The effect of lead-time variability on inventory: expected on-hand inventory vs. safety stock

Many papers and textbooks use safety stock as the inventory performance measure. But, this is only an approximation. Moreover, the lead-time variability causes conflicting effects on safety stock. In this paper, we argue that the right performance measure should be the expected on-hand inventory, which is consistent with the standard newsvendor problem. Then, the results always call for lead-time variability reduction, which always reduces both the expected on-hand inventory and the expected shortage inventory. These results are consistent and also indicate increased fill rates or service levels. We further show that the expected on-hand inventory and the expected shortage inventory are convex functions. When lead-time variability increases, lead-time demand spreads out further to both left and right tails, and thus causes higher expected on-hand inventory, higher expected shortage inventory, and higher cost. We finally present numerical examples to show managerial insights for decision makers in industry.