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1 results

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

  • Part of
  • Dacheng Yao, Xiuli Chao, Jingchen Wu
  • Journal:
    Journal of Applied Probability / Volume 52 / Issue 4 / December 2015
    Published online by Cambridge University Press:
    30 March 2016, pp. 909-925
    Print publication:
    December 2015
    • Article
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  • 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 (si, Si). 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).