Three-dimensional container loading models with cargo stability and load bearing constraints

Mathematical models for the problem of loading rectangular boxes into containers, trucks or railway cars have been proposed in the literature, however, there is a lack of studies which consider realistic constraints that often arise in practice. In this paper, we present mixed integer linear programming models for the container loading problem that consider the vertical and horizontal stability of the cargo and the load bearing strength of the cargo (including fragility). The models can also be used for loading rectangular boxes on pallets where the boxes do not need to be arranged in horizontal layers on the pallet. A comprehensive performance analysis using optimization software with 100s of randomly generated instances is presented. The computational results validate the models and show that they are able to handle only problems of a moderate size. However, these models might be useful to motivate future research exploring other solution approaches to solve this problem, such as decomposition methods, relaxation methods, heuristics, among others.