## 3 Methodology--Mathematical Modelling and Heuristic Optimization Method
#### 3.2.1 Black Hole Optimization-Based Clustering
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Routes**} & \multirow{2}{*}{**EGS 1**} & \multicolumn{6}{c}{**Emission**} \\ \cline{3-8}  & & **CO2** & **SO2** & **CO** & **HC** & **NOX** & **PM** \\ \hline \multirow{2}{*}{**Specific emissions in g/liter fuel consumption [114]**} & \multirow{2}{*}{-} & \multirow{2}{*}{2629} & \multirow{2}{*}{0.08} & \multirow{2}{*}{2.2} & \multirow{2}{*}{1.2} & \multirow{2}{*}{11.9} & \multirow{2}{*}{0.1} \\ \cline{3-8}  & & & & & & & \\ \hline \multirow{6}{*}{**Specific emission in g/liter fuel consumption [114]**} & \multirow{2}{*}{-} & \multirow{2}{*}{2629} & \multirow{2}{*}{0.08} & \multirow{2}{*}{2.2} & \multirow{2}{*}{1.2} & \multirow{2}{*}{11.9} & \multirow{2}{*}{0.1} \\ \cline{3-8}  & & & & & & & \\ \hline \multirow{6}{*}{**Specific emission 2**} & \multirow{2}{*}{
\begin{tabular}{c} Lignite \\ Coal \\ Oil \\ \end{tabular} } & 1054 & 0.032 & 0.880 & 0.480 & 4.760 & 0.040 \\  & Coal & 888 & 0.028 & 0.733 & 0.400 & 3.960 & 0.030 \\  & Oil & 733 & 0.022 & 0.615 & 0.335 & 3.324 & 0.028 \\  & Natural gas & 499 & 0.016 & 0.418 & 0.228 & 2.226 & 0.019 \\  & Photovoltaic & 85 & 0.002 & 0.073 & 0.040 & 0.396 & 0.003 \\  & Biomass & 45 & 0.001 & 0.038 & 0.021 & 0.205 & 0.002 \\  & Nuclear & 29 & \textless{}10^{-3}\) & 0.024 & 0.013 & 0.132 & 0.001 \\  & Water & 26 & \textless{}10^{-3}\) & 0.022 & 0.012 & 0.119 & 0.001 \\  & Wind & 26 & \textless{}10^{-3}\) & 0.022 & 0.012 & 0.119 & 0.001 \\ \hline \hline \end{tabular}  
* \({}^{1}\) EGS = Electricity Generation Source. 2 in CO2 emission in g/kWh.  
\end{table} 
Table 10: Calculated greenhouse gas (GHG) emission depending on the electricity generation source. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario 1**} & \multicolumn{6}{c}{**Emission**} \\ \cline{2-7}  & **CO2** & **SO2** & **CO** & **HC** & **NOX** & **PM** \\ \hline Extended scheduling of known supply-demands & 8600 & 0.26 & 7.1808 & 3.9168 & 38.841 & 0.3264 \\ Real-time scheduling with added new supply-demand & 9106 & 0.27 & 7.6032 & 4.1472 & 41.126 & 0.3456 \\ Separated route for new supply-demand & 1264 & 0.04 & 1.056 & 0.5760 & 5.7120 & 0.0480 \\ Emission reduction with real-time scheduling & 843.2 & 0.03 & 0.7004 & 0.3840 & 3.808. & 0.0320 \\ \hline \hline \end{tabular}  
* \({}^{1}\) We are calculating with 100 routes.  
\end{table} 
Table 11: Calculated GHG emission in the case of lignite-based electricity generation. The above-described scenario validated the presented model based on extended and real-time routing, scheduling, and assignment and justifies the fact that in matrix production the enhanced logistics performance must be optimized in order to increase energy efficiency and decrease GHG emission. Figure 19 demonstrates the physical appearance of a matrix production system, where the flexible manufacturing and assembly cells are arranged in a grid layout. To summarize, the proposed optimization model including a black hole algorithm-based clustering and a floral pollination-based routing and assignment makes it possible to analyze the impact of real-time routing in a complex, flexible cyber-physical manufacturing environment, where manufacturing and logistics are separated and the supply of categorized, standardized manufacturing and assembly cells is performed with autonomous electric vehicles. As the findings of the literature review show, the articles that addressed the in-plant supply of manufacturing processes are focusing on conventional production environments, but none of the articles aimed to identify the challenges of matrix production. The comparison of our results with those from other studies shows that the optimization of in-plant supply processes in a cyber-physical environment still needs more attention and research.