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Chaoyue Zhao (chaoyue.zhaookstate.edu) Abstract: The traditional twostage stochastic programming approach assumes the distribution of the random parameter in a problem is known. In most practices, however, the distribution is actually unknown. Instead, only a series of historic data are available. In this paper, we develop a datadriven stochastic optimization approach to providing a riskaverse decision making under uncertainty. In our approach, starting from a given set of historical data, we first construct a confidence set for the unknown probability distribution utilizing a family of ζstructure probability metrics. Then, we describe the reference distributions and solution approaches to solving the developed twostage riskaverse stochastic program, corresponding to the given set of historical data, for the cases in which the true probability distributions are discrete and continuous, respectively. More specifically, for the case in which the true probability distribution is discrete, we reformulate the riskaverse problem to a traditional twostage robust optimization problem. For the case in which the true probability distribution is continuous, we develop a sampling approach to obtaining the upper and lower bounds of the riskaverse problem, and prove that these two bounds converge to the optimal objective value uniformly at the sample size increases. Furthermore, we prove that, for both cases, the riskaverse problem converges to the riskneutral one as more data samples are observed. Finally, the experiment results on newsvendor and facility location problems show how numerically the optimal objective value of the riskaverse stochastic program converges to the riskneutral one, which indicates the value of data. Keywords: stochastic program, ζstructure probability metrics, riskaverse, value of data Category 1: Stochastic Programming Citation: Download: [PDF] Entry Submitted: 07/16/2015 Modify/Update this entry  
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