Many important decision problems in areas such as energy, finance, manufacturing, telecommunication, transportation, logistics, and health care are difficult to solve because they are characterized by uncertain outcomes when decisions are made, and furthermore the decisions and subsequent outcomes occur repeatedly, in multiple stages over time. Solving such complex problems easily exceeds the state-of-the-art capabilities of current desktop computers. To overcome this issue, typical methods discard or aggregate problem data, thereby losing information that may be critical. This award supports fundamental research to develop, evaluate, and implement a comprehensive methodology for optimizing such large-scale multi-stage problems under uncertainty by using a distributed computing environment. The need for this research is evident from the lack of generally applicable efficient solution methods for such problems. The results of this project will be directly applicable to sequential decision-making problems under uncertainty that are widely encountered in public and private sectors, therefore benefiting the U.S. economy and society. This research will positively impact engineering education by promoting the participation of underrepresented groups in research.
This research consists of theoretical and methodological advancements for solving large-scale multi-stage stochastic programs. Specifically, it involves designing bounding schemes and exact solution algorithms to solve such problems in a distributed fashion. There is a lack of efficient solutions methods, particularly when mixed-integer decision variables are involved. Existing methods typically make restrictive assumptions such as convexity. This methodology is broadly applicable, as it does not assume any special problem structure. Moreover, an inherent feature of this approach is its natural fit into a distributed computing environment, which makes it amenable to solving truly large-scale instances. In addition to developing methods, the research team will implement and evaluate their performance using large-scale instances on a state-of-the-art high-performance computing cluster.
