Distributionally robust newsvendor problem with censored demand

We usually can only observe the sales instead of the true demand in practice, which results in the censored demand problem - Partial demand information is censored by the stocking level. Under a newsvendor setting, we first adopt the distributionally robust optimization technique to address this problem. To the best of our knowledge, our study is the first distributionally robust newsvendor problem paper that considers censored demand. Specifically, we construct different ambiguity sets which include the moments information of the demand distribution conditioning on stocking out information from historical data. We derive closed-form solution for the proposed models and compare them with the counterpart without the stocking out information: 1) Under mean-support ambiguity set, the support determines the closed-form solution to the distributionally robust newsvendor model. 2) Under mean-variance-support ambiguity set, the closed-form solution to the distributionally robust newsvendor model is determined by mean, variance, ordering cost and selling price. 3) As the ratio of ordering cost to selling price increases, the optimal ordering quantities decrease. Numerical studies illustrate that the censored demand information can improve the expected revenue for the distributionally robust newsvendor model when the ratio is in some ranges. Furthermore, the revenue improves as censored level increases. © 2022, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.