Generating Pallet Loading Patterns: A Special Case of the Two-Dimensional Cutting Stock Problem

Abstract

A heuristic algorithm employing dynamic programming is presented for solving the two-dimensional cutting stock problem where all the small rectangles are of the same dimensions, but without the usual restriction that the cutting be done with “guillotine” cuts, i.e., cut which must be made in stages from one edge to the opposite edge of the large rectangle being cut. The objective of the algorithm is to determine a cutting or layout pattern for which the ratio of the unused area to the total area of the large rectangle tends to be small. To demonstrate the method, the common problem of establishing standardized loading patterns for rectangular items on pallets is examined in detail. The algorithm is described with a minimum of mathematics through the use of several pictorial displays and a simple example. The efficiency of the heuristic is then evaluated by comparing computer generated loading patterns for 182 different size items to the loading patterns recommended by the U.S. Navy, and shown to be 10.4 percent more efficient for 64 out of 182 cases when the number of items per layer were not identical. The algorithm is also shown to be an effective aid to management both in establishing standardized loading patterns and procedures, and in communicating these loading standards to production personnel via computer generated “shop paper.” This type of computer design flexibility and control is a valuable management tool not only for standardizing pallet arrangements, but for carton design and consolidation, warehouse design and layout, bin and shelf stocking, designing tapes for numerically controlled gas cutting machines, and numerous other industrial problems involved with the efficient layout of rectangular objects.