Newsvendor optimization with limited distribution information

We report preliminary results on stochastic optimization with limited distributional information. Lack of complete distribution calls for stochastically robust models that, after exploiting available limited or partial information, offer risk-shielded solutions, i.e., solutions that are insensitive to all possible distributions of random variables. We focus on the well-known newsvendor problem in this study, where the distribution of the random demand is only specified by its mean and one of the following: its standard deviation or its support. We propose a stochastically robust model for the newsvendor problem. More specifically, our model tries to minimize the regret that is defined as the ratio of the expected cost based on limited information to that based on complete information, called Relative Expected Value of Distribution (REVD). We show how to derive an optimal solution to the REVD model. Numerical examples are provided to compare our model with other similar approaches. The goal is to establish a confidence ratio that the decision from our model is not worse, relatively, too much than the decision based on the true distribution which would be never known exactly in real world applications.