This paper presents a three-stage optimization algorithm for solving two-stage robust decision making problems under uncertainty with min-max regret objective. The structure of the first stage problem is a general mixed integer (binary) linear programming model with a specific model of uncertainty that can occur in any of the parameters, and the second stage problem is a linear programming model. Each uncertain parameter can take its value from a finite set of real numbers with unknown probability distribution independently of other parameters’ settings. This structure of parametric uncertainty is referred to in this paper as the full-factorial scenario design of data uncertainty. The proposed algorithm is shown to be efficient for solving large-scale min-max regret robust optimization problems with this structure. The algorithm coordinates three mathematical programming formulations to solve the overall optimization problem. The main contributions of this paper are the theoretical development of the three-stage optimization algorithm, and improving its computational performance through model transformation, decomposition, and pre-processing techniques based on analysis of the problem structure. The proposed algorithm is applied to solve a number of robust facility location problems under this structure of parametric uncertainty. All results illustrate significant improvement in computation time of the proposed algorithm over existing approaches.
Industrial Engineering University of Houston, June 2007