## 3 Materials and Methods
### Uncertainty Propagation
Further research is needed to determine the relationship between our approach and the approach proposed in [PERSON]'s work. ## 4 Results

This example considers a steel manufacturer that is weighing the construction of a new production line for organic-coated sheets. The firm currently produces conventional sheets but now has an opportunity to adopt organic-coating technology. Management must determine whether building the new facility is economically justified. Before construction can begin, the company must prepare project documentation and complete environmental assessments to obtain the required permits; we assume these preparatory activities will cost USD 20,000. To assist in the decision-making process, the company conducts Net Present Value (NPV) and real option analyses. These analyses involve assessing the future cash flows with the help of experts. The key question is whether the company should invest the funds to obtain a return on investment. ### Model for Estimating the Value of Project in Hybrid Environment

In this section, we introduce the NPV model that underpins the real option valuation of a hypothetical production system (see Figure 2). The model extends the framework described in [58]. \[\inf\!\left(\widetilde{\sigma}_{i,\Delta}\right)\leq\sigma_{i}\leq\sup\!\left( \widetilde{\sigma}_{i,\Delta}\right)\!,0\leq\alpha\leq 1,i\in I. \tag{9}\]0 Calculation of Datar–Mathews method in hybrid environment. The project under consideration is the construction of a new plant for manufacturing an organic-coated (OC) steel sheet. The OC sheet is produced from hot-dip-galvanized (HDG) sheet and enjoys both a broader range of applications and a higher unit value. The main input to the process is cold-rolled (CR) sheet, which is first converted to HDG sheet; part of that output is sold directly, while the rest is further processed into OC sheet and sold. Both the HDG and OC stages generate steel-scrap by-products that are likewise sold. To apply the Datar-Mathews (DM) method we must derive \(\varphi\) (npv), the NPV density obtained from a Monte Carlo simulation of the new OC plant. This calls for incremental cash-flow modeling: cash flows in the investment scenario (which includes the OC facility) are compared with those in the baseline scenario (the status quo without the new plant). The project NPV can then be computed with Equations (18)-(32). \[\inf\!\left(\widetilde{\sigma}_{i,\Delta}\right)\leq\sigma_{i}\leq\sup\!\left( \widetilde{\sigma}_{i,\Delta}\right)\!,0\leq\alpha\leq 1,i\in I. \tag{9}\]1

\[\inf\!\left(\widetilde{\sigma}_{i,\Delta}\right)\leq\sigma_{i}\leq\sup\!\left( \widetilde{\sigma}_{i,\Delta}\right)\!,0\leq\alpha\leq 1,i\in I. \tag{9}\]2

\[ \begin{split} PAT_{t}^{scm}=Rev_{t}^{scm}-TC_{t}^{scm}-\max(Rev_{ t}^{scm}-TC_{t}^{scm},0)*TA,\\ scm\in\{base,inv\}\end{split}  \tag{20}\]

\[ \begin{split} Rev_{t}^{inv}=P_{t}^{OC}SV_{t}^{OC}+P_{t}^{HDG}SV_{ t}^{HDG,inv}\end{split}  \tag{21}\]

\[ \begin{split} RV_{t}^{base}=SV_{t}^{HDG,base}P_{t}^{HDG}\end{split}  \tag{22}\]

\[ \begin{split} SV_{t}^{OC,inv}=\min\Big{(}SF_{t}^{DC},CAP^{OC} \Big{)}\end{split}  \tag{23}\]

\[ \begin{split} SV_{t}^{HDG,base}=\min\Big{(}SF_{t}^{HDG},CAP^{HDG }\Big{)}\end{split}  \tag{24}\]

\[ \begin{split} SF_{t}^{prod}=ACF_{t}^{prod}MS^{prod},prod\in\{OC, HDG\}\end{split}  \tag{25}\]

\[ \begin{split} TC_{t}^{base}=SV_{t}^{HDG,base}(VC_{-}RM_{t}^{HDG}+VC _{-}O^{HDG})+DA^{HDG}+FC^{HDG}\end{split}  \tag{26}\]

\[ \begin{split} TC_{t}^{inv}=SV_{t}^{OC,inv}\Big{(}VC_{-}RM_{t}^{OC} +VC_{-}O^{OC}\Big{)}+SV_{t}^{HDG,inv}\big{(}VC_{-}RM_{t}^{HDG}+VC_{-}O^{HDG} \Big{)}\\ +DA^{HDG}+FC^{HDG}+DA^{OC}+FC^{OC}\end{split}  \tag{27}\]

\[ \begin{split} VC_{-}RM_{t}^{HDG}=PUC^{HDG}P_{t}^{CR}+\Big{(}1-PU ^{HDG}\Big{)}P_{t}^{scrap}\end{split}  \tag{28}\]

\[ \begin{split} VC_{-}RM_{t}^{OC}=PUC^{OC}P_{t}^{HDG}-\Big{(}1-PU ^{OC}\Big{)}P_{t}^{scrap}\end{split}  \tag{29}\]

\[ \begin{split}\Delta NWC_{t}^{scm}=NWC_{t}^{scm}-NWC_{t-1}^{scm},t= 1,\ldots,T\end{split}  \tag{30}\]

Figure 2: A description of the analyzed production setup. \[