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Optimal control policy for a Brownian inventory system with concave ordering cost. (English) Zbl 1332.90029
Summary: 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 $$(s, S)$$.

##### MSC:
 90B05 Inventory, storage, reservoirs 90B30 Production models
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##### References:
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