The Risk-Averse Newsvendor Problem With Random Emergency Supply Capacity

In this paper,we study the effect of emergency order capacity uncertainty on the inventory decisions of a risk-averse newsvendor.We consider two well-know risk-averse criteria,namely Conditional Value-at-Risk(CVaR)and Mean–Conditional Value-at-Risk(Mean–CVaR).Firstly,we give the equations that are satisfied by the optimal decisions for the risk-averse newsvendor problem under CVaR and Mean–CVaR criteria with one random emergency order opportunity respectively,analyze the impact of system parameters on the optimal order quantities and examine the conclusions by numerical simulation.Secondly,we explore the risk-averse newsvendor problem with two emergency order sources(one capacity is random,another is unlimited).We successively give the optimal quantities for newsvendor under CVaR and Mean–CVaR criteria,and analyze the influence of system parameters on the optimal decisions.For the risk neutral newsvendor,we find optimal order quantity is not affected by the sale price.However,this result does not hold for the risk-averse newsvendor problem.Specifically,we find increasing the sales price will reduce their order quantity for risk-averse newsvendor.In addition,we give the condition under which the optimal order quantity decreased by the cost of the first emergency order.