Distribution and Moment-Robust Optimization Models and Algorithms

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Optimization models and methods are widely used in decision problems. Incorporating parameter uncertainty is important in constructing representative optimization models. This parameter uncertainty may be described by a probability distribution, the moments of a probability distribution, or using bounds and confidence intervals on moments. When estimating uncertain parameters, information is also available on the error distribution of the estimated parameter. The research objective of this award is to study properties and develop algorithmic methods for solving multivariate optimization models that incorporate parameter uncertainty using limited knowledge on their distribution, and the parameter estimation errors. The optimization models will be based on using parameter distribution moment estimates. The models will incorporate moment estimation errors using a suitable penalty approach. If successful, the results of this research will lead to the development of a new class of decision optimization modeling tools with associated algorithmic techniques for solving these models. This award will contribute to better handling of parameter uncertainty in single and two-stage inventory planning models, the classical least squares model, and the models involving objectives described by quadratic functions. A better understanding of algorithmic implications of parameter uncertainty in these problems will provide foundation for handling parameter uncertainty in other application models that use the planning, the least squares and quadratic objectives as basic building blocks. The award will also contribute to the development of computational tools implementing the algorithms solution techniques. Experiments will be performed to validate the algorithms, and to compare the properties of the solutions generated from the models incorporating distributional knowledge with those that ignore this information.