EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 93(107), pp. 95–107 (2013)

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A NEW NONLINEAR MODEL FOR THE TWO-DIMENSIONAL RECTANGLE PACKING PROBLEM

Aleksandar Savi\c, Jozef Kratica, Vladimir Filipovic

Faculty of Mathematics, University of Belgrade, Belgrade, Serbia; Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

Abstract: This paper deals with the rectangle packing problem, of filling a big rectangle with smaller rectangles, while the rectangle dimensions are real numbers. A new nonlinear programming formulation is presented and the validity of the formulation is proved. In addition, two cases of the problem are presented, with and without rotation of smaller rectangles by $90^\circ$. The mixed integer piecewise linear formulation derived from the model is given, but with a simple form of the objective function.

Keywords: nonlinear programming; piecewise linear relaxation

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Electronic fulltext finalized on: 2 Apr 2013. This page was last modified: 8 Apr 2013.

© 2013 Mathematical Institute of the Serbian Academy of Science and Arts
© 2013 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition