| Stochastic programming is a mathematical tool for decision-making under uncertainty. However, it remains largely unused as a practical tool for decision making. One reason for its light use in practice may be that practical instances are of larger size than can be solved by available software tools on existing computational platforms. In this thesis, we focus on algorithms for solving large-scale two-stage stochastic programs on a parallel distributed computer platform known as a computational grid. An overarching theme of this work is to make use of hundreds of loosely-coupled processors over long time periods to effectively solve stochastic programs. We study how grid computing can be employed for effective solutions of stochastic programs in the following areas. First, we study a parallel implementation of the L-Shaped decomposition method for solving a sample average approximation(SAA) of large stochastic programs. We propose warm-starting methods for the L-Shaped decomposition method by using pre-sampling and scenario partitioning. Further, a method for managing cuts in the L-Shaped method is also discussed. Second, since evaluating the objective function is a computational task that can be easily and efficiently distributed on a computational grid, we study enhancements to traditional techniques that can help us exploit this fact. In particular, we propose a line search method and trust-region scaling methods to enhance the convergence rate. Finally, in order to estimate the bias of solution value estimates using the SAA method, we propose using a statistical technique known as the bootstrap method. The bootstrap estimate requires solution of a large number of bootstrap sample problems, a process that can be easily parallelized by using the power of grid computing. In all cases, extensive computational experiments were performed. We conclude with a case study demonstrating the application of our developed techniques to solve very large-scale instances. |
