The Big Data Newsvendor: Practical Insights from Machine Learning

Published in Operations Research 67(1):90-108.

55 Pages Posted: 3 Feb 2015 Last revised: 22 Aug 2019

See all articles by Gah‐Yi Ban

Gah‐Yi Ban

Imperial College Business School

Cynthia Rudin

Duke University - Department of Computer Science

Date Written: March 2, 2018


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 (i) the best ERM and KO algorithms beat the best practice benchmark by 23% and 24% respectively in the out-of-sample cost, and (ii) 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.

Keywords: big data, newsvendor, machine learning, Sample Average Approximation, statistical learning theory, quantile regression

JEL Classification: C44, C61, C80

Suggested Citation

Ban, Gah‐Yi and Rudin, Cynthia, The Big Data Newsvendor: Practical Insights from Machine Learning (March 2, 2018). Published in Operations Research 67(1):90-108., Available at SSRN: or

Gah‐Yi Ban (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London, SW7 2AZ
United Kingdom


Cynthia Rudin

Duke University - Department of Computer Science ( email )

LSRC Building
Durham, NC 27708-0204
United States

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