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Demand estimation and optimal policies in lost sales inventory systems Ding, Xiaomei

Abstract

In this thesis, we study the statistical issues in lost sales inventory systems, focusing on the complexity arising from the stochastic demand. We model the demand by the Zero Inflated Poisson (ZIP) distribution. The maximum likelihood estimator of the ZIP parameters taking censoring into account are derived separately for the newsvendor and the (s, S) inventory systems. We also investigate the effect of the estimation errors on the optimal policies and their costs. We observe from a simulation study that the MLE taking censoring into account performed the best in terms of cost as well as policy among various estimates. We then proceed to develop a Bayesian dynamic updating scheme of the ZIP parameters. It is applied to the newsvendor system. We perform a simulation study to investigate the advantage of the Bayesian updating approach over the traditional MLE approach. We conclude that the Bayesian pproach offers a better learning technique when one lacks of good understanding of the demand pattern in the first few periods. Since inventory policy affects the information acquisition and-the demand distribution updating process, how to determine the optimal inventory policy when the demand distribution is yet to be learned is the focus of the latter part of the thesis. We investigate the effect of demand censoring on the optimal policy in newsvendor inventory models with general parametric demand distribution and unknown parameter values. We provide theoretical proof of the conjecture that it is better off to adopt a higher than the myopic optimal policy in the initial periods when demand is learned in a censoring system. We show that the newsvendor problem with observable lost sales reduces to a sequence of single-period problems while the newsvendor problem with unobservable lost sales requires a dynamic analysis. We explore the economic rationality for this observation and illustrate it with numerical examples.

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