## 3 Case Study
### Calculations
#### 3.1.1 Development of the Calibration Model
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**Real**} & \multicolumn{2}{c}{**Simulation**} & \multirow{2}{*}{**Error**} \\ \cline{3-4}  & & & **Mean** & **Half-Width** \\ \hline Total Production & 332,752.3 & 334,780.1 & 107.1 & 0.61\% \\ Moved Tons Shovel 1 & 108,720.0 & 109,236.0 & 56.8 & 0.47\% \\ Moved Tons Shovel 2 & 93,503.3 & 94,376.5 & 52.3 & 0.93\% \\ Moved Tons Shovel 3 & 96,206.0 & 96,474.6 & 86.5 & 0.28\% \\ Moved Tons FEL 3 & 17,257.0 & 17,457.7 & 23.3 & 1.15\% \\ Moved Tons FEL 1 & 17,066.0 & 17,235.3 & 24.0 & 0.98\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Validation of the calibration model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Grade (\%)**} & **Velocity When** & **Velocity When** & **Grade (\%)** & **Velocity When** & **Velocity When** \\  & **Loaded (km/h)** & **Empty (km/h)** & **Loaded (km/h)** & **Empty (km/h)** \\ \hline \(-12\) & 14.3 & 30.8 & 12 & 10.5 & 12.7 \\ \(-11\) & 14.3 & 30.8 & 11 & 10.5 & 12.7 \\ \(-10\) & 14.3 & 30.8 & 10 & 10.5 & 12.7 \\ \(-9\) & 16.9 & 32.3 & 9 & 12.0 & 15.2 \\ \(-8\) & 19.6 & 33.8 & 8 & 13.4 & 17.6 \\ \(-7\) & 22.2 & 35.3 & 7 & 14.9 & 20.0 \\ \(-6\) & 24.9 & 36.8 & 6 & 16.3 & 22.4 \\ \(-5\) & 27.5 & 38.3 & 5 & 17.8 & 24.8 \\ \(-4\) & 29.0 & 39.8 & 4 & 21.2 & 29.0 \\ \(-3\) & 30.4 & 41.4 & 3 & 24.6 & 33.3 \\ \(-2\) & 31.9 & 42.9 & 2 & 28.0 & 37.5 \\ \(-1\) & 33.3 & 44.4 & 1 & 31.4 & 41.7 \\ \(0\) & 34.8 & 45 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Velocities reached by trucks according to road grade. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Equipment/Destination** & **Crusher** & **Stock 1** & **Stock 2** & **Stock 3** & **Waste Dump 2** \\ \hline Shovel 1 & 58,762 & & 39,558 & 10,400 & \\ Shovel 2 & 42,276 & 36,962 & & 13,500 & 766 \\ Shovel 3 & & 13,443 & & 38,987 & 43,776 \\ FEL 3 & & & & 17,257 \\ FEL 1 & & & & 17,066 \\ Total Tonnage & 101,038 & 50,405 & 39,558 & 62,887 & 78,865 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results to replicate by the simulation. From Table 6, the maximum prediction error for all the parameters was 1.15%. Having small error values is critical, considering that the more time is simulated, the more the deviation from the simulated output values. After 100 simulations for a 20-h day, all the information from the Arena model was processed, and the following results were obtained (Figure 3). In Figure 3, it can be observed that real tonnages moved during the chosen day were almost similar to the results obtained from the simulation. This difference could be reduced even more if the bucket payload was added, as this restriction would limit the total tonnage to load, and the result would be closer to the real tonnage. Regarding the number of trucks employed by the simulation for each piece of loading equipment, the simulation required 24 trucks in total during that day, as shown in Table 7.  
Considering that the mechanical availability that day was 83.43%, and the number of trucks required by the model was 24, then by applying Equation (5), the number of \begin{table}
\begin{tabular}{c c} \hline \hline
**Equipment** & **Number of Trucks** \\ \hline Shovel 1 & 6 \\ Shovel 2 & 7 \\ Shovel 3 & 7 \\ FEL 3 & 2 \\ FEL 1 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Truck distribution for each piece of loading equipment. Figure 3: Real tonnages versus simulated results. trucks in the truck fleet was 29. This figure was equal to the number of trucks used in the operation. On the other hand, the behavior of the overall cycle time reflected the times at the mine operation. These values are shown in Figure 4.  
These truck cycle times were reviewed for each destination to check whether they reflected the real cycle times at the mine or not. Otherwise, the velocities, road grades, or PDF would have been reviewed. Figures 5-8 show the behavior of these cycle times. After having reviewed the results generated by the simulation, the yearly plan was developed.