Aggregated Information in Supply Chains

Abstract

We study a two-stage supply chain where the retailer observes two demand streams coming

from two consumer populations. We further assume that each demand sequence is a station- ary Autoregressive Moving Average (ARMA) process with respect to a Gaussian white noise

sequence (shocks). The shock sequences for the two populations could be contemporaneously correlated. We show that it is typically optimal for the retailer to construct its order to its supplier based on forecasts for each demand stream (as opposed to the sum of the streams) and that doing so is never sub-optimal. We demonstrate that the retailer’s order to its supplier is ARMA and yet can be constructed as the sum of two ARMA order processes based upon the two populations. When there is no information sharing, the supplier only observes the retailer’s order which is the aggregate of the two aforementioned processes. In this paper, we determine when there is value to sharing the retailer’s individual orders, and when there is additional value to sharing the retailer’s individual shock sequences. We also determine the supplier’s mean squared forecast error under no sharing, process sharing, and shock sharing.