*4.4. Discussion of the Results of the Illustrative Example*

As mentioned previously, a discussion around the determination of the set of critical points for the different retrofit proposals of the illustrative example can be found in Appendix A.

Based on the results presented in Table 6, the proposal MER performs the most cost efficiently. This, however, relates to the used cost functions. Different cost functions will certainly lead to different results and another proposal may be most cost efficient. The influence of the cost functions can be illustrated by a comparison of the solutions of proposals 1 and MER. An analysis of the results of the multi-period design problem of proposals 1 and MER revealed that the TAC of proposal 1 consists of 23% annualized capital cost (and 77% operating cost) while the TAC of proposal MER consists of 56% annualized capital cost (and 44% operating cost). Thus, the used cost functions favor design proposals that allow more utilization of the HEX surface area. However, if the cost for the area is increased (e.g., increased parameters in investment cost functions), it can be assumed that design proposals that allow more utilization of utilities will be more cost efficient.

From Table 6, it can be seen that design proposal 2 has a significantly higher flexibility index than 1, which indicates overdesign of the HEX units. This overdesign results from the consideration of the chosen representative operating points. When the multi-period design problem for proposal 2 was solved considering only the identified set of critical points (and discard all operating cost), the flexibility index of the achieved design was calculated as 1. To check the influence of the representative operating periods and thereby the completeness of the identified sets of critical points, similar calculations were

also made for the other design proposals in the reduced superstructure and the results are shown in Table 7. The results in Table 7 indicate that the sets of critical points shown in Table A5 are complete as it was possible to achieve feasible design characteristics (flexibility index is 1) respecting only the sets of critical points. As all operating costs were discarded, the objective function of these design problems represented only the total annualized capital cost of a certain design.

**Table 7.** Total annualized (capital) cost and flexibility index of the different retrofit design proposals in the reduced superstructure without considering the representative operating points.

