Robust solutions to the newsvendor problem under the perspective of competitive analysis

The classical newsvendor problem is restudied under the perspective of competitive analysis in this paper. Unlike the approach of probabilistic analysis which may give some solutions that are far from the optimal solutions under some scenarios, competitive analysis provides very robust statements about the performance of an online solution, against all possible scenarios. With detailed competitive analysis, an optimal online order policy is given first. After that the approach of competitive analysis is integrated with probabilistic analysis to form a risk-mean effective frontier, on which the solutions have not only robust performance in each individual scenario but also satisfactory global expected profit, and thus it provides more flexibility for decision-making. Furthermore, different from the traditional mean-variance effective frontier, the risk defined under the perspective of competitive analysis provides us with a new way to handle uncertainty.