# Birth Allocation and Query Crane Assignment Considering the Uncertain Maintenance Requirements
## 6 Numerical Experiments  
In this section, we evaluate the effectiveness of the developed differential evolution algorithm through a series of computational experiments. The algorithm was implemented in Python 3.11 and executed on a system featuring an Intel Core i9-13900 HX 2.20 GHz processor and 16 GB of memory. The study focuses on analyzing quay crane (QC) maintenance sensitivity by simulating small-scale and large-scale scenarios for berth and crane allocation. The primary objective was to assess the impact of QC maintenance on overall operational efficiency, specifically targeting resource utilization and scheduling flexibility. To address this, two experimental setups were implemented. In the small-scale experiment, we examined a scenario involving 6 vessels, 4 berths, and 5 QCs. The arrival times of vessels were randomly generated to simulate real-world variability, and a predefined maintenance plan was applied, with Cranes 1 and 4 scheduled for maintenance. The maintenance durations were randomly assigned to introduce uncertainty into the schedule. The allocation of cranes to vessels was visualized under two conditions: one where all cranes were fully operational and another where crane availability  
Figure 3: Flowchart of the SWO-DE heuristic method. was constrained due to maintenance. These visualizations revealed shifts in scheduling and highlighted potential delays in vessel processing due to maintenance-induced interruptions (Figure 4). For the large-scale experiment, the model was expanded to 20 vessels, 10 berths, and 10 QCs. Similar to the small-scale scenario, vessel arrival times were randomly generated, but the maintenance plan was more complex, involving multiple cranes being unavailable at different times. This larger-scale scenario provided valuable insights into how increased operational loads and crane unavailability affected resource allocation and scheduling. The results underscored the greater complexity in managing larger instances, where crane unavailability led to more significant delays and required increased flexibility in resource management (Figure 5). In addition, a machine learning model was developed using Random Forest regression to predict cargo handling amounts based on vessel characteristics and crane usage data. The model was trained and evaluated using real data, with its performance measured  
Figure 4: Small-Scale Berth Allocation Scheme Comparing Scenarios with and Without Quay Crane Maintenance. Figure 5: Large-Scale Berth Allocation Scheme Comparing Scenarios with and Without Quay Crane Maintenance. by the mean squared error (MSE). Figure 6 illustrates a comparison between true and predicted cargo amounts. While the model performed well in predicting larger cargo amounts, some dispersion was observed for smaller loads, indicating slightly reduced accuracy in this range. Nevertheless, the model's overall performance remained robust, and its predictive capability was successfully incorporated into berth and crane scheduling strategies, improving operational planning and resource allocation. Additionally, the optimization scheme classified vessels based on their cargo-handling requirements, ensuring that cranes undergoing maintenance were allocated to vessels with fewer tasks and smaller sizes. This approach promoted a more consistent and efficient crane allocation, reducing reliance on traditional experience-based methods. By minimizing the impact of crane maintenance on the scheduling of berth and QC assignments, the flexibility and efficiency of the overall scheduling plan were significantly improved. The results showed that maintenance activities led to a 34.8% increase in the objective value, demonstrating the substantial effect of crane maintenance on vessel turnaround times. Moreover, variations in input data, such as the timing of maintenance activities, resulted in schedules with different objective values. These findings emphasize the need for effective planning and execution of QC maintenance activities to ensure optimal berth and crane operations.