Analytical Solution of Safety Stock Determination in Case of Uncertain Unimodal Lead-Time Demand

Gerrit Karel Janssens, Lotte Verdonck, Katrien Ramaekers


As companies state that a delivery service is important to their customers, an out-of-stock is considered harmful and therefore they keep safety stock in case of uncertain demand. For decision making on the level of safety stock a complete formulation of the distributional form of the demand during lead time is required. In practice, this information may not be available. In such a case, only partial information on the distribution might be available, such as the range, the mode, the mean or the variance. Given a value for a service performance measure, the decision maker, in this case, is not confronted with a single value for the safety stock but rather with an interval. The present research shows how upper and lower bounds of the safety stock are obtained in an analytical way, given a pre-specified service level using a service performance measure, called ‘expected number of units short’. The technique is also illustrated and compared within the framework of the research.


Inventory management; uncertain demand; safety stock; unimodal distributions

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DOI: 10.7250/itms-2018-0012


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