On the Convexity of Discrete (r,Q) and (S,T) Inventory Systems

We consider single-item (r, Q) and (s, T ) inventory systems with discrete demand processes. While most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space, we show that these properties no longer hold in the discrete space, in the sense of linear interpolation extension and L-convexity. This nonconvexity can lead to failure of optimization techniques based on local optimality. It can also make certain comparative properties established previously using continuous variables invalid.