Packing Rectangular Pieces--A Heuristic Approach

The following two-dimensional bin packing problems are considered. (1) Find a way to pack an arbitrary collection of rectangular pieces into an open-ended, rectangular bin so as to minimize the height to which the pieces fill the bin. (2) Given rectangular sheets, i.e. bins of fixed width and height, allocate the rectangular pieces, the object being to obtain an arrangement that minimizes the number of sheets needed. Approximation algorithms are given where the solutions are achieved with heuristic search methods. Test results are presented to support the feasibility of the methods.