Data-driven two-stage inventory problem

Abstract

In this thesis, we consider two-stage newsvendor problem where the decision maker selling a seasonal product only uses the historical demand information in her decisions. In our setting, there are two decisions to be made: the order quan-tity, and a marked-down price. We decide on how many products to order for the first stage, as well as how to set a marked-down price for remaining unsold inventory in the second stage. To solve the problem considered, data-driven mod-els which do not require any distributional assumption are provided. Specifically, we propose six data-driven methods that solve the problem hierarchically in ad-dition to another method which finds the order quantity and the marked-down price for the remaining inventory simultaneously by using a mixed integer linear program. We generate the data from selected demand distributions and divide it into a training data and a testing data. The generated data is a function of the way that decisions were made historically. We make a definition of the relevancy level based on what decisions the data depends on. We conduct a numerical study to evaluate: (a) the effect of data relevancy, (b) the effect of training data size, (c) the performance of proposed models. We investigate the performances of proposed models in three ways: (1) comparison the best model with the worst one, (2) comparison with respective expected values, (3) comparison with respec-tive the inverse coefficient of variation. Lastly, we measure how many times one model is the best among testing samples and compare models based on their performances.