In this dissertation, we present novel sampling-based algorithms for solving two-stage stochastic programming problems. Sampling-based methods provide an efficient approach to solving large-scale stochastic programs where uncertainty is possibly defined on continuous support. When sampling-based methods are employed, the process is usually viewed in two steps - sampling and optimization. When these two steps are performed in sequence, the overall process can be computationally very expensive. In this dissertation, we utilize the framework of internal-sampling where sampling and optimization steps are performed concurrently. The dissertation comprises of two parts. In the first part, we design a new sampling technique for solving two-stage stochastic linear programs with continuous recourse. We incorporate this technique within an internal-sampling framework of stochastic decomposition. In the second part of the dissertation, we design an internal-sampling-based algorithm for solving two-stage stochastic mixed-integer programs with continuous recourse. We design a new stochastic branch-and-cut procedure for solving this class of optimization problems. Finally, we show the efficiency of this method for solving large-scale practical problems arising in logistics and finance.
Operations Research and Engineering Management
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Tabrizian, Siavash, "Sampling-Based Algorithms for Two-Stage Stochastic Programs and Applications" (2021). Operations Research and Engineering Management Theses and Dissertations. 18.