On properties of discrete (r, q) and (s, T) inventory systems

We consider single-item (r, q) and (s, T) inventory systems with integer-valued demand processes. While most of the inventor y literature studies continuo us 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 extensio n and L-convexity. This nonconvexity can lead to failure of optimi zation techniques based on local optimality to obtain the optimal inventory policies. It can also make certain comparative properties establishe d previously using continuous variables invalid. We revise these properties in the discrete space. 2013 Elsevier B.V. All rights reserved.