Packing and stacking rings into rectangular bins

In this paper, we propose a new variant of the circular packing problem whose objective is to pack rings with unequal outer and inner radii into larger rings and finally into rectangular bins of unequal sizes. This problem arises in industrial contexts where rings are cut from rectangular raw material. We divide this problem into three partial problems, formulate a model for these partial problems and provide heuristic algorithms. Our algorithms are based on some simplifications that make it possible to identify eco-efficient packing layouts also for large numbers of ring sizes and moderate numbers of bin sizes. In a computational evaluation of our algorithms, we demonstrate that the packing problem can be solved in approximately 70 seconds on average when 7,500 rings with 50 different outer circle sizes are packed into bins of seven different sizes.