A price-setting newsvendor model under CVaR decision criterion with emergency procurement

Abstract

In this paper, we consider a newsvendor model in which a risk-averse manager faces a stochastic price-dependent demand in either an additive or a multiplicative form. An emergency purchase option is allowed after the realization of demand to satisfy the units that are short. By adopting conditional value-at-risk (CVaR) as the decision criterion, we aim to investigate the optimal pricing and ordering decisions, and the effects of parameter changes in such a setting. We provide sufficient conditions for the uniqueness of the optimal policy for both demand models. We perform comparative statics analysis to show how the optimal pricing and ordering decision behaves when changing parameters. We also compare our results with those of the newsvendor with a general utility function and with CVaR criterion under lost sales assumption. Our key results include: (i) For both demand models, the optimal selling price is decreasing in risk aversion. Hence, the optimal price of a risk-averse newsvendor is not greater than the optimal price of a risk-neutral newsvendor. (ii) In contrary to the lost sales case, for the multiplicative demand model, the optimal order quantity may not be monotonic in risk aversion. Consequently, the optimal risk-averse order quantity may be lower or higher than the optimal risk-neutral counterpart. (iii) For the additive model, the optimal order quantity is strictly increasing in the emergency purchase price, while for the multiplicative model the optimal order quantity has no such a monotonic property. Some numerical examples are conducted to verify our claims and gain more insights about the risk-averse decision-making behaviors.