Technical Note—A Risk- and Ambiguity-Averse Extension of the Max-Min Newsvendor Order Formula

Scarf's max-min order formula for the risk-neutral and ambiguity-averse newsvendor problem is a classical result in the field of inventory management. In this article, we extend Scarf's formula by deriving an analogous closed-form order formula for the risk- and ambiguity-averse newsvendor problem. Specifically, we provide and analyze the newsvendor order quantity that maximizes the worst-case expected profit versus risk trade-off (risk-averse) when only the mean and standard deviation of the product's demand distribution are known (ambiguity-averse), and the risk is measured by the standard deviation of the newsvendor's profit. We provide both analytical and numerical results to illustrate the combined effect of considering risk aversion and ambiguity aversion in computing the newsvendor order.