Evolution of ARMA Demand in Supply Chains

This paper shows that an ARMA demand generates an ARMA order history when ordering decisions are made based on an order-up-to policy. The order history preserves the autoregressive structure of the demand and transforms its moving average structure according to a simple algorithm. We apply this ARMA-in-ARMA-out property to examine the evolution of the demand signal in supply chains. Its practical implications are discussed in the context of quantifying the bullwhip effect, coordinating forecasting, and evaluating information sharing.