The Berth Allocation Problem (BAP) is considered as one of the most important operational problems in the seaside area of ports. It refers to the problem of assigning a set of vessels to a given berth layout within a given time horizon. In this paper, we study the dynamic and hybrid case of the BAP in the context of bulk ports with multiple quays, different water depths, and heterogeneous loading equipment, considering routing constraints (routes between storage hangars and berths). This study is motivated by the operations of OCP Group, a world leader in the phosphate industry, at the bulk port of Jorf Lasfar in Morocco, recognized as the largest ore port in Africa. The objective of the problem is to enhance the coordination between the berthing and yard activities, besides maximizing the difference between the despatch money and the demurrage charges of all berthed vessels. We propose an integer linear programming model formulated with predicates, which ensures maximum flexibility in the implementation of the model. Finally, the proposed model is tested and validated through numerical experiments based on instances inspired by real bulk port data. The results show that the model can be used to solve to optimality instances with up to 40 vessels within reasonable computational time.