Optimal Feature-Based Newsvendor Policies under Censored Demand

Source abstract

We investigate a newsvendor problem where a decision-maker observes a $z$-dimensional vector of covariates, and wants to learn how much stock to order given a sample of size $n$ of censored demand data to minimize costs. Demand is censored when insufficient stock is available to meet it, and past stocking quantities are known. We propose a new model-agnostic loss function approach to estimate optimal order quantities using observational data, and characterize the optimal newsvendor policy as the policy that minimizes our proposed loss function. Our method requires only a single estimation step, can be scaled to datasets with hundreds of thousands of data points, and does not suffer from the same instabilities as inverse censoring probability weighting methods. We describe how this loss function can be implemented in linear empirical risk minimization, kernel weights optimization and deep neural network algorithms, and provide excess risk generalization bounds for their out-of-sample performance. Moreover, we show through numerical experiments that our method quickly converges to the optimal policy on synthetic data, and leads to improved performance on real world retail data.