Mathematical model to the irregular strip packing problem with continuous rotations

Resumo

In the irregular strip packing problems a set of convex and non-convex two-dimensional pieces must be cut from a board with fixed height and infinite length aimming to reduce the length of the board used to cut all the pieces. These problems arise in many industries as garment manufacturing, metal mechanic, furniture, footwear, among others.

An important characteristic observed in real applications, mainly in the leather and metal industry, is the possibility of rotate the pieces by any angle to be placed in the board. Mixed integer non-linear models to irregular strip packing problems with continuous rotations were proposed by some authors as [4], [2], [3] and [5].

In this study, a mathematical formulation for the irregular strip packing problem with continuous rotations of the pieces is proposed and solved by exact methods proposed in the free academic solvers COUENNE, SCIP and BARON. The formulation has linear and quadratic constraints and can handle with non-convex pieces.