Recursive behavior of safety stock reduction: The effect of lead-time uncertainty

Motivated by a recent paper on the effect of lead-time variability reduction on safety stocks, we provide evidence of the recursive nature of safety stock changes. When lead times follow a gamma distribution we demonstrate that, for cycle service levels between .60 and .70, the reduction of lead-time variability will first increase safety stock and then either recursively decrease safety stock or make it remain constant. We also numerically show the existence of the recursive effect. A two-by-two matrix is introduced to assist managers in making decisions regarding safety stock policy.