Evaluation and redesign for improving flexibility in linear systems with infeasible nominal conditions

This note deals with the problem of evaluating the flexibility index for existing designs for which the new nominal value of operation of the uncertain parameters is infeasible. In this case one can not inscribe within the region of operation the largest hyperrectangle to determine the flexibility index. However, it is shown that for linear systems a negative value of the index can be defined in terms of active sets of constraints that limit flexibility. Furthermore, it is shown that the optimal redesign to increase flexibility can easily be obtained with the procedure by Pistikopoulos and Grossmann (1987). A small example is presented to illustrate these ideas.