A heuristic approach to the three-dimensional cargo-loading problem

Abstract

Since no exact analytical method for solving the three-dimensional cargo-loading problem has been developed, the heuristic approaches with practical assumptions are still useful. A dynamic programming approach to this problem is proposed in this paper. Loading a three-dimensional cargo space is done layer by layer,a special property which is taken advantage of in the proposed algorithm. The computational performance of this heuristic is demonstrated by comparing its results with suggested values published by the General Services Administration, Washington, DC.

3-D Container Packing Heuristics

“…For homogeneous problems, because wasted space is located largely on the boundaries, a 2D recycling method was developed. Its performance surpasses that of [18] which was developed specifically for packing identical boxes. The improvements of volume utilization for the basic heuristic is about 15% for homogeneous problems and about 5% for heterogeneous problems in [29].…”

“…All boxes are identical in this problem. Compared with the volume utilization of [18] (95.75%), the volume utilization of our basic heuristic is about 82.5%. However, with application of wasted space recycling as given here, the volume utilization is boosted to 96.0%.…”

“…With this dimension fixed, the maximum number of boxes which can be accommodated in the cross-section is then determined by means of the two-dimensional packing routine. Han et al [18] provided a heuristic based on the dynamic programming method and wall-building method. In his study, the objective was to maximize the volume utilization and there were no orientation constraints.…”

Solving the Three-Dimensional Palet-Paking Problem Using Mixed 0 - 1 Model

“…The weakness in the approach of Han et al [10] is a result of maximizing the utilization of the perimeter of the "L" module. No evidence was presented to suggest why an L-shaped module approach should be adopted.…”

“…Packing where boxes do straddle between layers can produce a more cohesive load. Han, Knott and Egbelu [10] showed that the idea of walls needs not to be restricted to the vertical sides of the container. They described an algorithm in which the container (major prism) is packed with identical boxes (minor prisms).…”