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Integer Programming Approaches to Risk-Averse Optimization

Liu, Xiao
http://rave.ohiolink.edu/etdc/view?acc_num=osu1480461192784862

Abstract Details

2016, Doctor of Philosophy, Ohio State University, Industrial and Systems Engineering.
Risk-averse stochastic optimization problems widely exist in practice, but are generally challenging computationally. In this dissertation, we conduct both theoretical and computational research on these problems. First, we study chance-constrained two-stage stochastic optimization problems where second-stage feasible recourse decisions incur additional cost. We also propose a new model, where recovery decisions are made for the infeasible scenarios, and develop strong decomposition algorithms. Our computational results show the effectiveness of the proposed method. Second, we study the static probabilistic lot-sizing problem (SPLS), as an application of a two-stage chance-constrained problem in supply chains. We propose a new formulation that exploits the simple recourse structure, and give two classes of strong valid inequalities, which are shown to be computationally effective. Third, we study two-sided chance-constrained programs with a finite probability space. We reformulate this class of problems as a mixed-integer program. We study the polyhedral structure of the reformulation and propose a class of facet-defining inequalities. We propose a polynomial dynamic programming algorithm for the separation problem. Preliminary computational results are encouraging. Finally, we study risk-averse models for multicriteria stochastic optimization problems. We propose a new model that optimizes the worst-case multivariate conditional value-at-risk (CVaR), and develop a finitely convergent delayed cut generation algorithm.
Guzin Bayraksan (Committee Chair)
Simge Kucukyavuz (Committee Co-Chair)
Ramteen Sioshansi (Committee Member)
Sam Davanloo Tajbakhsh (Committee Member)
182 p.
Industrial Engineering; Operations Research
Integer Programming Approaches, Risk-Averse Optimization

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Citations

  • Liu, X. (2016). Integer Programming Approaches to Risk-Averse Optimization [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1480461192784862

    APA Style (7th edition)

  • Liu, Xiao. Integer Programming Approaches to Risk-Averse Optimization. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1480461192784862.

    MLA Style (8th edition)

  • Liu, Xiao. "Integer Programming Approaches to Risk-Averse Optimization." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1480461192784862

    Chicago Manual of Style (17th edition)

osu1480461192784862
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© 2016, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.