Optimal policies for inventory systems with concave ordering costs

In this paper we study the structure of optimal policies for periodic review inventory systems with concave ordering costs and general demand distributions. By extending the Scarf (1959) model to systems with piecewise linear concave ordering costs, we show that, except for a bounded region, the generalized (s, S) policy is optimal. We do so by (a) introducing the notion of c-convexity and (b) proving a conditional monotonicity property for the optimal order-up-to levels. We also provide conditions under which the generalized (s, S) policy is optimal for all regions of the state space.