9702217 Morton Optimization algorithms from linear, nonlinear, and integer programming are powerful tools for solving mathematical models of many important planning problems. Strictly deterministic models, however, do not capture the uncertainty inherent in many systems, and their "optimal solutions" often fail to hedge against model uncertainties. Stochastic programming techniques, on the other hand, explicitly capture uncertainty, but have to date suffered from a high degree of computational complexity. The research plan of this CAREER award is directed toward developing and constructing computationally tractable algorithms for two approaches to solving stochastic programs. The first approach is based on solving an approximating problem generated by randomly sampling a set of scenarios. The second approach takes advantage of the associated special structure within a sequential approximation method. Both approaches will make use of promising variance reduction techniques to reduce computational overhead. In the educational plan, the investigator will undertake a number of activities, including facilitating the active involvement of students in local industry, developing a new course in stochastic optimization, and building a computational operations research laboratory. In the past decade, advances in computing technology have prompted renewed interest in developing optimization algorithms that directly incorporate uncertainty for a wide range of short- and long-term planning problems. Large-scale stochastic programming models have been used quite successfully in such diverse industries as electric and natural gas utilities, freight vehicle transportation, manufacturing, structural design, and telecommunications. This work has the potential to significantly advance the state-of-the-art in planning models for these fields, and should therefore lead to improvements in the delivery of the products and services produced by these industries.
