Continuous Review Model - Lost Sales Case: Risk Perspective

Inventory systems play a significant role within the modern supply chain. Models for managing inventory have received considerable attention. Most developed models concentrate on the expected inventory cost with limited attention to total cost variation, which indicates risk. Total inventory cost is a random variable that fluctuates around its mean (the expected cost). In real-world practices, accounting systems record and follow the total cost, not the expected cost. Therefore, this variation is important as it represents the actual inventory costs encountered at any used inventory policy. This work considers the continuous review model where orders are lost and where a cost function that addresses risk is developed. The total inventory cost function developed allows for evaluating inventory costs at certain multiple standard deviations away from the mean, which shows the actual variation the inventory cost experiences upon adopting a specific inventory policy. The optimal inventory policy was determined at a certain confidence level and compared to the policy derived using expectation. Results show that the optimal policies obtained do not need to be identical. However, we managed to show that both policies are almost the same under certain conditions. Moreover, we managed to extract the boundary limits of variation of the total cost. Results are developed analytically and validated independently through simulation.