Given an originally robust optimal decision and allowing perturbation parameters of the linear programming problem to run through a maximum uncertainty set controlled by a variable of perturbation radius, we do robust sensitivity analysis for the robust linear programming problem in two scenarios. One is to keep the original decision still robust optimal, the other is to ensure some properties of the original decision preserved in the robust optimal solution set. In each scenario, we do analyses in three cases with different perturbation styles. All models in our study are formulated into either linear programs or second-order conic programs except for some cases considering more than one row perturbation in the constraint matrix. For those, we develop a binary search algorithm.
Department of Mathematical Sciences, Tsinghua University, Beijing, China,