Real-world optimization problems are often sensitive to uncertainties caused by estimation errors, forecasting inaccuracy, and imprecise data information. These uncertainties bring significant challenges to decision-making in many areas. Robust optimization (RO) is a tool for addressing the challenges of parameter uncertainty. In this dissertation, we focus on the studies of RO on two problems. (1) In the study of finance, we proposed a tractable RO model for a Mean-Variance portfolio selection problem. We consider Markowitz's Mean-Variance Optimization when stock returns are modeled using Sharpe's single-index framework, but the model coefficients Alpha and Beta, are not precisely known. This study assumes the Alpha and Beta coefficients estimated using least-square estimators are within a prespecified epsilon of optimality and builds a tractable robust optimization model to address this problem. The approach combines both predictive analytics in the estimation of Alpha and Beta and prescriptive analytics in the optimization of the portfolio. In the numerical experiments, we found that there exists an optimal epsilon for which the optimal robust portfolio achieves higher expected return and lower volatility than the benchmark. (2) The study of renewable energy focuses on using a RO approach for long-term renewable energy planning under uncertainty. The objective is to determine capacity expansion for infrastructures and electricity generation to meet state-level environmental targets, including Renewable Portfolio Standards and clean electricity requirements, over a decade-long planning horizon. The proposed model incorporates realistic factors, including the construction leading time and potential capacity for renewable energy based on geographic factors. To address the parameter uncertainty in long-term planning, we develop a tractable reformulation for the robust optimization problem. We analyzed numerical experiments based on real California data and provided decision-makers with various strategies for capacity investment and generation profiles.
Operations Research and Engineering Management
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Jiang, Hao, "Essays in Robust Optimization with Applications to Finance and Renewable Energy" (2023). Operations Research and Engineering Management Theses and Dissertations. 24.