Possible Sharing Arrangements in ARMA Supply Chains

Abstract

We introduce a class of new sharing arrangements in a multi-stage supply chain in which the retailer observes stationary autoregressive moving average demand with Gaussian white noise (shocks). Similar to previous research, we assume each supply chain player constructs its best linear forecast of the leadtime demand and uses it to determine the order quantity via a periodic review myopic order-up-to policy. We demonstrate how a typical supply chain player can create a sequence of partial information shocks (PIS) from its full information shocks FIS and share these with an adjacent upstream player. We go on to show how such a sharing arrangement may be benecial to the upstream player by characterizing the player's FIS in such a case. Hence, we study how a player can determine its available information under PIS sharing, and use this information to forecast leadtime demand. We characterize the value of FIS sharing for a typical supply chain player. Furthermore, we show conditions under which a player is able to form and share valuable PIS without (i) revealing its historic demand sequence or (ii) revealing its FIS sequence. We also provide a way of comparing various PIS sharing arrangements with each other and with conventional sharing arrangements involving demand sharing or FIS sharing. We show that demand propagates through a supply chain where any player may share nothing or a sequence of PIS shocks with an adjacent upstream player as quasi-ARMA in - quasi-ARMA out.