Exploring the structural properties of the (D, 0) inventory model

We consider the (D, 0) inventory model, where the demand per unit time, D, is stationary and independently and identically distributed (iid) and the lead time, L, is deterministic. In the case of the re-order point, order quantity (s, Q) system, where the cost function is convex in s and Q, this yields two equations that are solved iteratively to yield the optimal policy. The question that we address here concerns the effect of the variability in lead time demand on the total cost and the policy parameters. Simply stated: given other parameters, such as ordering, holding, and shortage costs, can we write the optimal total cost and the policy parameters as linear or quadratic functions of the standard deviation of demand during lead time?