Bilevel newsvendor models considering retailer with CVaR objective

In this paper, the bilevel newsvendor model in two-echelon systems is presented. In this model, CVaR (conditional value-at-risk) measure is considered as the retailer’s objective. We obtain an analytical solution when the product’s demand is uniformly distribution. Several examples are given to illustrate our model and for comparable with the basic two-echelon newsvendor model. For the circumstance when the manufacturer knows the retailer’s objective, we get a counter-intuitive result: the retailer’s CVaR measure is larger when his objective is minimizing CVaR than that when his objective is maximizing the expected profit. The reason is that the manufacturer changes the wholesale price to maximize his own profit when he knows the retailer’s objective is CVaR. Some effects of parameters (such as unit shortage penalty) on the optimal wholesale price and order quantity are also revealed in the paper.