A matheuristic framework for the Three-dimensional Single Large Object Placement Problem with practical constraints

•Well-performing matheuristic considering multiple practical constraints.•Structured in an easy way to include or remove new constraints.•Directly adaptable to consider different problem variants. The Three-dimensional Single Large Object Placement Problem consists of a set of weakly heterogeneous items that must be placed inside a single larger object without overlapping each other. Many constraints can be considered depending on the practical specifications of the problem being solved, such as orientation, stability, weight limit and positioning. Although this is a well-known problem which has received considerable academic attention, most of the research limits itself to considering only three basic constraints: non-overlap, orientation and stability of the placed items. Recent literature concerning the problem has indicated that there is a pressing need for solution methods which consider a more realistic number of sets of practical constraints given that it is very uncommon to find real-world situations where only a few of these constraints are considered together. Therefore, this paper introduced a well-performing matheuristic framework which considers multiple practical constraints: orientation, load balance, loading priorities, positioning, stability, stacking and weight limit. An extension of the developed method considering multiple containers is also discussed. Results are compared against the state of the art from the literature and demonstrate the robustness of the proposed matheuristic with respect to different combinations of constraints.