*Appendix A.3. Adding Critical Points via Flexibility Assessment*

If it is not possible to identify the critical points of the HEN by following the strategies described in [44] and the above suggested modifications and investigations (e.g., different combinations of control variables when applying the two-level formulation), the results of the feasibility check may be utilized. Although it was possible to identify the complete sets of critical points for all design proposals of the reduced superstructure, this step is demonstrated on the example of the proposal MER. Utilizing the KKT formulation, the set of critical points shown in Table A3 were identified. The operating point that limits the flexibility was obtained and the normalized vector between the limiting point and the average operating point (see stream data in Figure 3) was calculated. As the obtained vector was a direction of the corner point [240.0, 210.0, 21.0, 165.0, 10.0, 30.0, 19.2, 28.0], this corner point was added to the set of critical points and the multi-period design problem was solved again. The solution obtained was similar to the feasible design of the proposal MER shown in Table 6. Consequently, in this example, one iteration was necessary to achieve the complete set of critical points and thereby a feasible design. There is, however, no guarantee that one iteration would be sufficient for any other example. It is assumed that especially for examples with one or several critical points that are not corner points, more iterations (and probably trial and error evaluations) are necessary.
