Robust Goal Programming and Risk Assessment using Cardinality-Constrained and Strict Robustness via Alternative Uncertainty Sets
Within many disciplinary applications, data uncertainty is problematic to informing parameters for optimization modeling. Although there exist alternative methods to account for such uncertainty, this research considers robust optimization (RO), wherein variability can be estimated but the probability distribution for different outcomes cannot be reasonably approximated. Within this context, this research sets forth three robust goal programming (RGP) models that alternatively combine cardinality-constrained robustness and norm-based uncertainty sets, as well as strict robustness and ellipsoidal uncertainty sets. With a view towards parametrizing these models for any given decision maker (DM), we also propose a mapping methodology that considers a DMs risk preference a priori and relates this risk preference from the decision analysis subdiscipline to an RO risk parameter in the optimization subdiscipline. Finally, we demonstrate the applicability of the RGP model that applies cardinality-constrained robustness via 2-norm uncertainty sets in unison with the aforementioned mapping methodology to a transportation rate setting problem addressed annually by the United States Transportation Command.