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Risk-Averse and Distributionally Robust Optimization: Methodology and Applications

Rahimian, Hamed
http://orcid.org/0000-0003-1385-4120
http://rave.ohiolink.edu/etdc/view?acc_num=osu1531822931371766

Abstract Details

2018, Doctor of Philosophy, Ohio State University, Industrial and Systems Engineering.
Many decision-making problems arising in science, engineering, and business involve uncertainties. One way to address these problems is to use stochastic optimization. A crucial task when building stochastic optimization models is quantifying a probability distribution to represent the uncertainty. Most often, partial information about the uncertainty is available through a series of historical data. In such circumstances, classical stochastic optimization models rely on approximating the underlying probability distribution. However, in many real-world applications, the underlying probability distribution cannot be accurately determined, even when historical data are available. This distributional ambiguity might lead to highly suboptimal decisions. An alternative approach to handle such an issue is to use distributionally robust stochastic optimization (DRSO for short), which assumes the underlying probability distribution is unknown but lies in an ambiguity set of distributions. Many existing studies on DRSO focus on how to construct the ambiguity set and how to transform the resulting DRSO into equivalent (well-studied) models such as mixed-integer programming and semide finite programming. This dissertation, however, addresses more fundamental questions, in a different manner than the literature. An overarching question that motivates most of this dissertation is which scenarios/uncertainties are critical to a stochastic optimization problem? A major contribution of this dissertation is a precise mathematical defi nition of what is meant by a critical scenario and investigation on how to identify them for DRSO. As has never been done before for DRSO (to the best of our knowledge), we introduce the notion of effective and ineffective scenarios for DRSO. This dissertation considers DRSOs for which the ambiguity set contains all probability distributions that are not far---in the sense of the so-called total variation distance---from a nominal distribution (which may be obtained from data). This dissertation then identifi es effective scenarios for two classes of DRSO problems formed via the total variation distance: (1) a class of convex stochastic optimization problems with a discrete sample space and (2) a class of inventory problems with a continuous sample space. All these classes of DRSO problems have equivalent risk-averse optimization problems that lay the foundation to identify effective scenarios. We elaborate how effective scenarios, along with other notions, can be used to choose an appropriate size for the ambiguity set of distributions. Then, we devise customized algorithms to solve DRSO formed via the total variation distance. Moreover, we survey existing algorithms to solve a closely related risk-averse optimization problem to those induced by the studied DRSO problems, and we propose new variations. Finally, to highlight the practical relevance of our findings, we implement all our modeling, theoretical, and computational results to solve problems arising in environment, energy, healthcare, and finance.
Guzin Bayraksan, PhD (Advisor)
Antonio Conejo, PhD (Committee Member)
David Sivakoff, PhD (Committee Member)
242 p.
Industrial Engineering; Operations Research
Decision-Making under Uncertainty, Mathematical Programming, Stochastic Optimization, Risk-Averse Optimization, Distributionally Robust Optimization

Recommended Citations

Citations

  • Rahimian, H. (2018). Risk-Averse and Distributionally Robust Optimization: Methodology and Applications [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531822931371766

    APA Style (7th edition)

  • Rahimian, Hamed. Risk-Averse and Distributionally Robust Optimization: Methodology and Applications. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1531822931371766.

    MLA Style (8th edition)

  • Rahimian, Hamed. "Risk-Averse and Distributionally Robust Optimization: Methodology and Applications." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531822931371766

    Chicago Manual of Style (17th edition)

osu1531822931371766
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This open access ETD is published by The Ohio State University and OhioLINK.