# Birth Allocation and Query Crane Assignment Considering the Uncertain Maintenance Requirements
## 6 Numerical Experiments
### Sensitivity Analysis  
Furthermore, a sensitivity analysis was conducted to explore how varying key operational parameters impacted system performance. Parameters such as the number of vessels, berths, QCs, and maintenance duration, as well as the handling capacity of cranes, were adjusted. For each adjustment, the effect on the objective function comprising total costs, waiting times, crane movements, and overlap penalties was evaluated. The analysis revealed that increasing vessel numbers or extending maintenance duration led to higher costs and longer completion times, providing valuable insights into the key factors influencing scheduling outcomes. Specifically, we examined the impact of varying fault locations and the preferred berth segments of vessels on rescheduling strategies. A consistent relative fault degree for quay cranes was assumed across vessels of varying sizes. Additionally, sensitivity analysis was performed to assess the effect of different QC fault locations on the rescheduling process. For each vessel, five distinct fault scenarios were generated based on different fault locations, and five experiments were conducted to calculate average values, as depicted in Figure 8.  
In the Small Scale Sensitivity Analysis (Figure 8), distinct trends emerge regarding the influence of different parameters on the objective value as the adjustment level changes. The most significant factor is the number of vessels, where an increase leads to a sharp rise in the objective value, reflecting the higher scheduling complexity and costs associated with handling a larger fleet. Conversely, the number of berths demonstrates an inverse relationship with the objective value, as more berths lead to greater operational efficiency and reduced costs. The number of quay cranes and the maintenance duration show more subtle effects. While an initial increase in quay cranes raises the objective value, the effect stabilizes at higher levels, suggesting diminishing returns once a certain crane capacity is reached. Maintenance duration exerts only a minor influence, indicating that its impact is secondary to other operational factors in this small-scale setting. Figure 9 provides the results of the Large Scale Sensitivity Analysis, where similar trends are observed, though with notable differences in magnitude and patterns of influence. The number of vessels remains a critical driver of the objective value. However, in this larger-scale context, the number of quay cranes takes on an even more prominent role. At higher adjustment levels, increasing the number of quay cranes results in a significant rise  
Figure 7: Iterative curve of differential evolution algorithm. in the objective value, emphasizing the importance of efficient crane management in larger, more complex operations. While the number of berths still contributes to reducing the objective value, its effect is less pronounced compared to the small-scale case, likely due to diminishing returns as system size grows. Maintenance duration continues to have a relatively minor impact, with its influence remaining stable across adjustments. These findings underscore that, in large-scale scheduling problems, both the number of vessels and the allocation of quay cranes are primary cost drivers. In contrast, the availability of berths, while still beneficial, plays a diminishing role as operational complexity increases. Effective crane management becomes critical in larger port operations to avoid significant cost escalations. In conclusion, the sensitivity analysis demonstrates that the number of vessels and quay cranes are crucial determinants of scheduling efficiency and overall costs. As the scale of the problem increases, the relative importance of these factors shifts, with crane management becoming increasingly dominant. Although berth availability helps lower costs, its influence weakens in larger-scale scenarios, stressing the need for strategies that prioritize the efficient utilization of cranes and vessel handling.