The concept of semi-variance as a tool for safety inventory decisions in case of uncertain demand

Abstract

An inventory system containing uncertainty, e.g. in demand or in lead-time requires to determine a safety inventory for re-ordering. The decision models need a probability distribution of the demand during lead-time. In the literature on inventory control, mostly a Normal distribution for describing this demand is assumed. Based on the knowledge of the variance and on the distribution assumption, the safety inventory is calculated, given a prescribed customer service level. However, the functional form of the probability distribution in practice might look different from the shape of a Normal distribution and by this wrong decisions are made which result in high costs or low service level. It is investigated here whether the use of semi-variance is more robust to a deviation in the shape from the Normal distribution. The determination of the safety inventory is worked out for a triangular distribution as an illustrative example.