In a linear optimization problem, objective function, coefficients matrix, and the right-hand side might be perturbed with distinct parameters independently. For such a problem, we are interested in finding the region that contains the origin, and the optimal partition remains invariant. A computational methodology is presented here for detecting the boundary of this region. The cases where perturbation occurs only in the coefficients matrix and right-hand side vector or the objective function are specified as special cases. The findings are illustrated with some simple examples.