Data-driven distributionally robust newsvendor models with censored demand

In this paper we generalize classic maximin model (Scarf, 1958) of the distributionally robust newsvendor problem, creating data-driven models for sales (i.e., censored demand). In particular, we focus on a single-period single-item distributionally robust newsvendor context, where only observations of sales (censored demand) data are available. We first calculate confidence intervals for the first two sales moments and then derive necessary and sufficient conditions to ensure that a valid demand distribution exists for any combination of sales moments contained in the union of the confidence intervals, which lead to guidance on appropriate confidence levels. Once the confidence intervals are well-posed, their union forms the data-driven ambiguity set in our new distributionally robust newsvendor models. Focusing on the case where confidence intervals for only the first two moments are utilized, we derive a closed-form solution for the optimal order quantity. Moreover, we extend our models by incorporating information about the probability of demand censoring as well as allowing the sales data to be censored by multiple inventory levels. For the general case where demands are censored by multiple capacities, we show that the model can be solved via semidefinite programming. Extensive experiments, based on real data, explore the impact of various parameters and complement our theoretical contributions. Our paper provides the first robust newsvendor models that can accommodate censored demand using only data, whose solutions may be implemented easily via either closed-form solutions or tractable semidefinite programs.