## 3 Methodology
### Algorithms for Determining and Evaluating the Optimal Amount of Ore Hailing Equipment
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**Minimize \(k\)**} & & & \multicolumn{3}{c}{**Minimize \(C_{max}\)**} \\ \cline{4-9} \(v\) & \(m\) & \(P\) & \(C_{maxub}\) & \(k\) & \(Tc\) & \(C_{maxlb}\) & \(k\) & \(Tc\) \\ \hline
19 & 4 & 200 & 51 & 2350 & 151.46 & 33 & 6998 & 54.97 \\
18 & 4 & 200 & 51 & 2350 & 219.68 & 33 & 6648 & 46.31 \\
17 & 4 & 200 & 51 & 2350 & 117.08 & 33 & 6298 & 38.57 \\
16 & 4 & 200 & 51 & 2350 & 99.44 & 33 & 5948 & 33.81 \\
15 & 4 & 200 & 51 & 2350 & 125.16 & 33 & 5598 & 31.16 \\
14 & 4 & 200 & 51 & 2350 & 162.80 & 33 & 5248 & 26.78 \\
13 & 4 & 200 & 51 & 2350 & 75.34 & 34 & 4898 & 24.63 \\
12 & 4 & 200 & 51 & 2350 & 58.55 & 35 & 4548 & 20.73 \\
11 & 4 & 200 & 51 & 2350 & 111.22 & 37 & 4198 & 21.40 \\
10 & 4 & 200 & 51 & 2350 & 103.30 & 40 & 3848 & 32.76 \\
9 & 4 & 200 & 50 & 2350 & 44.62 & 44 & 3498 & 19.40 \\
8 & 4 & 200 & 51 & 2350 & 76.94 & 49 & 3148 & 15.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of optimizing the proposed algorithms. Decision-makers must weigh the cost increase associated with using more equipment against reducing hauling time. Beyond a certain point, adding more hauling units diminishes the benefit of lowering completion time but incurs substantially higher costs. Pinpointing the moment when the additional cost no longer justifies the decrease in hauling time is critical for optimizing operations and managing resources efficiently. ### Operational Approach Insights

Figure 5 shows the schedule, for instance 34, which considers eight hauling and four loading equipment. This visualizes the ore loading program for a mining operation during the first 50 trips of the production target. It is interesting to see how the allocation is organized to ensure that the minimum necessary amount of hauling equipment is kept in constant motion, indicating a careful assessment of loading times and intervals between tasks. This strategy ensures that no loading equipment remains idle and that the hauling equipment is effectively distributed to meet the production target. By minimizing the amount of hauling equipment, the operation can become more cost-effective and improve logistics by reducing congestion and potential bottlenecks in the ore hauling operation. This balanced approach between efficiency and effectiveness in scheduling is crucial for a successful operation that adapts to the dynamic and often unpredictable demands of mining. Table 6 provides a detailed distribution of loading and hauling equipment utilization in a mining operation, highlighting the allocation and usage of these resources in production. It is observed that loading equipment two and three are the most utilized, with utilization percentages of 32% and 30%, respectively, indicating high demand and frequent use. In contrast, loading vehicle four is the least utilized, operating at only 12% utilization. This suggests that resources are not being fully optimized, particularly considering that loading vehicle four might be the most costly to operate, as less frequently used equipment typically requires regular maintenance and occupies valuable space that could be better utilized. The under-utilization of the costly loading equipment fourraises significant cost management and operational efficiency considerations. The high cost of this equipment may be due to specialized features that necessitate more sophisticated maintenance or a higher initial investment. However, its sub-optimal utilization implies that this investment needs to yield the expected returns, which is critical in operations aiming to maximize efficiency and profitability. This situation underscores the urgent need to reassess task distribution and resource allocation to ensure that all loading equipment are utilized in a manner that justifies their cost, thereby optimizing the entire operation and reducing potential resource wastage.