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

Abstract

Stockouts are inevitable random phenomena in inventory systems when dealing with real demand. For inventory managers, knowing the size of these stockouts is crucial for designing the policy to manage the inventory system. The Expected Shortage per Replenishment Cycle (ESPRC) is the measure that models the quantity of the stockouts managers expect to have during the replenishment cycle and is an essential indicator in inventory management for several reasons. It provides information about the number of units not served in each cycle and is fundamental in determining service levels and shortage costs. Traditionally, ESPRC estimation for the continuous review base-stock policy (s, S) is based on the assumption that inventory levels reach exactly the reorder point, neglecting undershoots. This paper demonstrates that this traditional estimation is biased and proposes a new and unbiased approximation, ESPRCW. By estimating the probability vector of the stock levels at the reorder point while considering undershoots, this approach provides a more accurate estimation. The results show that ESPRCW significantly outperforms the traditional method, reducing bias and leading to better decision-making in inventory management. This improvement has substantial practical implications, such as more accurate service level calculations and optimized inventory policies, ultimately enhancing the efficiency and cost-effectiveness of inventory systems.