In this article, we emphasize on one hand the importance of quantifying the shortage cost in order to measure the optimal parameters for any selected inventory policy and thus enhance the performance of the supply chain and on the other hand the complexity of doing so. Then, we provide a detailed literature review of the existing various models for quantifying the shortage cost in an inventory management context along with a classification of this literature under three categories: Theoretical descriptive models, empirical approaches and simulation based models. Finally, we point out some gaps in this literature such as the lack of continuity of research in this field and the absence of generic fairly easy to apply but accurate methods and we suggest a few future perspectives.