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

Abstract

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.