Inventory control based on advanced probability theory, an application

Whenever stock is placed as a buffer between consumption and supply the decision when to replenish the stock is based on uncertain values of future demand and supply variables. Uncertainty exists about the replenishment lead time, about the number of demands and the quantities demanded during this period. We develop a new analytical expression for the reorder point, which is based on the desired service level and three distributions: the distribution of the quantity of single demands during lead time, the distribution of the lengths of time intervals between successive demands, and the distribution of the lead time itself. The distribution of lead time demand is derived from the distributions of individual demand quantities and not from the demand per period. It is not surprising that the resulting formulae for the mean and variance are different from those currently used. The theory developed is also applicable to periodic review systems. The system has been implemented at CERN and enables a significant enhancement of the service level, while reducing the average stock.