Optimal decisions for the loss-averse newsvendor problem under CVaR

Most of the existing literature about the newsvendor problem mainly focused on choosing an optimal order quantity to maximize the expected profit of a risk-neutral newsvendor. However, some studies pointed out that in practice managers׳ decisions as to order quantities always deviate from the profit-maximization order quantity, which is referred to as decision bias in the newsvendor problem. Then, many studies introduced other preferences rather than risk neutrality of the newsvendor to explain such a decision bias. This paper thus introduces loss aversion to the research of the newsvendor decision bias. We propose a new definition to the loss-averse newsvendor problem–legacy loss, which is defined either as the loss for excess order or the shortage penalty for lost sales when sales time is due. The optimal decisions of a loss-averse newsvendor are obtained through the following three ways: (i) minimizing the expected legacy loss, (ii) minimizing CVaR of legacy loss by combining the CVaR measure in risk management, (iii) minimizing the combination of expected legacy loss and CVaR of legacy loss; and are compared with other existing results. Besides, we present some properties of the optimal decisions as well as relations among them. Some numerical examples are given to illustrate the obtained results.