A measure of the bullwhip effect in supply chains with stochastic lead time

In this paper, we exactly quantify the bullwhip effect, the variance amplification in replenishment orders, for cases of stochastic demand and stochastic lead time in a simple two-stage supply chain with one supplier and one retailer. In most of the previous research, the impact of order lead time on the bullwhip effect in supply chains with pre-specified demand processes is investigated mostly for cases of deterministic lead time. In this paper, we deal with a first-order autoregressive, AR(1), demand process and investigate the behavior of a measure for the bullwhip effect with respect to autoregressive coefficient and stochastic order lead time. Extension to a mixed first-order autoregressive-moving average, ARMA(1,1), demand process is also considered.