In this paper, a robustified control technique is applied to a production-inventory system. A linear model is considered for the demand/inventory system with a variable dead-time and a variable yield. The inventory is firstly controlled with a MPC (Model Predictive Control) law designed for some nominal values of the delay and yield. Using a Youla parameter-based procedure, this initial controller is robustified towards different types of uncertainties in order to manage the possible variations of the yield and of the dead-time. The robustification problem leads to a convex optimization, solved with LMI (Linear Matrix Inequality) tools. This robustified controller is further compared to another MPC law, which is slower, but remains stable for all the considered variations of the uncertain parameters. Therefore a trade-off between robust stability towards parametric uncertainties and nominal performances for the nominal system is highlighted.