This paper investigates the vulnerability of optimal solutions to Linear Programming (LP) problems when subjected to small data perturbations. Using the well-known NETLIB collection of 90 LP problems, the authors demonstrate that nominal optimal solutions can become severely infeasible under slight uncertainty. They apply Robust Optimization methodology to generate "robust" solutions that are immune to data perturbations, with minimal loss in optimality. The study begins with an example from the PILOT4 problem, where a nominal optimal solution is found to violate constraints under small perturbations of uncertain coefficients. The authors argue that many coefficients in LP problems are "ugly reals" that likely reflect uncertain data, and that small perturbations can lead to significant infeasibility. The paper introduces a reliability index to quantify the infeasibility of nominal solutions under uncertainty. It defines an ε-reliability index for each constraint, which measures the likelihood of constraint violation under random perturbations. The analysis shows that many NETLIB problems have nominal solutions that are infeasible under even small uncertainty levels. The authors then apply Robust Optimization techniques to generate robust solutions that are immune to data perturbations. Two approaches are considered: "unknown-but-bounded" uncertainty and "random symmetric uncertainty." The results show that robust solutions can be found with minimal loss in optimality, often less than 1% for 0.1% data perturbations. The study concludes that robust optimization provides a systematic and computationally feasible way to generate reliable solutions that can withstand data uncertainty. The methodology is essential for real-world applications where data uncertainty is inherent. The results demonstrate that robust solutions maintain high optimality while being immune to data perturbations, making them valuable for practical use.This paper investigates the vulnerability of optimal solutions to Linear Programming (LP) problems when subjected to small data perturbations. Using the well-known NETLIB collection of 90 LP problems, the authors demonstrate that nominal optimal solutions can become severely infeasible under slight uncertainty. They apply Robust Optimization methodology to generate "robust" solutions that are immune to data perturbations, with minimal loss in optimality. The study begins with an example from the PILOT4 problem, where a nominal optimal solution is found to violate constraints under small perturbations of uncertain coefficients. The authors argue that many coefficients in LP problems are "ugly reals" that likely reflect uncertain data, and that small perturbations can lead to significant infeasibility. The paper introduces a reliability index to quantify the infeasibility of nominal solutions under uncertainty. It defines an ε-reliability index for each constraint, which measures the likelihood of constraint violation under random perturbations. The analysis shows that many NETLIB problems have nominal solutions that are infeasible under even small uncertainty levels. The authors then apply Robust Optimization techniques to generate robust solutions that are immune to data perturbations. Two approaches are considered: "unknown-but-bounded" uncertainty and "random symmetric uncertainty." The results show that robust solutions can be found with minimal loss in optimality, often less than 1% for 0.1% data perturbations. The study concludes that robust optimization provides a systematic and computationally feasible way to generate reliable solutions that can withstand data uncertainty. The methodology is essential for real-world applications where data uncertainty is inherent. The results demonstrate that robust solutions maintain high optimality while being immune to data perturbations, making them valuable for practical use.