Flexibility Assessment via Affine Bounds Evaluation

Process design deals with the problem of finding the best process set-up, subject to a set of constraints defining the design space (DSp). This selection is guided primarily by economic considerations. Flexibility may also play an important factor in process design, since it embodies �how far� from the design space�s bounds are the candidate optimal designs, which in some cases may lead to off-spec products. This work proposes a novel approach for flexibility assessment. In design problems where the design space is constrained by a set of affine bounds, flexibility may be expressed either as the minimum or the maximum distance with respect to the feasible (design) space bounds. For any point in the DSp, the minimum distance provides a good indicator on the minimum flexibility, as the direction that represents the highest risk of violating the constraints. An analogous conclusion can be drawn between the maximum distance and maximum flexibility. These distances can be computed exactly via geometrical approaches, enabling the calculation of a minimum-based and maximum-based flexibility metrics for all points in the DSp. This class of problems are in fact multiparametric programming problems as the goal is to obtain comprehensive flexibility maps, rather than investigating unique points in the DSp. In the case of minimum flexibility, their solutions comprise: (i) a set of critical regions defining a convex hull within the DSp (each associated with a unique nearest bound of the feasible space), (ii) the corresponding optimizer functions (projection at nearest bound), and (iii) objective functions (minimum distance). A novel framework is under development for this class of problems. It enables a new paradigm for flexibility assessment, which can be applied to design problems of any dimension. Complexity is significantly reduced in comparison with the classic multiparametric programming approaches, since only a limited number of active sets need to be considered during solution calculation.