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The data-driven (s,S) policy: why you can have confidence in censored demand data

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If you have a question about this talk, please contact Quentin Berthet.

I revisit the classical dynamic inventory management problem of Scarf (1959) from a distribution-free, data-driven perspective. I propose a nonparametric estimation procedure for the optimal (s, S) policy that yields an asymptotically optimal estimated policy and analytically derive confidence intervals around this policy. I also derive a confidence bound on the estimated total cost, which, in the case of zero setup cost, interestingly is directly proportional to the size of the confidence intervals of the estimated policy. I further consider having a portion of the data censored from past ordering decisions. I show that the intuitive procedure of correcting for censoring in the demand data directly yields an inconsistent estimate of the optimal policy. I then show how to correctly use the censored data to obtain consistent decisions and derive confidence intervals for this policy. Remarkably, under some conditions, ordering decisions estimated with partially censored data may be more precise than with fully uncensored data, and there exists an optimal amount of censored data to minimise the mean square error (MSE).

This talk is part of the Statistics series.

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