This work investigates a new dynamic berth and quay crane allocation problem by comprehensively considering practical factors such as tidal effects and constraints on the berthing areas of different types of vessels, aiming to optimally determine the berthing time, berthing location, and specific quay crane allocation for different types of vessels to minimize the costs of vessel delay and berth deviation. First, we formulate the problem into a mixed-integer linear programming model. Then, we address complex constraints such as non-overlapping spatial and temporal intervals for vessels and non-crossing of quay cranes through a dynamic time-berth-quay table and a quay crane numbering directed acyclic graph. Based on this, an adaptive variable neighborhood search algorithm (AVNS) includes neighborhood structure operators based on the number of quay cranes and types of berths, and integrates a vessel berthing sequence perturbation operator to enhance the algorithm’s optimization capability. Extensive numerical experiments based on the real-world case of Jiangyin Port in Fuzhou show that the AVNS achieves an average deviation of 3.24% from the best solution obtained by the commercial solver CPLEX. For large-scale cases, the AVNS on average requires only 33.51 s to obtain high-quality near-optimal solutions. Compared to the solutions obtained using the variable neighborhood descent algorithm, the proposed AVNS achieves an average cost saving of 38.69%.