For high-dimensional systems with more outputs than inputs, some outputs must be controlled within ranges, instead of at set-points. This may also be true if the outputs are equal in number to the inputs and disturbances of high magnitude exist. A linear programming framework is postulated to calculate the tightest achievable operating ranges of the outputs, given the ranges of the inputs and the expected disturbances, for any linear input-output control system at the steady-state. This approach removes the computational constraints on the size of the problem that a previous communication of the authors [1] could address. The hyper-volume obtained for the tightest achievable outputs' region of a high-dimensional industrial process is calculated to be four orders of magnitude smaller than the one initially assumed, enabling much tighter control. (C) 2010 Elsevier Ltd. All rights reserved.