An ARIMA Supply Chain Model

This paper presents a multistage supply chain model that is based on Autoregressive Integrated Moving Average (ARIMA) time-series models. Given an ARIMA model of consumer demand and the lead times at each stage, it is shown that the orders and inventories at each stage are also ARIMA, and closed-form expressions for these models are given. The paper also discusses the causes of the bullwhip effect, a phenomenon in which variation in demand produces larger variations in upstream orders and inventory. This discussion reveals how different modeling can lead to different insights because they make different assumptions about the cause of the bullwhip effect. These observations are used to develop managerial insights about reducing the bullwhip effect.