Dynamic Programming and Inventory Control

An expository account is given of the Dynamic Programming approach to inventory analysis in terms of the problem of the optimal storage policy for repair parts. The demand distribution is assumed to be Poisson or some modification thereof; the delivery time is assumed to be fixed or Gamma distributed while preserving the sequence of the orders. No demand is lost. It is shown that the demand distribution for the delivery period is negative binomial. Formulae are derived for the re-ordering point and the order quantity and these are solved for the geometric demand distribution. An example is calculated which is based on the stocking of repair parts by a can manufacturer in Chicago.