Supply chain uncertainty under ARIMA demand process

Abstract

This paper discusses a typical supply chain system based on Auto- Regressive Integrated Moving Average (ARIMA) demand process. Minimum Mean Square Error principle and stochastic optimal control theory are introduced to build a new framework for supply chain uncertainty study under general ARIMA demand process. After formulating the order and inventory quantity at time period t, this paper analyzes the optimal order policy as to decrease the bullwhip effect and stock fluctuations under non-stationary demand. The theoretical analysis reveals that a reasonable order quantity can reduce the bullwhip effect generated by demand uncertainty. We also show the negative correlation between the bullwhip effect and inventory stability in the discussed supply chain model. © Springer International Publishing Switzerland 2014.