Impact of Emergency Order in Price-Dependent Newsvendor Problems

This paper investigates the impact of emergency order in a price-dependent newsvendor setting. To this end, we compare two ways handling the excess demand: the excess demand is lost and a penalty cost is incurred, or the excess demand can be satisfied by an emergency order. Which way is better depends on the emergency purchase cost e in emergency-order way and the price p plus penalty cost g in lost-sales way. For a risk-neutral newsvendor, our results indicate that, when e is not larger than p + g, the emergency order way can lead to smaller order quantity and higher expected profit. We continue to discuss the impact of newsvendor’s risk aversion and demand uncertainty on the optimal decisions of the two ways. Theoretical analysis and numerical examples indicate that when the emergency purchase cost is not high, the differentials of the optimal order quantities and expected profits will be larger as the degree of risk aversion/demand uncertainty increases. What is more, we prove that there exists a threshold value of the emergency purchase cost so that the two ways handling excess demand can obtain the same expected profit, and this threshold value increases as the degree of risk aversion decreases.