On a stochastic inventory model with a generalized holding costs

This paper is concerned with finding the optimal replenishment policy for an inventory model that minimizes the total expected discounted costs over an infinite planning horizon. The demand is assumed to be driven by a Brownian motion with drift and the holding costs (inventory and shortages) are assumed to take some general form. This generalizes the earlier work where holding costs were assumed linear. It turns out that problem of finding the optimal replenishment schedule reduces to the problem of solving a Quasi-Variational Inequality Problem (QVI). This QVI is then shown to lead to an (s, S) policy, where s and S are determined uniquely as a solution of some algebraic equations.