Confidence Intervals for Data-Driven Inventory Policies with Demand Censoring

Published in Operations Research 68(2):309-326

47 Pages Posted: 4 Sep 2015 Last revised: 14 May 2020

See all articles by Gah‐Yi Ban

Gah‐Yi Ban

Imperial College Business School

Date Written: April 20, 2019


We revisit the classical dynamic inventory management problem of Scarf (1959) from the perspective of a decision-maker who has n historical selling seasons of data and must make ordering decisions for the upcoming season. We develop a nonparametric estimation procedure for the (S, s) policy that is consistent, then characterize the finite-sample properties of the estimated (S, s) levels by deriving their asymptotic confidence intervals. We also consider having at least some of the past selling seasons of data censored from the absence of backlogging, and show that the intuitive procedure of first correcting for censoring in the demand data yields inconsistent estimates. We then show how to correctly use the censored data to obtain consistent estimates and derive asymptotic confidence intervals for this policy using Stein's method. We further show the confidence intervals can be used to effectively bound the difference between the expected total cost of an estimated policy and that of the optimal policy. We validate our results with extensive computations on simulated data. Our results extend to the repeated newsvendor problem and the base-stock policy problem by appropriate parameter choices.

Keywords: demand censoring, inventory management, estimation, nonparametric, dynamic programming

Suggested Citation

Ban, Gah‐Yi, Confidence Intervals for Data-Driven Inventory Policies with Demand Censoring (April 20, 2019). Published in Operations Research 68(2):309-326, Available at SSRN: or

Gah‐Yi Ban (Contact Author)

Imperial College Business School ( email )

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


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