The Big Data Newsvendor: Practical Insights from Machine Learning

We investigate the data-driven newsvendor problem when one has n observations of p features related to the demand as well as historical demand data. Rather than a two-step process of first estimating a demand distribution then optimizing for the optimal order quantity, we propose solving the “big data” newsvendor problem via single-step machine-learning algorithms. Specifically, we propose algorithms based on the empirical risk minimization (ERM) principle, with and without regularization, and an algorithm based on kernel-weights optimization (KO). The ERM approaches, equivalent to high-dimensional quantile regression, can be solved by convex optimization problems and the KO approach by a sorting algorithm. We analytically justify the use of features by showing that their omission yields inconsistent decisions. We then derive finite-sample performance bounds on the out-of-sample costs of the feature-based algorithms, which quantify the effects of dimensionality and cost parameters. Our bounds, based on algorithmic stability theory, generalize known analyses for the newsvendor problem without feature information. Finally, we apply the feature-based algorithms for nurse staffing in a hospital emergency room using a data set from a large UK teaching hospital and find that (1) the best ERM and KO algorithms beat the best practice benchmark by 23% and 24%, respectively, in the out-of-sample cost, and (2) the best KO algorithm is faster than the best ERM algorithm by three orders of magnitude and the best practice benchmark by two orders of magnitude.