| 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. |
