A newsvendor model with autocorrelated demand under a time-consistent dynamic CVaR measure

Abstract

As a result of autocorrelation, static risk measures such as value at risk and Conditional Value at Risk (CVaR) are time inconsistent and can thus result in inconsistent decisions over time. In this article, we present a time-consistent dynamic CVaR measure and examine it in the context of a newsvendor problem with autocorrelated demand. Due to the concavity of our CVaR measure, the dynamic program formulation associated with our dynamic newsvendor problem is not immediately separable. However, by exploring certain properties of the dynamic CVaR measure and underlying profit function, our dynamic program can be transformed into a sequence of (single-period) risk-averse newsvendor problems that depend on the observed demand history. By examining the structure of the optimal order quantities, we find both intuitive and counterintuitive results. When demands are positively correlated, the optimal order quantity is monotonically increasing in the degree of risk aversion. However, when demands are negatively correlated and the underlying cost structure satisfies certain conditions, the optimal order quantity is no longer monotonically increasing in the degree of risk aversion. Instead, the optimal order quantity is a decreasing (increasing) function of the degree of risk aversion when it is below (above) a certain threshold. We also show that these results continue to hold when demands follow a general ARMA process, and when inventory carryover is considered.