Order Smoothing and Information Sharing under Endogenous Inventory Cost Parameters

We consider a two-tier inventory management system with one retailer and one supplier. Theretailer serves a demand driven by a stationary moving average process (of possibly in nite order) and places periodic inventory replenishment orders to the supplier. In this setting, we study the interplay between information sharing and order smoothing under the assumption that rms' inventory cost parameters (e.g., per unit holding and backordering costs) are functions of two forms of supply chain variability: (i) on-hand inventory variability and (ii) replenishment order variability. We show that there is a natural tension between these two sources of variability and characterize a "Pareto frontier" between them by identifying optimal inventory replenishment strategies that trade-o one type of variability for the other in a cost efficient way. For the case in which the retailer is able to share her complete demand history, we provide a full characterization of the efficient frontier, as well as of an optimal replenishment policy. On the other hand, when the retailer is not able (or willing) to share any demand information we provide a partial characterization of an optimal solution and show that information sharing does not always add value.We also show that the question of identifying conditions under which information sharing does o er value reduces to a delicate analysis of the invertibility (in a time series sense) of a specific stationary process