Decomposition Methods for Two-Stage Stochastic Optimization

Description

We are interested in developing a decomposition method to solve a large-scale two-stage stochastic optimization model. Our problem includes integer variables in the second stage, and thus standard Benders decomposition does not apply. In our existing work, we have also proven that the model has so-called relatively complete recourse, i.e., the second-stage decisions are completely determined by the first-stage decisions. This fact motivates the potential of a scheme to solve the model in a computationally tractable manner. In this short stay, we seek to accomplish three tasks: (i) mathematically formulate the considered optimization model to fit in a decomposition framework, (ii) implement the above framework into a modeling language, and (iii) analyze the computational performance of the scheme as compared to a naive solution method. Applications of the above task include the allocation of vaccines available in scarce quantities during the COVID-19 pandemic. For details, see: Singh, Bismark. "Optimal spatiotemporal resource allocation in public health and renewable energy." PhD diss., The University of Texas at Austin, 2016.