# Multi-Agent Simulation Approach for Modular Integrated Construction Supply Chain
## 4 Results and Discussion
### Results
#### 4.2.1 Results of Scenario 1  
In this scenario, prefabricated components are supplied directly to the construction site by five suppliers. Figure 7 presents the GIS map from AnyLogic's simulation showing the locations of each supplier and construction site.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Scenario 1** & **Scenario 2** & **Unit** \\ \hline Number of Suppliers & 5 & 5 & - \\ Number of MiC Factories & - & 1 & - \\ Number of Vehicles (\(T_{1}\)) per Supplier & [1, 2, 3, 4, 5] & [1, 2, 3, 4, 5] & - \\ Number of Vehicles (\(T_{2}\)) per Factory & - & 1 & - \\ Average Requests per Day & 60 C by the construction site & 60 C by the MiC Factory, 3 M & C: Components, \\ Fixed Cost per Vehicle per Day & 150 & 150 for \(T_{1}\), 200 for \(T_{2}\) & EUR \\ Variable Cost per km & 2 & 2 for \(T_{1}\), 3 for \(T_{2}\) & EUR \\ Project Delay Penalty per Day & 500 & 500 & EUR \\ Initial Components In Storage per supplier & uniform(5, 10) & uniform(5, 10) & Components \\ Production Capacity per Day & uniform(10, 15) C per supplier & uniform(10, 15) C per supplier & C: Components, \\  & 3 M per factory & M: Modules \\ Vehicle Speed & uniform(50, 70) & uniform(50, 70) for \(T_{1}\), & km/h \\ Supplier Locations (from the & Supplier 1: 85, Supplier 2: 130, & Supplier 1: 85, Supplier 2: 130, & \\  & Supplier 3: 145, Supplier 4: 75, & Supplier 3: 145, Supplier 4: 75, & km \\  & Supplier 5: 135 & Supplier 5: 135 & \\  & & Supplier 1: 70, Supplier 2: 125, & \\ Supplier Locations (from the MiC factory) & - & Supplier 3: 155, Supplier 4: 75, & km \\  & & Supplier 5: 125 & \\ MiC Factory Location (from the & - & 20 & km \\ construction site) & - & Paris, France & - \\  & Normal Project Completion Time & 120 & days \\ \hline \end{tabular}
\end{table}
Table 3: Summary of parameters for study scenarios.  
The results for Scenario 1 are presented in Table 4.  
In Scenario 1, we analyze the costs associated with the delivery of prefabricated components. Table 4 shows how the total cost varies with the number of vehicles used by each supplier.  
The variable cost remains constant at EUR 1,938,540 across all configurations. This indicates that the total distance traveled by all vehicles does not change with the number of vehicles, suggesting a stable demand and consistent routing efficiency.  
The fixed cost increases with the number of vehicles. For instance, with one vehicle per supplier, the total fixed cost is EUR 237,000, which rises to EUR 322,500 when five vehicles are used per supplier.  
Penalties are incurred due to project delays. When only one vehicle per supplier is used, the delay costs EUR 98,000, reflecting significant delays. As the number of vehicles increases, the penalty decreases, eventually reaching zero when three or more vehicles are used. This demonstrates that having more vehicles reduces the likelihood of project delays, ensuring the timely delivery of components.  
The optimal number of vehicles appears to be three, as this configuration has the lowest total cost of EUR 2,177,040, with no penalty costs and balanced fixed costs. Adding more vehicles increases the fixed costs without further reducing penalties, leading to higher total costs.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number of Vehicles per Supplier**} & \multirow{2}{*}{**Total Variable Cost (EUR)**} & \multicolumn{2}{c}{**Total Fixed Cost**} & \multirow{2}{*}{**Penalty (EUR)**} & \multirow{2}{*}{**Total Cost (EUR)**} \\  & & **(EUR)** & & \\ \hline
1 & 1,938,540 & 237,000 & 98,000 & 2,273,540 \\
2 & 1,938,540 & 238,500 & 19,500 & 2,196,540 \\
3 & 1,938,540 & 238,500 & 0 & 2,177,040 \\
4 & 1,938,540 & 258,000 & 0 & 2,196,540 \\
5 & 1,938,540 & 322,500 & 0 & 2,261,040 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results of Scenario 1.  
Figure 7: Scenario 1: locations of each supplier and construction site.