Adaptive Data-Driven Inventory Control with Censored Demand Based on Kaplan-Meier Estimator

Abstract

Using the well-known product-limit form of the Kaplan-Meier estimator from statistics, we propose a new class of nonparametric adaptive data-driven policies for stochastic inventory control problems. We focus on the distribution-free newsvendor model with censored demands. The assumption is that the demand distribution is not known and there are only sales data available. We study the theoretical performance of the new policies and show that for discrete demand distributions they converge almost surely to the set of optimal solutions. Computational experiments suggest that the new policies converge for general demand distributions, not necessarily discrete, and demonstrate that they are significantly more robust than previously known policies. As a by-product of the theoretical analysis, we obtain new results on the asymptotic consistency of the Kaplan-Meier estimator for discrete random variables that extend existing work in statistics. To the best of our knowledge, this is the first application of the Kaplan-Meier estimator within an adaptive optimization algorithm, in particular, the first application to stochastic inventory control models. We believe that this work will lead to additional applications in other domains.

The Data-Driven Newsvendor Problem: New Bounds and Insights

“…Huh and Rusmevichientong (2009) propose an online algorithm for the newsvendor problem with censored demand data (i.e., data is on sales instead of demand) based on stochastic gradient descent. Another nonparametric method for censored demand is proposed by Huh et al (2008), based on the well-known Kaplan-Meier estimator. Robust optimization addresses distribution uncertainty by providing solutions that are robust against different distribution scenarios.…”

Robust newsvendor problem with autoregressive demand

“…Three different distributions for the error terms were tested in our experiments, all of them chosen so as to generate non-negative demand series. First, a t ∼ N (4, 1); also, we found of interest to check the behavior of the methods when heavy-tails are incorporated in the generator model, as done in Huh et al (2011). They choose Pareto and Lognormal distributions to check the performance of their inventory approach under samples of timeindependent demand generated with heavy-tailed distributions.…”

The Big Data Newsvendor: Practical Insights from Machine Learning

“…Other perspectives on the data-driven newsvendor include those of Liyanage and Shanthikumar (2005), who proposed ordering according to a statistic (function) of past demand data whose form is cleverly chosen based on a priori assumptions on the class of distributions the demand belongs to, Huh et al (2011) and Besbes and Muharremoglu (2013) who provided theoretical insights into the newsvendor problem with iid censored demand data, and Levi et al (2012), who improved upon the bound of Levi et al (2007) by incorporating more information about the (featureless) demand distribution, namely through the weighted mean spread.…”