Mathematical models and heuristic algorithms for pallet building problems with practical constraints

In the pallet building problem, we aim at loading a given set of items into one or more pallets, by satisfying specific constraints and minimizing the number of pallets used. In this paper, we address a practical case of this problem that originates from a real-world robotized application, subject to some non-trivial operational constraints. In practice, items are grouped into families and must be packed into horizontal layers. To facilitate loading/unloading operations, items of the same type packed into the same layer should be contiguous and at least one of them should be visible from the outside. We present a formal mathematical description for layer and pallet creation subproblems and then we propose heuristic, metaheuristic, matheuristic algorithms to solve the overall problem. The performance of the algorithms is assessed through extensive computational tests on real-world instances.