Optimal Online Risk-Tolerant Ordering Policy for the Newsvendor with Forecast

The classical newsvendor problem is to find a product's order quantity to maximize the expected profit under probabilistic demand. This paper restudies the problem under the perspective of competitive analysis, in which only the lower bound and upper bound rather than the distribution of the future demand are known. Some preliminary results of the problem with competitive analysis are given first in brief. And then it is considered in the risk-reward framework which provides the flexibility to develop some risky online strategies, as conventional competitive analysis seems too conservative and some decision-makers may incline to increase their risk for some reward in practice. In this framework, it is assumed that the vendor may have some forecast of the future demand and he can tolerate a certain level of risk for better reward. Based on his forecast and risk tolerance, an optimal online risk-tolerant ordering policy for the newsvendor is developed.