Min-Max Regret Robust Optimization Approach on Interval Data Uncertainty

This paper presents a three-stage optimization algorithm for solving two-stage deviation robust decision making problems under uncertainty. The structure of the first-stage problem is a mixed integer linear program and the structure of the second-stage problem is a linear program. Each uncertain model parameter can independently take its value from a real compact interval with unknown probability distribution. The algorithm coordinates three mathematical programming formulations to iteratively solve the overall problem. This paper provides the application of the algorithm on the robust facility location problem and a counterexample illustrating the insufficiency of the solution obtained by considering only a finite number of scenarios generated by the endpoints of all intervals.