Analyzing the effect of inventory policies on the nonstationary performance with transfer functions

Abstract

In this paper we apply transfer function methods to analyze the performance of supply chains in response to nonstationary demand and, in particular, we investigate how various inventory policies and demand forecasting parameters affect supply chain responsiveness. In a single-echelon inventory system we investigate the performance of a common base stock policy. Specifically, we describe the order and inventory trajectories using discrete transfer functions, and we derive closed-form analytical expressions for the transient behavior in response to a step change in demand. We introduce performance measures commonly used to analyze nonstationary performance and derive closed-form expressions for these measures. Next, we study the performance of a two-echelon supply chain under installation stock and echelon stock policies. We explicate the performance tradeoff in response to stationary versus nonstationary demand, and show that the transient response of orders and inventory levels can be either underdamped or overdamped depending on the exponential smoothing parameter. We show that the echelon stock policy is more responsive than the installation stock policy when both policies have similar stationary performances.

Keywords:

• Supply chain management
• control theory
• multiechelon inventory control
• nonstationary performance