An extension of Queiroz and Miyazawa's method for vertical stability in two-dimensional packing problems to deal with horizontal stability

A method to handle the cargo horizontal stability in two-dimensional packing problems is proposed. Mechanical equilibrium concepts are used to assess the cargo stability at which vertical and horizontal forces act on packing. The proposed method improves the methods based on either a support factor for an item's lateral sides or the number of supporting sides that cannot guarantee the stability. The method deals with the horizontal stability for which there is no other method based on the mechanical equilibrium. It is proved that the proposed method has the worst-case time complexity of , therefore improving a previous result in the literature. Numerical experiments are provided over instances of the two-dimensional knapsack problem. For that, an exact two-level algorithm is developed and it obtained the optimal stable solution of of the instances.