On the choice of a demand distribution for inventory management models

Abstract

An inventory system containing uncertainty, e.g., in demand, in costs, in lead time, or in supplied quantity or quality, needs a probability distribution of demand for reorder point models. In the literature on inventory control, many times reference is made to the Normal or Gamma distribution for describing the demand in the lead time. The Poisson distribution has been found to provide a reasonable fit when the demand is very low. However, information about the functional form of the probability distribution is often incomplete in practice. For example, it might be that only the first moments of the probability distribution are known. This incomplete information is a problem as the shape of the distribution is important in terms of the performance of inventory control. A procedure is described to determine shape characteristics when only the first two moments of the distribution of demand during the lead time are known, using a compound Poisson distribution and the Pearson chart. [Received 18 August 2006; Revised 15 November 2007; Accepted 11 February 2008]