# Birth Allocation and Query Crane Assignment Considering the Uncertain Maintenance Requirements
## 2 Literature Review  
Over the past decades, research on integrated planning for berth allocation and quay crane scheduling has primarily focused on deterministic issues. This article provides an overview of these studies and examines the problem of integrating Berth Allocation and Quay Crane Assignment (BACAP), which involves making operational decisions regarding berthing position, berthing time, and the allocation of QCs. [PERSON] and [PERSON] [8] investigated this problem, presenting a Mixed-Integer Programming (MIP) model and a Lagrangian-based heuristic method to solve the BAP and QCSP simultaneously. Similarly, [PERSON] [9] and [PERSON] [10] addressed these problems sequentially. [PERSON] et al. [11] integrated the specific QC assignment into BACAP, treating it as a single, compact problem. [PERSON] [12] explored the energy efficiency optimization of Automated Quay Crane (AQC) operation sequences with time window constraints, formulating a Mixed-Integer Linear Programming (MILP) based on a detailed decomposition of the AQC operations. [PERSON] [13] analyzed BACAP by con sidering QC interference and the increased QC capacity demand resulting from deviations from the preferred berthing position. [PERSON] [14] developed an integrated mathematical model and solution algorithm to optimize the berth and quay crane scheduling processes. The literature on uncertainties in quayside operations remains relatively underexplored, with [PERSON] et al. [15] being among the first to address these challenges. [PERSON] et al. [16] examined scheduling for machines with deadline-constrained maintenance, proposing polynomial-time algorithms for various objectives. [PERSON] et al. [17] developed a model aimed at minimizing tardiness in parallel machine scheduling involving a single maintenance activity. Other researchers have focused on uncertainties in vessel arrivals and operations. For instance, [PERSON] et al. [18] studied the Berth Allocation Problem (BAP) and Quay Crane Assignment Problem (QCAP), considering variability in vessel arrival and container processing times. [PERSON] et al. [19] introduced a mixed-integer linear programming model for berth planning that aimed to reduce quay crane peak loads while taking into account agreed-upon arrival windows. Similarly, [PERSON] et al. [20] explored berth allocation from a proactive standpoint to enhance robustness. Despite these contributions, research on proactive strategies for planning berth and quay crane operations remains limited. [PERSON] et al. [21] introduced a robust Berth Allocation Problem (BAP) model that accounts for uncertain vessel arrivals and processing times by incorporating non-vessel-specific buffer times and a hybrid heuristic algorithm for solutions. In contrast, [PERSON] and [PERSON] [22] investigated berth scheduling by balancing baseline schedule costs and solution robustness, incorporating time buffers to manage uncertainties in vessel arrivals and handling times. [PERSON] [23] analyzed the conflicts between port operations and quay crane maintenance. [PERSON] et al. [24] developed two robust optimization models aimed at effectively addressing data uncertainty. Furthermore, recent studies have proposed various methods for addressing these challenges: [PERSON] et al. [25] introduced a reactive strategy under uncertainty for berth allocation and quay crane assignment, highlighting the role of flexibility in operational planning; [PERSON] and [PERSON] [26] applied a recoverable robustness approach to improve resilience in weekly berth and crane planning; [PERSON] et al. [27] developed an integrated model using set partitioning for efficient resource allocation; and [PERSON] et al. [28] enhanced the model with an Adaptive Large Neighborhood Search heuristic, providing insights into advanced optimization techniques for integrated berth allocation and quay crane assignment.