Optimal decisions when balancing expected profit and conditional value-at-risk in newsvendor models

This paper investigates a risk-averse inventory model by balancing the expected profit and conditional value-at-risk (CVaR) in a newsvendor model setting. We find out that: i) The optimal order quantity is increasing in the shortage cost for both the CVaR only criterion and the tradeoff objective. ii) For the case of zero shortage cost, the optimal order quantity to the CVaR criterion or tradeoff objective is increasing in the selling price, respectively. However, it may not be monotonic in the selling price when incorporating a substantial shortage cost. Moreover, it may be larger or less than the risk-neutral solution. iii) Under the tradeoff objective function, although the optimal order quantity for the model without shortage cost is increasing in the weight put on the expected profit, this property may not be true in general for the model with a substantial shortage cost. Some numerical examples are conducted to verify our results and observations.