Exact methods for three-dimensional cutting and packing : a comparative study concerning single container problems.

Abstract

Three-dimensional Cutting and Packing Problems consist of a set of items that must be placed inside one or more larger items (containers). Such problems enforce non-overlapping constraints which ensure that the smaller items being assigned must completely fit inside their respective container. Despite extensive preexisting literature, there is the distinct absence of a study comparing exact methods for threedimensional Cutting and Packing Problems. Therefore, the primary ambition of the present research is to provide a comparative study of the most significant exact methods which have been designed for two variants of this problem class: the Single Large Object Placement Problem and the Single Knapsack Problem. By adapting the selected methods in accordance with the problems being analyzed, a detailed comparison is possible via experimentation using classic benchmarks datasets and newly-generated instances using a Cutting and Packing Generator from the literature. Over 15,000 h of experiments provide information concerning which methods perform best for the considered problems in addition to the scaling behavior and influence of the percentage of the larger item occupancy for each of the tested methods. These results provide further insight concerning performance improvements of existing exact methods and the development of new formulations.