  Robust optimization is a framework for modeling optimization problems
involving data uncertainty and during the last decades has been an area of
active research. If we focus on linear programming (LP) problems with i)
uncertain data, ii) binary decisions and iii) hard constraints within an
ellipsoidal uncertainty set, this paper provides a different interpretation of
their robust counterpart (RC) inspired from decomposition techniques. This new
interpretation allows the proposal of an ad-hoc decomposition technique to
solve the RC problem with the following advantages: i) it improves
tractability, specially for large-scale problems, and ii) it provides the exact
probability of constraint violation in case the probability distribution of
uncertain parameters are completely defined by using first and second-order
probability moments. An attractive aspect of our method is that it decomposes
the second-order cone programming problem, associated with the robust
counterpart, into a linear master problem and different quadratically
constrained problems (QCP) of considerable lower size. The optimal solution is
achieved through the solution of these master and subproblems within an
iterative scheme based on cutting plane approximations of the second-order cone
constraints. In addition, proof of convergence of the iterative method is
given.
