Reducing order and inventory variability under stochastic lead-time and correlated demand

Logistic volatility is considered to be an important contributor to supply chain inefficiency. In this paper we investigate the amplification of order and inventory fluctuations in a state-space model with stochastic lead time, ARMA(p, q) demand and a proportional order-up-to policy. We derive the exact distribution functions for order and inventory. For i.i.d. Gaussian demand, we prove that the proportional outperforms the classical order-up-to policy in reducing inventory and order variances simultaneously. Numerical experiments are carried out to show the complex interaction between demand correlation and stochastic lead-time.