Efficient management of inventory in supply chains is critical to the profitable operation of modern enterprises. The supply/demand networks characteristic of discrete-parts industries such as semiconductor manufacturing represent highly stochastic, nonlinear, and constrained dynamical systems whose study merits a control-oriented approach. Model Predictive Control (MPC) is presented in this paper as the basis for a novel inventory management policy for supply chains whose dynamic behavior can be adequately represented by fluid analogies. A Simultaneous Perturbation Stochastic Approximation (SPSA) optimization algorithm is presented as a means to obtain optimal tuning parameters for the proposed policies. The SPSA technique is capable of optimizing important system parameters, such as safety stock targets and/or controller tuning parameters. Two case studies are presented. The results of the optimization on a single-echelon system show that it is advantageous to act cautiously to forecasted information and gradually become more aggressive (with respect to factory starts) as more accurate demand information becomes available. For a three-echelon problem, the results of the optimization demonstrate that safety stock levels can be significantly reduced and financial benefit gained while maintaining robust operation in the supply chain.