**Appendix A. Discussion on the Determination of Critical Points**

As mentioned in Section 4, the determination of critical points for the illustrative example was connected to difficulties. These difficulties are described in the following subsections and explanation attempts, and future work is proposed. This section of the appendix is intended for the interested reader and concerns specific issues related to the mathematical formulation of the critical point analysis.

For the determination of critical points, the three different strategies and the set covering algorithm presented by Pintariˇc and Kravanja in [44] were considered. As previously mentioned, the approximate one-level formulation depends on a heuristically chosen Big-M parameter and solutions can be very sensitive to this parameter [44]. For this reason, the approximate one-level formulation was discarded from this study. It was identified that depending on the chosen strategy, different aspects need to be considered, which may relate to the structure of the HEN under investigation.
