Stochastic Dynamic Mixed-Integer Programming (SD-MIP)
Final rept. Feb 2014-Dec 2015
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES
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Mixed-Integer Programming has traditionally been restricted to deterministic models. Recent research has opened the door to stochastic optimization models, which are typically dynamic in nature. This project lays the foundation for stochastic dynamic mixed-integer and linear programming SD-MIP. This project has produced several new ideas in connection with a convexification of two-stage mixed-integer sets and b multi-stage including two-stage stochastic linear programming. Together a and b provide the foundations for SD-MIP problems. From new concepts and algorithms to applications and software, this project has made significant breakthroughs in all aspects. This report provides a synopsis of both theoretical and computational results. As a preview, we mention that currently available deterministic MIP solvers, as powerful as they are known to be, are unable to solve SD-MIP models of modest size within an hour of computing. In contrast, our decomposition approach provides provably optimal solutions within the hour time-limit.
- Statistics and Probability
- Operations Research