# Birth Allocation and Query Crane Assignment Considering the Uncertain Maintenance Requirements
## 1 Introduction  
The significance of container ports in international trade has grown substantially due to the increase in global container port traffic [1]. As critical hubs in the supply chain, ports facilitate value-added operations and manage complex logistics activities [2]. The rising volume of container handling has introduced significant planning challenges and has exacerbated congestion and operational uncertainties at terminals. Disruptions to these critical transportation systems can have profound consequences for the supply chains that depend on them. Physical damage to ports can severely impair their functioning, leading to high costs for rebuilding port infrastructure and causing long-term reputational damage. Such damage may result from adverse weather conditions, equipment breakdowns, or armed attacks. For instance, some carriers were forced to reroute cargo due to armed attacks that posed threats in the Red Sea area, leading to increased prices on Asia-to-Europe and other trade routes, extended shipping times and higher costs. Additionally, the COVID-19 pandemic is recognized as one of the most significant recent disruptions, having a considerable impact on maritime supply chains [3]. A successful port operation must integrate efficiency, resilience, and the capacity for seamless recovery from disruptions. Resilient ports possess the capacity to anticipate and prepare for anticipated disasters, adapt to changing conditions, endure various disruptions, and mitigate their impactsthrough robust internal capabilities [4; 5; 6; 7]. A resilient port can absorb damage while maintaining a certain level of service and strategically allocate resources for rapid recovery from disasters. Clearly, the berths and quay cranes are critical components of port operations, and effective, regular maintenance of QC is essential for minimizing the risk of equipment failure, thereby reducing the likelihood of port disruptions. Even in the event of an unexpected QC shutdown, efficient planning for internal capabilities--such as berth allocation and quay crane schedule--enhances resource utilization and strengthens port resilience. To maintain operational efficiency during maintenance interruptions, it is crucial to effectively coordinate berth allocation and quay crane scheduling activities. During transitional phases, critical equipment such as QCs and their associated components are vulnerable to normal wear and tear, and adverse conditions can exacerbate the likelihood of malfunctions. This underscores the importance of proactive maintenance measures. Regular maintenance significantly reduces the risk of breakdowns, ensuring continuity from of operations from both short-term and medium-term strategic perspectives. During maintenance periods, the designated quay where the quay crane is stationed becomes inaccessible, rendering both the crane and occupied berth segment unavailable for vessel procedures. Additionally, non-crossover constraints prevent adjacent quay cranes from serving vessels on the opposite side during maintenance activities. Consequently, careful consideration of the quay crane maintenance is essential when optimizing container handling services along the waterfront. This requires a synchronized approach that integrates berth allocation and quay crane scheduling. Based on our observations concerning QC maintenance, we conducted a study on berths allocation and QC assignment in dynamic scenarios involving preventive QC maintenance activities with strict time constraints.