A Risk-Averse Newsvendor Model Under the Framework of Uncertainty Theory

Abstract

Due to the ever-changing and complex market environment, companies frequently face highly uncertain demand where data are so insufficient that the use of random or fuzzy variables, which are typically assumed in the literature, is impractical. Furthermore, companies are often risk-averse when making decisions. To address these two challenges, in this paper, we present the first study on a risk-averse newsvendor problem using the framework of uncertainty theory. To measure risk aversion, we adopt the measure of tail value-at-risk redefined based on uncertainty theory. We are able to analytically derive the optimal order quantity that maximizes the newsvendor's expected utility. We find that the optimal order quantity of a risk-averse newsvendor is less than that of a risk-neutral newsvendor. Furthermore, as the degree of risk aversion increases, the optimal order quantity decreases. Also, we show that the optimal order quantity may be independent of the risk confidence level when the degree of risk aversion is below a threshold. Moreover, we use numerical examples to illustrate how various parameters, such as the degree of risk aversion, salvage value, and unit ordering cost, affect the optimal order quantity.

Keywords

• Newsvendor problem
• uncertainty theory
• uncertain variable
• risk aversion