The use of semi-variance for safety inventory determination in case of uncertain Compound Poisson distributed demand

Abstract

An inventory system containing uncertainty in demand during lead-time requires to determine a safety inventory for re-ordering. Many textbooks on inventory control propose to use a Normal distribution for describing the demand during lead-time. Based on the knowledge of the standard deviation and on the distribution assumption, the safety inventory is calculated, given a prescribed customer service level. In case the real distribution is different from the Normal distribution, errors in the obtained service level may occur and, by this, also in the incurred cost. In other disciplines other risk measures than the standard deviation have been used. One of these is the concept of semi-variance. This research investigates whether the use of semi-variance is a valid alternative for the standard deviation in the determination of safety stock. The investigation is tested on compound Poisson distributed lead-time demand.