On the Impact of Input Price Variability and Correlation in Stochastic Inventory Systems

In this paper, we explore the impact of input price variability and correlation in the context of an inventory system with stochastic demand and stochastic input prices. For a general class of such systems, we show that the expected cost function is concave in the input price. From this, it follows that higher input price variability in the sense of the convex order always leads to lower expected cost. We show that this is true under a wide range of assumptions for price evolution, including cases with i.i.d. prices and cases where prices are correlated and evolve according to an AR(1) process, a geometric Brownian motion, or a Markovian martingale. In addition, the result holds in cases where there is just a single period. We also examine the impact of price correlation over time and across inputs, and we find that expected cost is increasing in price correlation over time and decreasing in price correlation across components. We present results of a numerical study that provide insights on how various parameters influence the effects of price variability and correlation.