The effect of demand uncertainty in a price setting newsvendor model

This paper considers the classical newsvendor problem with a price-dependent, random, demand. At the beginning of a selling season, a joint decision on order quantity and selling price is made for the season, to maximize the expected profit. We analyze the impact of demand uncertainty on the profit, price and order quantity. Intuition has that when the demand is more uncertain, the optimal price will be higher, the order quantity will be smaller, and the maximal achievable profit will be lower. Our analysis demonstrates that this is true for many demand functions and random distributions that are both theoretically plausible and commonly used in practice. However, in general, exceptions exist, for which this intuition does not hold true. In other words, a reduction in demand uncertainty may not result in lower price, or higher profit. Whether the profit increase occurs depends on many factors such as the definitions of uncertainty, the cost structure, and demand functional form. Many firms commit resources to reduce forecasting errors or variability through information collecting efforts and process improvement initiatives (e.g., collaborative forecasting, accurate response, delayed differentiation, and so on). Such efforts may assume that stochastically less variable demand is beneficial. Hence, the result in this paper is of practical importance.