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TITLE: Risk-Averse Two-Stage Stochastic Program with Distributional Ambiguity
ABSTRACT:
In this talk, we present a risk-averse two-stage stochastic program (RTSP) which explicitly incorporates the distributional ambiguity covering both discrete and continuous distributions. We formulate RTSP from the perspective of distributional robustness by hedging against the worst-case distribution within the ambiguity set and considering the corresponding expected total cost. In particular, we derive an equivalent reformulation for RTSP which indicates that each worst-case expectation over L1-norm-based ambiguity sets reduces to a convex combination of a CVaR and an essential supremum. Accordingly, we develop solution algorithms for the reformulations of RTSP based on the sample average approximation method. Our studies are also extended to other norms and joint norm and moment-based ambiguity sets. Furthermore, starting from a set of historical data samples, we construct ambiguity sets for the probability distributions through nonparametric statistical estimation of their density functions. We perform convergence analysis to show that the ambiguity-aversion of RTSP vanishes as the data sample size grows to infinity, in the sense that the optimal objective value and the set of optimal solutions of RTSP converge to those of risk-neutral TSP. Finally, numerical experiments on newsvendor and lot-sizing problems explain and demonstrate the effectiveness of our proposed method. This is a joint work with Ruiwei Jiang at the University of Michigan.
BIO: Yongpei Guan serves as Professor of Industrial and Systems Engineering and Director of the Computational and Stochastic Optimization Lab at the University of Florida. His research interests include stochastic and discrete optimization, energy system optimization with renewable energy integration, and supply chain management. His works in these areas have led to NSF Career Award 2008 and Office of Naval Research Young Investigator Award 2010 and have been published in IEEE Transactions on Power Systems, IIE Transactions, Mathematical Programming, Operations Research, and Transportation Science. Some of his research results have been tested by various energy companies including MISO and GE grid. His awards also include as a faculty adviser for the Nicholson Best Student Paper Award, first place, from INFORMS and Pritsker Doctoral Dissertation Awards, second and third places, from IIE. Yongpei Guanserved as the Acting Chair for the Department of Industrial and Systems Engineering at the University of Florida from May 2015 to August 2016. He was also nominated and served as the chair for 2014 IIE Annual Conference ISERC Program. Yongpei Guan earned his Ph.D. from Georgia Tech in 2005. Before that, he obtained his M.Phil degree from Hong Kong University of Science and Technology in 2001 and his dual BS degrees from Shanghai Jiao Tong University in 1998.
