This paper presents a model predictive control (MPC) approach for production and inventory control systems. Model predictive control previously has been successfully applied to supply chain problems; however most systems that have been proposed so far possess no information on future demand. The incorporation of a forecasting methodology in an MPC framework can promote the efficiency of control actions by providing more insights in the future demands. In this paper, we investigate the applicability of advanced and traditional methods to forecasting lumpy demand at supply chains. Neural networks can be better model for forecast the nonlinear and chaotic behavior of lumpy demands in comparison with traditional and usual methods such as exponential smoothing. This paper efficiently employs neural networks as the main core in the proposed control design. To highlight efficiency of the proposed method, real datasets are used for investigation and comparison studies.