Improving expected shortage estimations in the base-stock policy by accounting for undershoots

Abstract

[EN] Shortage events are inevitable random phenomena in inventory systems when dealing with real demand. For inventory managers, knowing the size of these shortages becomes crucial to deciding the optimal policy for the inventory system. Therefore, the Expected Shortage per Replenishment Cycle, ESPCR, is an essential indicator in inventory management for several reasons. On the one hand, it gives information about the number of units not served in each cycle, and on the other hand, it is fundamental in determining service levels or shortage costs. Therefore, ESPCR estimation for the continuous review base-stock policy (s, S) is traditionally based on the assumption that inventory levels reach exactly the reorder point, i.e., inventory levels are never below the reorder point, and undershoots are not considered. This paper shows that the traditional estimation based on neglecting undershoots is biased and proposes a new and unbiased approximation, ESPCRW. This approach is based on estimating the probability vector of the stock levels at the reorder point considering the presence of undershoots. Results of this paper show that our approach outperforms the biased nature of the traditional approximation, which may have significant practical implications for the inventory systems.