A simple and effective recursive procedure for the manufacturer's pallet loading problem

Abstract

In this paper we present a simple and effective heuristic to solve the problem of packing the maximum number of rectangles of sizes lY w and wY l into a larger rectangle LY W without overlapping. This problem appears in the loading of identical boxes on pallets, namely the manufacturer's pallet loading (MPL), as well as in package design and truck or rail car loading. Although apparently easy to be optimally solved, the MPL is claimed to be NP-complete and several authors have proposed approximate methods to deal with it. The procedure described in the present paper can be seen as a re®nement of Bischoff and Dowsland's heuristic and can easily be implemented on a microcomputer. Using moderate computational resources, the procedure was able to ®nd the optimal solution of 99.9% of more than 20 000 examples analysed.

Solving the pallet loading problem

“…There is no a priori limitation on the number of recursive calls. The heuristic proposed by Morabito and Morales (1998), referred to here as M&M, uses 1st-order cuts and generates 1st-order patterns. A 1st-order pattern is a pattern generated by successive guillotine or 1st-order cuts.…”

“…The Higher-Order Non-Guillotine (HONG) heuristics look for arrangement similar to the optimal eight-block arrangement found by Morabito and Morales (1998) for instance (43,26,7,3). The HONG heuristics divide the pallet into at most eight blocks, distributed as shown in Fig.…”

Method of sentinels for packing items within arbitrary convex regions

“…One of the most popular and useful problem in this area is to find the maximum number of rectangles that can be orthogonally packed into a larger rectangle. Polynomial algorithms for the guillotine version of the problem exist (Tarnowski et al, 1994) whereas the NP-completeness of the non-guillotine problem has been conjectured (Dowsland, 1987;Morabito and Morales, 1998). In (Lins et al, 2003; c ) a very efficient heuristic to solve this problem was introduced.…”

Orthogonal packing of identical rectangles within isotropic convex regions

“…When the convex region takes the particular form of a rectangle, we are faced with the well known pallet loading problem [6,14,20,30], for which dedicated solution methods exist. Numerical experiments presented in [9] show that nonlinear-based methods, such as the one presented here, are not competitive with clever methods developed for this particular case.…”