Coping with Risk Aversion in the Newsvendor Model with a Backorder Case

In this paper, we study the optimal order quantity decisions for a risk-averse newsvendor with a backorder case, where it is assumed that all or part of the excess demands of the customers can be backlogged. The optimal decisions are obtained under the popular Conditional Value-at-Risk (CVaR) criterion, which is to control the risk of the profit due to uncertain market demands. We study two basic models. The first is the pure CVaR model. It is found that the optimal order quantity for a risk-averse newsvendor is less than that for a risk-neutral newsvendor, who is to maximize the expected profit. It also shows that low risk means low expected profit while high expected profit comes with high risk. The second is the mixed model that balances the CVaR and the expected profit model. Important monotone properties are obtained for the two models and their relationships with the existing results are revealed. Finally, a numerical example is given to demonstrate the obtained results companied by interesting interpretation of some management insights.