stock cutting. Reference to this paper should be made as follows: Kashkoush, M.N., Shalaby, M.A. and Abdelhafiez, E.A. (2012) ‘A mixed-integer model for two-dimensional polyominoes strip packing and tiling problems’, Int. J. Operational Research, Vol. 15, No. 4, pp.391–405. Biographical notes: Mohamed N. Kashkoush is currently an Assistant Lecturer at the Faculty of Engineering, Cairo University. He received his BSc in 2006 and MSc in 2010; both degrees are in Mechanical Design and Production Engineering from Cairo University with specialty in Industrial Engineering. His MSc thesis was on the application of a new particle swarm optimisation algorithm to the 2D irregular strip packing problem. His research interests include cutting and packing, integer programming, modelling of manufacturing systems, meta-heuristic optimisation algorithms, and production planning and control. Mohamed A. Shalaby is currently a Professor of IE at the Faculty of Engineering, Cairo University. He received his BSc in Production Engineering from Cairo University with Honours in 1970, an Engineering Management Diploma from the American University in Cairo in 1973, MSc and PhD