Optimal control policy for a Brownian inventory system with concave ordering cost

Abstract

In this paper we consider an inventory system with increasing concave ordering cost and average cost optimization criterion. The demand process is modeled as a Brownian motion. Porteus (1971) studied a discrete-time version of this problem and under the strong condition that the demand distribution belongs to the class of densities that are finite convolutions of uniform and/or exponential densities (note that normal density does not belong to this class), an optimal control policy is a generalized (s, S) policy consisting of a sequence of (s_i, S_i). Using a lower bound approach, we show that an optimal control policy for the Brownian inventory model is determined by a single pair (s, S).