The risk-averse newsvendor problem under spectral risk measures: A classification with extensions

We study the risk-averse newsvendor problem by defining the objective function as a spectral risk measure. We analyze the problem under different types of return formulations, focusing on the impact of risk aversion and cost parameters on the optimal ordering decision. We show that the monotonicity of the return function with respect to random demand determines the structural properties of the problem. When the return function is monotone in demand realization, optimal order quantity does not depend on the return margin but only on the overage and underage costs, and it has a monotone relation to risk aversion. However, if return is non-monotone in demand impact of risk aversion depends on the specific setting and it can also be non-monotone. Additionally, it is non-increasing in the margin which leads to varying impact of selling price under distinct settings.