An Improvised Approach to Robustness in Linear Optimization

We treat uncertain linear programming problems by utilizing the notion of weighted an-alytic centers and notions from the area of multi-criteria decision making. After introducing ourapproach, we develop interactive cutting-plane algorithms for robust optimization, based on concaveand quasi-concave utility functions. In addition to practical advantages, due to the flexibility of ourapproach, we are able to prove that under a theoretical framework due to Bertsimas and Sim [12],which establishes the existence of certain convex formulation of robust optimization problems, therobust optimal solutions generated by our algorithms are at least as desirable to the decision makeras any solution generated by many other robust optimization algorithms in the theoretical framework.We present some probabilistic bounds for feasibility of robust solutions and evaluate our approach bymeans of computational experiments.