## 4 Numerical Experiments
### Comparison of Results  
In this section, the results are compared, considering problem size and capacity change. First, the problem size is increased by introducing more factories and more processes into the process whereby production takes place. The number of connected smart factories is increased to 12, in two separate units. In addition, the number of processes is increased to 10, in two units. Demand is fixed at 100. In all cases, the computation time required to solve each problem was less than one second. In Figure 5, the number before the parentheses represents the number of connected smart factories, and the number within parentheses represents the number of processes required.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Day 1** & **Day 2** & **Day 3** & **Day 4** & **Day 5** & **Day 6** & **Day 7** \\ \hline Process 1 (Factory 1) & 10 & 10 & 10 & 10 & 3 & 0 \\ Process 1 (Factory 2) & 10 & 10 & 10 & 10 & 7 & 0 & 0 \\ Process 2 (Factory 1) & 9 & 20 & 20 & 20 & 19 & 12 & 0 \\ Process 3 (Factory 1) & 7 & 9 & 10 & 10 & 10 & 10 & 0 \\ Process 3 (Factory 3) & 0 & 2 & 8 & 10 & 10 & 10 & 4 \\ Process 4 (Factory 4) & 0 & 9 & 16 & 20 & 20 & 20 & 15 \\ \hline \end{tabular}
\end{table}
Table 6: Production plan–Demand for marketing test.  
Figure 4: Dynamic supply chain design and operation. (**a**) Individual request; (**b**) Demand for marketing test.  
\begin{table}
\begin{tabular}{c c c} \hline  & **Day 1** & **Day 2** & **Day 3** \\ \hline Process 1 (Factory 1) & 1 & 0 & 0 \\ Process 2 (Factory 2) & 0 & 1 & 0 \\ Process 3 (Factory 2) & 0 & 1 & 0 \\ Process 4 (Factory 2) & 0 & 1 & 0 \\ \hline \end{tabular}
\end{table}
Table 5: Production plan–Individual request.  
With a demand of 100, it is observed that the total cost increases as the size of the problem increases, as shown in Figure 5. The greater the number of processes required to complete the product, the higher the total cost, with a significant increase in transportation costs. Also, it is observed that fixed costs account for a smaller proportion of total cost as the problem increases in size. Therefore, efforts should be made to reduce the number of processes required for personalized products during design.  
Next, the number of processes was fixed at eight and network-connected factories at ten, to investigate the effect of a change in capacity. Figure 6a,b show the structure of the supply chain that is designed for 20% less and 30% more capacity respectively. If capacity is small, more factories are needed for each process, which leads to a complicated supply chain design and an increase in cost. One interesting fact is that the supply chain or network of nodes with a larger capacity is not a subset of the supply chain with a lower capacity. Therefore, it should be emphasized that the dynamic supply chain design should be based on real-time data, including demand and available capacity.  
The cost structures of the experiments with factory capacities that vary from \(-20\%\) to \(30\%\) are shown in Figure 7. If the capacities of the factories located in the network become smaller, it becomes impossible to allocate products to less expensive factories, which increases the total cost. Because a given product can be produced in a smaller number of factories at a lower cost, the fixed cost and production cost are somewhat lower, and the transportation cost decreases significantly. For example, when we have 20% less capacity, the percentage of transportation costs is 53%, while the portion of transportation cost decreases to 42% with 20% more capacity.  
Figure 5: Cost comparison based on change in problem size.  
Figure 6: Dynamic supply chain design. (**a**) 20% less capacity; (**b**) 30% more capacity.