A Relative Robust Optimization Approach for Full Factorial Scenario Design of Data Uncertainty and Ambiguity

Summary

This chapter presents a relative robust optimization algorithm for two-stage decision making under uncertainty (ambiguity) where the structure of the first-stage problem is a mixed integer linear programming model and the structure of the second-stage problem is a linear programming model. In the structure of the considered problem, 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 chapter as the full-factorial scenario design of data uncertainty. The algorithm is shown to be efficient for solving large-scale relative robust optimization problems under this structure of the parametric uncertainty. The algorithm coordinates three computational stages to efficiently solve the overall optimization problem. Bi-level programming formulations are the main components in two of these three computational stages. The main contributions of this chapter are the theoretical development of the robust optimization algorithm and its applications in robust strategic decision making under uncertainty (e.g., supply chain network infrastructure design problems).