1. A new nonlinear model for the two-dimensional rectangle packing problem
- Author
-
Jozef Kratica, Aleksandar Savić, and Vladimir Filipović
- Subjects
Piecewise linear function ,Combinatorics ,Integer ,General Mathematics ,Largest empty rectangle ,Applied mathematics ,Rectangle ,Computer Science::Computational Geometry ,Rectangle method ,Rotation (mathematics) ,Real number ,Nonlinear programming ,Mathematics - 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?. The mixed integer piecewise linear formulation derived from the model is given, but with a simple form of the objective function.
- Published
- 2013