Efficient Algorithm Based on Adaptive Window–Model Predictive Control for Automatic Stacking in Warehouse Center

In this article, three-dimensional (3D) stacking problem, as a mandatory task in the warehouse distribution centers, is smartly represented by a new mathematical formulation. A model predictive control (MPC) scheme is proposed to optimally solve the problem. The MPC cost function consists of several sequential criteria to suitably put the incoming packages on the dedicated cart and fully use up the cart capacity as much as possible. The practical and hard constraints are taken into consideration without confronting with a complicated optimization problem. A theorem is presented to guarantee the constraints satisfaction. Regarding the burden of computations, the proposed strategy is efficiently applicable to large carts by introducing the adaptive window (AW) idea. The efficacy of the proposed AW-MPC framework is shown by a numerical case study.