A New Upper Bound for the Cylinder Packing Problem

Abstract

This paper introduces a new upper bound to the problem of fitting identical circles into a rectangle. This problem is usually referred to as the ‘cylinder packing problem’ or ‘cylinder palletization’. In practice, it arises when it is desired to maximize the number of cylindrical items packed in an upright position onto a rectangle/pallet. The upper bound developed consists in determining the reduced pallet area by deducting a lower bound for the unused pallet area from the total area of the pallet. The upper bound for the number of identical circles to pack into the pallet is computed by the ratio reduced pallet area/circle area . The results obtained for five distinct sets of problems are analyzed and compared with previous bounds found in the published literature.