Distributionally robust optimization of a newsvendor model under capital constraint and risk aversion

This paper proposes a capital-constrained newsvendor model with risk aversion under a partially known demand distribution with only knowledge of its mean and variance. We adopt the robust conditional value- at-risk (RCVaR) to characterize the vendor's risk aversion. Firstly, we obtain the closed-form RCVaR optimal order quantity that depends on the demand volatility level: When demand volatility is low, the vendor has four financing-ordering strategies contingent upon different capital levels. When demand volatility is medium, the vendor does not seek bank loans and is left with two ordering strategies. When demand volatility is high, the vendor does not bother placing an order at all. Then, we investigate the impact of capital constraint, risk aversion and demand volatility on the RCVaR optimal order quantity. Finally, we demonstrate the robustness of the RCVaR optimal ordering policy by numerical experiments based on both randomly generated and real-world data.