The loss-averse newsvendor solutions via conditional value-at-risk measure

Abstract

This paper studies the optimal order quantity in the loss-averse newsvendor model with shortage cost. The retailer's loss aversion is characterized by introducing a loss version coefficient and then a novel utility functions proposed for the retailer. The optimal order quantity for the retailer has been obtained to maximize the expected utility. In order to reduce the risk arising from the uncertainty in market demand, the CVaR measure has been introduced and the optimal order quantity for the retailer has been obatined to maximize the CVaR objective about utility. It is found that the optimal order quantity with CVaR objective decreased in the retail price under certain conditions. This significant finding has never been reported in the previous newsvendor literature. Under the optimal order quantity with CVaR objective, it is proved that the retailer's expected utility is decreasing in the confidence level. This confirms the fact that low risk means low return while high return comes with high risk. A numerical example is given to illustrate the results and some management insights are suggested for the loss-averse newsvendor model.