The effect of lead-time on the supply chain: The mean versus the variance

In a study on stochastic inventory systems, Chopra et al. (Decision Sciences 35(1) (2004) 124) argue that decreasing lead time is the right lever if they want to cut inventories, not reducing lead time variability. According to Chopra et al., reducing the mean lead time, μ, is more important than reducing the lead time variance, σ², to reduce total inventory cost via a reduced safety stock. This paper is a criticism of Chopra et al., where the optimal z was derived based upon a predetermined Q, instead of solving the optimal z and Q simultaneously in a (z, Q) inventory system. We argue that such an approach is inappropriate because the two decision variables, z and Q, are in general interdependent, and, moreover, reducing reorder point (safety stock), z, does not necessarily decrease the total inventory cost. We demonstrate by means of a truncated lead time (z, Q) model that it is lead time variability, not mean lead time, that affects the inventory policy and total supply chain cost.