an:06554302
Zbl 1332.90029
Yao, Dacheng; Chao, Xiuli; Wu, Jingchen
Optimal control policy for a Brownian inventory system with concave ordering cost
EN
J. Appl. Probab. 52, No. 4, 909-925 (2015).
00351204
2015
j
90B05 90B30
Brownian inventory system; \((s, S)\) policy; concave ordering cost
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 \((s, S)\).