Forecasting and information sharing in supply chains under ARMA demand

Abstract

This article considers the problem of determining the value of information sharing in a multi-stage supply chain in which the retailer faces AutoRegressive Moving Average (ARMA) demand, all players use a myopic order-up-to policy, and information sharing can only occur between adjacent players in the chain. It is shown that an upstream supply chain player can determine whether information sharing is of any value directly from the parameters of the model for the adjacent downstream player's order. This can be done by examining the location of the roots of the moving average polynomial of the model for the downstream player's order. If at least one of these roots is inside the unit circle or if the polynomial is applied to a lagged set of the downstream player's shocks, there is value of information sharing for the upstream player. It is also shown that under credible assumptions, neither player k−1's order nor player k's demand is necessarily an ARMA process with respect to the relevant shocks. It is shown that demand activity propagates in general to a process that is called quasi-ARMA, or QUARMA, in which the most recent shock(s) may be absent. It is shown that the typical player faces QUARMA demand and places orders that are also QUARMA. Thus, the demand propagation model is QUARMA in–QUARMA out. The presented analysis hence reverses and sharpens several previous results in the literature involving information sharing and also opens up many questions for future research.

Keywords:

• Supply chain management
• information sharing
• time series
• ARMA
• invertibility
• order-demand non-equivalence