The IMF Working Papers series is designed to make IMF staff research available to a wide audience. Almost 300 Working Papers are released each year, covering a wide range of theoretical and analytical topics, including balance of payments, monetary and fiscal issues, global liquidity, and national and international economic developments.
This paper analyzes the stochastic inventory control problem when the demand distribution is not known. In contrast to previous Bayesian inventory models, this paper adopts a non-parametric Bayesian approach in which the firm’s prior information is characterized by a Dirichlet process prior. This provides considerable freedom in the specification of prior information about demand and it permits the accommodation of fixed order costs. As information on the demand distribution accumulates, optimal history-dependent (s,S) rules are shown to converge to an (s,S) rule that is optimal when the underlying demand distribution is known.