Inventory Control with Return Policy Under Conditional Value-at-Risk Criterion

The classical risk-neutral newsvendor problem is to decide the order quantity to maximize the one period expected profit under a given demand distribution. In this paper, we consider a risk-averse newsvendor problem with return policy under the Conditional Value-at-Risk (CVaR) criterion. Unlike the traditional research, we don't use CVaR as the single decision criterion because it only consider the worst outcomes, while we choose the combination of the expected profit and CVaR as the objective function. Such a joint objective reflects the desire of the risk-averse retailer to maximize the profit and the desire to minimize the downside risk of his profit. Finally under the joint framework, we get the explicit form of the optimal inventory level.