  Packing rings into a minimum number of rectangles is an optimization problem
which appears naturally in the logistics operations of the tube industry. It
encompasses two major difficulties, namely the positioning of rings in
rectangles and the recursive packing of rings into other rings. This problem is
known as the Recursive Circle Packing Problem (RCPP). We present the first
dedicated method for solving RCPP that provides strong dual bounds based on an
exact Dantzig--Wolfe reformulation of a nonconvex mixed-integer nonlinear
programming formulation. The key idea of this reformulation is to break
symmetry on each recursion level by enumerating one-level packings, i.e.,
packings of circles into other circles, and by dynamically generating packings
of circles into rectangles. We use column generation techniques to design a
"price-and-verify" algorithm that solves this reformulation to global
optimality. Extensive computational experiments on a large test set show that
our method not only computes tight dual bounds, but often produces primal
solutions better than those computed by heuristics from the literature.
