Generating pallet loading patterns with considerations of item stacking on end and side surfaces

In late 1979 a two phase heuristic algorithm employing dynamic programming was presented by Steudel for solving the two-dimensional cutting stock problem where all the small rectangles were of the same dimensions, but withour any restrictions that the cutting be performed in a purely “guillotine” fashion. The algorithm was applied to solving the common problem of loading rectangular items of size l by w on a rectangular pallet of size L and W so as to maximize the number of items per layer on the pallet deckboard. In this paper, a new three-phase heuristic is presented which extends the 1979 recursive procedure and evaluates the option of stacking items on their end and/or side surface within the best loading pattern of bottom-stacked items. The resulting pattern is then projected into the third dimension to generate the total “cubic” pallet load. Computation results show that end and/or side stacking (when applicable) can yield average improvements in the range of 5% in items per pallet load.