The unsteady chemical processes, designed according to the nominal operating conditions and fixed model parameters, have traditionally been evaluated with economic criteria. This design strategy often ends up with a plant which may become inoperable if some of the process conditions/parameters unexpectedly deviate from their normal levels. Two alternative performance measures, the dynamic and temporal flexibility indices, have thus been devised in recent years to characterize designs from a different viewpoint. However, not only their significances still have not been adequately interpreted and their roles clarified, but also their numerical values cannot be determined efficiently with the available algorithms. In this study, the simple trapezoidal rule is applied to discretize and integrate the dynamic models and a heuristic strategy is then utilized to implement the vertex method for computing the aforementioned metrics efficiently. To demonstrate the effectiveness of the proposed computation approaches, comprehensive case studies concerning two dynamic systems, that is, the buffer system and the solar driven membrane distillation desalination system (SMDDS), have been carried out. The resulting insights have also been summarized in a heuristic design procedure to incorporate both indices for general applications.